main.ipynb

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   "source": [
    "# System Properties and Validation Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The risk-adjusted bonding curve system requires certain properties to be considered a good estimator of project risk and token price. We also require that it is a fair system, where agents are rewarded according to how accurately they predict the project's future success. \n",
    "\n",
    "To validate that these properties are indeed present in the modeled system, we conduct validation tests for the following: <br/>\n",
    "**1. Convergence of Alpha** <br/>\n",
    "**2. Convergence of Price** <br/>\n",
    "**3. Empirically demonstrate correlation of agents' payouts to their beliefs**\n",
    "\n",
    "Each validation test is a controlled experiment performed in an environment set up to most clearly and obviously reveal the system property or behaviour. "
   ]
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   "cell_type": "markdown",
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   "source": [
    "## 1. Convergence of Alpha\n",
    "\n",
    "### Introduction\n",
    "The Prediction Market in the risk-adjusted bonding curve system acts as an estimator for Alpha, the likelihood of project success.\n",
    "\n",
    "$$ \\alpha \\in [0,1] $$\n",
    "where $\\alpha = 0$ indicates that the project is estimated to fail, and $\\alpha = 1$ indicates the highest likelhood of project success. Refer [Mathematical Model of a Risk-Adjusted Bonding Curve](Math_Specification/1_System_Specification.ipynb) for context.\n",
    "\n",
    "### Hypothesis\n",
    "Alpha converges to a stable value based on agents' positive and negative attestations on project success. \n",
    " \n",
    "### Experiment set up\n",
    "We set up a 2-agent system. Each agent is initialized with two extreme private beliefs of Alpha. <br/>\n",
    "Agent 1's private belief of Alpha = 0.1 <br/>\n",
    "Agent 2's private belief of Alpha = 0.9\n",
    "\n",
    "The agents maintain this private belief of Alpha throughout the system execution.\n",
    "\n",
    "All other agent parameters are initalized as equivalent for both agents. They start out with the same private belief of Price, the same amount of supply tokens, and so on.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "config_ids =  [{'M': {'starting_kappa': 2, 'starting_alpha': 0.5, 'money_raised': 1000, 'C': 2000, 'f': 0.03, 'm': 0.15, 'beta': 0.9, 'dust': 1e-08, 'period': 2000, 'rules_price': 'martin', 'E': 0.2}, 'simulation_id': 0, 'run_id': 0}, {'M': {'starting_kappa': 2, 'starting_alpha': 0.5, 'money_raised': 1000, 'C': 2000, 'f': 0.03, 'm': 0.15, 'beta': 0.9, 'dust': 1e-08, 'period': 2000, 'rules_price': 'martin', 'E': 0.2}, 'simulation_id': 0, 'run_id': 1}]\n"
    }
   ],
   "source": [
    "# import sys\n",
    "# sys.path.append('../')\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "# import run2\n",
    "\n",
    "from src.sim import run\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "# For analysis\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "experiments = run.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
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     },
     "metadata": {}
    }
   ],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "#     secondary_label = experiments.iloc[cc_idx]['string']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "        df = df[df.run == 1]  \n",
    "\n",
    "# MAKE A FOR LOOP or FUNCTION FOR ALL AGENTS\n",
    "        chosen_agents = df['chosen_agent'].tolist()\n",
    "        chosen_agents_private_alphas = []\n",
    "        for agent in chosen_agents:\n",
    "            chosen_agents_private_alphas.append(agent['agent_private_alpha'])\n",
    "        \n",
    "        df['private_alpha'] = chosen_agents_private_alphas\n",
    "            \n",
    "        df['agent_1_private_alpha'] = df.agents.apply(lambda x: np.array(x['agent_private_alpha'][0]))\n",
    "        df['agent_2_private_alpha'] = df.agents.apply(lambda x: np.array(x['agent_private_alpha'][1]))\n",
    "        \n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Agent Private Alpha vs Global Alpha' + '\\n' \n",
    "        # + 'Scenario: ' + str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Alpha Value')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r', 'k' ]\n",
    "        \n",
    "        plt.hlines(y= max(df['agent_1_private_alpha']), xmin=0, xmax=max(df.timestep), label = 'Agent 1 Private Alpha',  color = colors[0])\n",
    "        plt.hlines(y= max(df['agent_2_private_alpha']), xmin=0, xmax=max(df.timestep), label = 'Agent 2 Private Alpha',  color = colors[1])\n",
    "\n",
    "        df.plot(x='timestep', y='private_alpha', label='Private Alpha', ax=ax, legend=True, kind= 'scatter')\n",
    "        df.plot(x='timestep', y='alpha', label='Alpha', ax=ax, legend=True, color = colors[5])\n",
    "\n",
    "        ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alpha converges as the agents make attestations over time. \n",
    "\n",
    "The system responds well to the agents' attestations, incorporating each attestation into the estimation of system Alpha. We conclude that the system is a good estimator of likelihood of project success."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Convergence of Price\n",
    "\n",
    "### Introduction\n",
    "The Bonding Curve in the risk-adjusted bonding curve system acts as an estimator for the Price of the system's supply token.\n",
    "$$ P = \\kappa \\frac{R}{S}\\space\\space\\space ; \\space\\space\\space P \\in [0,\\infty)$$\n",
    "Refer [Mathematical Model of a Risk-Adjusted Bonding Curve](Math_Specification/1_System_Specification.ipynb) for context.\n",
    "\n",
    "### Hypothesis\n",
    "Price converges to a stable value based on agents' bond actions to obtain supply tokens and burn actions to sell their supply tokens. \n",
    " \n",
    "### Experiment set up\n",
    "We set up a 2-agent system. Each agent is initialized with two extreme private beliefs of Price. <br/>\n",
    "Agent 1's private belief of Price = 0.2 <br/>\n",
    "Agent 2's private belief of Price = 2\n",
    "\n",
    "The agents maintain this private belief of Price throughout the system execution.\n",
    "\n",
    "They start out with the different private beliefs of Alpha. All other variables are equivalent, such as the same amount of supply tokens, and so on.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 1080x504 with 1 Axes>",
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FBoOBsLCwCq9TykcFDBEREREREbmp/f7774SHh2MwGLC3tyciIoJZs2bRu3dvHnjgAeLi4gD466+/2LBhA4sWLSIvL4+PPvqIpKQk4uPjiYmJwWAwMGzYMDp27Ii/v7+Ft+rGowKGiIiIiIiIWNzQoUMtduXClbeQ/G3WrFnFHuV5+PBhWrZsia2tLc7OzowZM4b4+HhOnDjBsGHDADh//jzJyckqYNQAPYVEREREREREpARXPxHD39+fv/76C6PRSH5+Pk899RT+/v4EBgYSFRVFdHQ0/fv3p1mzZhaK+MamKzBEREREREREyqFFixZ06tSJwYMHYzQaGTx4MM2bNyc4OJjBgweTl5dHy5Yt8fLysnSoNyQVMEREREREROSm1b59e9q3b19senR0tPnn/v37m39+9tlnefbZZ4ss+/TTT/P000/XXJAC6BYSEREREREREfkHUAFDRERERERERKyeChgiIiIiIiIiYvVUwBARERERERERq6cChoiIiIiIiIhYPRUwRERERERERMTq2Y4dO3aspYMoy+nTp6lfv76lwyhRVlYWtWvXBuBMVi5Jp7KwtzVwKa/Q/LOLQ9lPq72yrYuDXbHXpS1/9boq0rY8sVWkbXX2XZ6+rsz/9YylIvmvyr6t6LoqqiLtS1q2tPzXVBwlLV9a+6r2Xdn1Vsd2ltXXnuTTuNeuVePvtYoe01U5rqrSd3XGVZ4cXpn/qmxHRT8vyspheedVtK+S5ldkO6oz/1C18391vs+v52dqTZ6fKhp3VY7/iuTBkr93WHLflpWT0s7/Vc1ZdZ8ra6qvmvysKc92VNfvQDXFmr8/Xc2aYp0xYwYvvfQSQ4YMwc6ues6dq1evxtXVFVdX12Lzdu3axahRo4o8ovVvISEh/PTTT3z//ffExcWxbt06OnfujIODQ5HlXnzxRcLCwioUU2xsLEFBQdja2pa5bE3GUZprHRfV+4l2E1u68zijl+zG3saGS/kFGAwGnOxsyTca+fCRljzc6tZytc03GhnY1oeF21PMr69uX9q6KtK2PLGVFmdN9l3WdlQ11qrEcuXrsvJf1uuycliRddVkjqqSz+qMo6TlS8tDVfsura+K5r86c/h3X7YGKDQl1eh7rSLvh4rmpTr7rmhf1Zn/isZd2vu6Ot/H1Xn8l5XjsrajJs8hVd2OqrzPr+dnalWO/5o4Z1f2+K/K/riev3dUJYdV3bfl2dfXOv9XNWc18VlVE33V5GeNJc9fYnnLly8nLCyMlStXllhUqIyoqCjGjh2Ll5dXkekzZ85k2bJlODs7X7Pt7NmzcXR0BGDSpEnExcUxdOjQIst89tlnFY7pq6++om/fvuVevqbiqAyDyWQyXZc1VUFCQgItWrSwdBglyo2/FxtbO3YkZ2C8RiptDAZa+3pgb1v8jp38QmOpba9uX57lK9K2tNjKirMm+y5tO66Um5eH41XVv5qOpTpVZd+W1ldZKpKj0pY1FhYUy39FVHRfVeRYAarcd2l9XWu9Fe27PPuruvqq6fNNWf1VNJby9g1l75/yxlWWmj5HVNf7GKrv+LfkZ09pKnP+r873+fX+TL1WLBWNuyqq+5xQlWP4en/WX899e611Q9VyUpO/y1U0D1Xt62rV+VlT3pycbhmLt7d3hbblerLm709XuzrWrl2rt//168u33JYtW4iKiuLVV19l1KhRLFmyhN27dzNu3Dhq1aqFp6cnjo6OREZGEh0dzYoVKzAYDISFhTF06FBef/11HBwcOH78OGlpaURGRpKens7IkSNp0qQJMTExRa5a+PHHHwkKCuK1115j4cKFxeIJCQlh1apVODo6YjQaGTt2LC1btsTGxoYlS5ZgNBoZMWIEI0eOZPny5QwZMoT4+HgMBgPjxo3j3nvvxd3d3VxYyMnJYeLEiWzbto13332XTp06MX36dD766CP++OMPTCYTw4YNo2fPnpWOY9OmTezatYvx48djMpnw8vJi8uTJHD16lPfffx8ADw8PJkyYUOYVTNc6hjUGRjXILTBiMFx7vsFweZnKtL26fXmWr0jb0mIrK86a7Ptq5e3resRSnaqyb0vrqywVyVFV8lmdcVxr+av93b46+i6tr2utt6J9V9T1fK9Vx/uhIsdVZfuuTF/Vmf/qVF3v4+o8/q81vzTV9flQUVX5rKqO90dNfqZeK5bq/gwtTXWfE6pyDF/vz/rruW+vte6q5qQmc3q1mu7ratX5WWOp85dY3qJFixgwYAD+/v44ODiwa9cu3nnnHSIjI4mKisLX1xeAAwcOEB8fT0xMDDExMaxZs4ZDhw4B0LBhQ77++mvCw8OJjY2la9eutGjRgokTJxa75aJHjx5l3qYyfPhwwsPDGTZsGG5ubuarJtzc3Jg/fz7BwcEA1K1bl6CgILZt20ZeXh5bt26lW7duJCUlMWnSJKKioggJCeGHH35gwIAB1K9fnylTpvDLL7+QkpLCggULiIqK4ssvvyQzM7PScQBERETwwQcfsGjRIoKDgzl48CARERG88847REdH07lzZ2bNmlXJvaRbSKrsbOslONSuS/jEdeTkl3wyc7K3YdOgEFxdHYvNy83KLbXt1e3Ls3xF2pYWW1lx1mTfpW3Hlc6mpharftd0LNWpKvu2tL7KUpEclbbshQtnq/TXh4ruq4ocK0CV+y6tr2utt6J9l2d/VVdfNX2+Kau/isZS3r6h7P1T3rjKUtPniOp6H0P1Hf+W/OwpTWXO/9X5Pr/en6nXiqWicVdFdZ8TqnIMX+/P+uu5b6+1bqhaTmryd7mK5qGqfV2tOj9ryn2MXjhboe2Q8ivvFRPV6fz582zYsIGzZ88SHR1NVlYWc+fOJS0tjaZNmwLQtm1b4uPjSUxM5MSJEwwbNszcNjk5GcB8xcAtt9zC//73vyrHdeWtG1fy8/MrNm3gwIF89913pKenExISgp2dHV5eXowfPx4XFxdOnTpFmzZtirRJTEzkzz//JDw8HICCggJOnDiBm5tbpeM4c+YMAQEBAAwZMgSAgwcPMm7cOADy8/NLbFdeugKjGni6OvLhIy1xsrehtqMddjZgb2ugtqMdTvY2fPhISzyvcbK+uq2TvQ1Dg32LvL6yfVnrqkjbsmIrK86a7Lu07ahqrFWN5crXZeW/rNdl5bAi66qpHFUln9UZx7WWv1YeqqPv0vqqSP6rM4dX9lXLwaZG32sVfT9UJC/V2Xdl+qrO/Fc07tLe19X1Pq7O4788+6u07ajJc0h1bEdl3+fX+zO1Ksd/TZyzK3v8V2V/XM/fOyqbw+rYt+XZ1yWd/6uas5r6rKqJvmrys8ZS5y+xrGXLlvHII48we/Zsvv76axYuXMimTZtwdHTkwIEDwOUBNwH8/f0JDAwkKiqK6Oho+vfvT7NmzQAwlHDJj8FgoLpHbbCxKf41Pjg4mISEBJYsWcKjjz4KwJgxY5gwYQKRkZE0aNDAHIfBYMBoNOLv70/79u2Jjo5mzpw59OzZEx8fnyrF0aBBA44cOQJcHhR19erV+Pn5MXHiRKKjoxk1ahRdunSpxFZfpjEwqij1ir8AncnKJeXcJXzqXB6I5e+fy3OSu7Ktp6tjsdelLX/1uirStqIn4OvZd3n6Si3hL3DXI5aK5L8q+7ai66qoirQvadnS8l9TcZS0fGntq9p3ZddbHdtZVl87k47RqmmjGn+vVfSYrspxVZW+qzOu8uTwyvxXZTugYp8XZeWwvPMq2ldJ8yuyHdWZf6ja+b863+fX8zO1Js9PFY27Ksd/RfJgyd87LLlvy8pJaef/quasus+VNdVXTX7WlGc7qut3oJpizd+frmYNsT788MN8+OGHNG/e3Dxt7Nix1KtXjw0bNuDi4oK9vT1eXl68//77zJo1izVr1pCXl0fLli2JiIjgrbfeIiwsjM6dO7Nhwwbi4+OJjIxkypQpbNy4kdmzZ+Ph4VFkvSkpKbzyyitljoFxpbi4OA4dOsTIkSMBuO+++9i0aRMAX375Jb/99htRUVEAfPDBB2zcuBE3Nzfq1auHh4cH77//PqNHj+bEiRNERUURGRnJnj17yM7O5v777+fFF1+sUhy7d+8mMjISGxsb6tevz8SJE0lMTGTixIkUFhYCMH78+DKvwrjWcaECRhVZ+8nrRqf8W5byb1nKv2Up/5al/FuW8m9Zyr/lWfs+sObvT1ez5ljnzZtHz549qVu3LlOmTMHe3r7YF3ypGdc6LjQGhoiIiIiIiMhVPD09GT58OC4uLtSuXZvIyEhLh3TTUwFDRERERERE5CqhoaGEhoZaOgy5ggbxFBERERERERGrpwKGiIiIiIiIiFg9FTBERERERERExOqpgCEiIiIiIiIiVk+DeIqIiIiIiMhNb8aMGURFRbF27VocHR2rpc/Vq1fTsmVLvLy8zNPy8/N58803OX78OHl5eTz33HN07969SLuQkBC8vb2xsbHBZDLh4eFBZGQkrq6uRZZ78cUX+eyzzyoUU2xsLP3798fe3r7MZWsyjsrQFRgiIiIiIiJy01u+fDlhYWGsXLmy2vqMiooiKyuryLRly5bh4eFBTEwMM2fO5L333iux7ezZs4mOjmbu3Lk0btyYuLi4YstUpmjw1VdfYTQay718TcVRGboCQ0RERERERKzDmq7V29/968u12JYtW/D19WXQoEGMGjWK/v37s3v3bsaNG0etWrXw9PTE0dGRyMhIoqOjWbFiBQaDgbCwMIYOHcrrr7+Og4MDx48fJy0tjcjISNLT00lISGD06NHExMTg4OAAXH48a48ePczrtrW1LTU2o9HIhQsX8PPzIy4ujiVLlmA0GhkxYgQjR45k+fLlDBkyhPj4eAwGA+PGjePee+/F3d3dXFjIyclh4sSJbNu2jfT0dP773/8yffp0PvroI/744w9MJhPDhg2jZ8+elY5j06ZN7Nq1i/Hjx2MymfDy8mLy5MkcPXqU999/HwAPDw8mTJhA7dq1y7VfrqYrMEREREREROSmtmjRIgYMGIC/vz8ODg7s2rWLd955h8jISKKiovD19QXgwIEDxMfHExMTQ0xMDGvWrOHQoUMANGzYkK+//prw8HBiY2Pp2rUrLVq0YOLEiebiBUCtWrVwdXUlKyuLESNG8PLLL5cY0/DhwwkPD2fYsGG4ubnRt29fANzc3Jg/fz7BwcEA1K1bl6CgILZt20ZeXh5bt26lW7duJCUlMWnSJKKioggJCeGHH35gwIAB1K9fnylTpvDLL7+QkpLCggULiIqK4ssvvyQzM7PScQBERETwwQcfsGjRIoKDgzl48CARERG88847REdH07lzZ2bNmlXp/aQrMERERERERMQ6lPOKiep0/vx5NmzYwNmzZ4mOjiYrK4u5c+eSlpZG06ZNAWjbti3x8fEkJiZy4sQJhg0bZm6bnJwMQIsWLQC45ZZb+N///lfqOlNTU3nhhRd4/PHH6d27d4nLzJ49u8SxOPz8/IpNGzhwIN999x3p6emEhIRgZ2eHl5cX48ePx8XFhVOnTtGmTZsibRITE/nzzz8JDw8HoKCggBMnTuDm5lbpOM6cOUNAQAAAQ4YMAeDgwYOMGzcOuDz+R0ntyksFDBEREREREblpLVu2jEceeYTRo0cDcOnSJbp3746TkxMHDhwgMDCQXbt2AeDv709gYCCzZs3CYDDw7bff0qxZM3744QcMBkOxvg0GAyaTqci006dPM3z4cN5+++0iVy+Ul41N8RspgoODmTRpEqdOneLtt98GYMyYMaxZswZXV1dGjx5tjsNgMGA0GvH396d9+/a89957GI1Gpk+fjo+PT5XiaNCgAUeOHKFJkybMmDEDPz8//Pz8mDhxIg0bNmT79u2kp6dXeJv/pgKGiIiIiIiI3LQWLVrEhx9+aH7t7OzMgw8+SL169XjzzTdxcXHB3t4eLy8vmjdvTnBwMIMHDyYvL6/YE0au1rp1a1577TVmz56Nh4cHgPlWjenTpzN9+nQAZs6ciZOTU6W3wWAw0KNHD3777TcaN24MQJ8+fRg4cCBubm7Uq1ePtLQ0ANq1a8e///1voqKi2Lp1K48//jjZ2dncf//9xZ4uUlHjxo3jzTffxMbGhvr16zNs2DC8vb0ZPXo0hYWFAIwfP77y2/BRyCYAACAASURBVGm6uhxkhRISEsyX41ib1NRUvL29LR3GTUv5tyzl37KUf8tS/i1L+bcs5d+ylH/Ls/Z9YM3fn65mzbHOmzePnj17UrduXaZMmYK9vT0vvviipcO6KVzruNAVGCIiIiIiIiJX8fT0ZPjw4bi4uFC7dm0iIyMtHdJNTwUMERERERERkauEhoYSGhpq6TDkCnqMqoiIiIiIiIhYPRUwRERERERERMTqqYAhIiIiIiIiIlZPBQwRERERERERsXoqYIiIiIiIiMhNacuWLQQHBxMeHk54eDgDBw4kOjq62HIbNmwgNja2Qn1nZGSwfPlyi8dRHnPnzq1S+9WrV3Pq1CnS09MZO3Zs9QRVAj2FRERERERERP4xzmTlknLuEj51nPF0daxyfx06dGDKlCkA5OXlERoaSp8+fXBzczMv07lz5wr3u3//ftatW0fv3r0tGkd5fPHFFzzxxBOVbh8VFcXYsWMJCAhQAUNERERERERk6c7jjF6yG3sbG/KNRj58pCUPt7q12vrPysrCxsYGW1tbwsPDqVOnDpmZmfTq1YujR4/SoEEDMjMzefHFF8nLy+Phhx9m2bJlTJs2jb1793Lx4kUCAgL44IMP+PLLL9m3bx+xsbF07tyZiIgIcnNzcXR05L333sPb27vScYwcOZLp06ezZs0aCgsLGTx4MIMGDSI6OpoVK1ZgMBgICwtj6NChRfr94YcfmDdvnvn1J598QmxsLOfPn2fs2LFFig+JiYlERkZiNBrJzMxkzJgxtGnThkWLFjF//nyMRiPdu3fnzjvvJCEhgdGjRzNp0iRGjx7NwoUL2bRpE1OnTsXR0REPDw8mTJhAQkICM2fOxN7enpSUFMLCwnjuuefKvX9UwBARERERERGrdyYrl9FLdpOTbyQHIwCvLdnNfYH1qnQlxu+//054eDgGgwF7e3siIiKoVasWAL179+aBBx4gLi4OgD59+vD444/zwgsvsHbtWrp160ZeXh5ubm588803GI1GevXqxalTp/i///s/FixYwGOPPcbLL79MeHg4Xbp0YfPmzUyePJmPPvqo0nH89ddfbNiwgUWLFpGXl8dHH31EUlIS8fHxxMTEYDAYGDZsGB07dsTf39+8jiNHjjBjxgycnZ15++23+fXXX3nuueeYO3dusSsnDhw4wOjRowkKCmL58uXExcXRuHFjZs6cybJly3BwcCAyMpK7776bFi1aMHbsWOzt7QEwmUxEREQwf/58vLy8mDNnDl988QVdu3blxIkTLFu2jLy8PDp16qQChoiIiIiIiNxYUs5dwt7Gxly8ALC3sSHl3KUqFTCuvHXjan5+fkVeu7u706JFC7Zv3853333H6NGjcXR05OzZs7zyyiu4uLiQnZ1Nfn5+kXaJiYl89dVXzJo1C5PJZP6iX9k4Dh8+TMuWLbG1tcXZ2ZkxY8YQHx/PiRMnGDZsGADnz58nOTm5SAHD09OT0aNHU6tWLQ4dOkSrVq2umZcGDRowffp0nJycuHjxIq6urhw7doymTZvi5OQEwJtvvlli23PnzuHq6oqXlxcAd999Nx9//DFdu3alWbNm2NnZYWdnZ+6nvFTAEBEREREREavnU8eZfKOxyLR8oxGfOs41tk6DwVBs2sCBA5kzZw45OTkEBASwdu1aUlNTmTp1KmfPnmX16tWYTCZsbGww/r94/f39GT58OG3atOHgwYP88ccfVYrD39/ffBtHYWEh//73vxk9ejSBgYHMmjULg8HAt99+S7NmzcxtLly4wKeffsr69esBeOqppzCZTADm/680fvx4Jk+eTEBAAJ9++inHjx/H19eXQ4cOkZeXh4ODAyNGjOCtt97CYDAU6aNOnTpkZWWRlpZGgwYN2Lp1K02aNLlmTstLBQwRERERERGxep6ujnz4SEteu2oMjOoYyLMi7rnnHiIiIsy3PrRs2ZLp06czcOBAHBwcaNSoEWlpafj6+pKYmMi3337L6NGjGTt2LLm5ueTk5PDWW29VKYYWLVrQqVMnBg8ejNFoZPDgwTRv3pzg4GAGDx5MXl4eLVu2NF8BAeDq6kqbNm3o168fLi4uuLm5kZaWBkBAQAAjR45k8uTJ5uUffvhhnn/+eTw9Pbnllls4d+4cdevW5ZlnnuGJJ57AYDDQrVs3vLy8aN26Na+99hrvvfcecLlI8f777/Of//wHg8GAu7s7H3zwAUlJSVXaboOppFKLlUlISKBFixaWDqNEqamppQ6+IjVL+bcs5d+ylH/LUv4tS/m3LOXfspR/y7P2fWDN35+uVplYq/spJGJ9rnVc6AoMERERERER+cfwdHVU4eImZWPpAEREREREREREyqIChoiIiIiIiIhYvRorYOzatYvw8PBrzo+IiCgyQIiIiIiIiIjcfP4BwzLKdVTa8VAjBYyZM2cyZswYcnNzS5y/YMECEhMTa2LVIiIiIiIi8g/h5OTEmTNnVMQQ4HLx4syZMzg5OZU4v0YG8fT19WXatGm89tprxebt2LGDXbt28dhjj3Ho0KFy9VdQUEBqamp1h1ltrDm2m4Hyb1nKv2Up/5al/FuW8m9Zyr9lKf+Wp31QPXx8fEhJSSE9Pd3SoYiVcHJywsfHp8R5NVLA6NGjBykpKcWmp6Wl8dlnn/HZZ5+xatWqcvdnZ2dntY8psvZHKN3olH/LUv4tS/m3LOXfspR/y1L+LUv5tzxr3wcZGRmWDqHc7O3t8fPzs3QY8g9xXR+j+sMPP3Du3Dn+/e9/k56eTk5ODv7+/vTv3/96hiEiIiIiIiIi/zDXtYAxdOhQhg4dCkBcXByHDh1S8UJEREREREREynRdHqO6fPlyYmNjr8eqREREREREROQGVGNXYPj4+LBw4UIAevfuXWy+rrwQERERERERkfK6LldgiIiIiIiIiIhUhQoYIiIiIiIiImL1VMAQEREREREREaunAoaIiIiIiIiIWD0VMERERERERETE6qmAISIiIiIiIiJWTwUMEREREREREbF6KmCIiIiIiIiIiNVTAUNERERERERErJ4KGCIiIiIiIiJi9VTAEBERERERERGrpwKGiIiIiIiIiFg9FTBERERERERExOqpgCEiIiIiIiIiVk8FDBERERERERGxeipgiIiIiIiIiIjVUwFDRERERERERKyeChgiIiIiIiIiYvVUwBARERERERERq6cChoiIiIiIiIhYPRUwRERERERERMTqqYAhIiIiIiIiIlZPBQwRERERERERsXoqYIiIiIiIiIiI1VMBQ0RERERERESsngoYIiIiIiIiImL1VMAQEREREREREaunAoaIiIiIiIiIWD0VMERERERERETE6qmAISIiIiIiIiJWTwUMEREREREREbF6KmCIiIiIiIiIiNVTAUNERERERERErJ4KGCIiIiIiIiJi9VTAEBERERERERGrpwKGiIiIiIiIiFg9FTBERERERERExOqpgCEiIiIiIiIiVk8FDBERERERERGxeipgiIiIiIiIiIjVUwFDRERERERERKyeChgiIiIiIiIiYvVUwBARERERERERq6cChoiIiIiIiIhYPRUwRERERERERMTqqYAhIiIiIiIiIlZPBQwRERERERERsXoqYIiIiIiIiIiI1VMBQ0RERERERESsngoYIiIiIiIiImL1VMAQEREREREREaunAoaIiIiIiIiIWD0VMERERERERETE6qmAISIiIiIiIiJWTwUMEREREREREbF6KmCIiIiIiIiIiNVTAUNERERERERErJ4KGCIiIiIiIiJi9VTAEBERERERERGrpwKGiIiIiIiIiFg9FTBERERERERExOqpgCEiIiIiIiIiVk8FDBERERERERGxeipgiIiIiIiIiIjVUwFDRERERERERKyeChgiIiIiIiIiYvVUwBARERERERERq6cChoiIiIiIiIhYvRorYOzatYvw8PBi01esWMGAAQMYNGgQb7/9NkajsaZCEBEREREREZEbRI0UMGbOnMmYMWPIzc0tMj0nJ4epU6cSFRXFggULyMrK4ueff66JEERERERERETkBlIjBQxfX1+mTZtWbLqDgwMLFizA2dkZgIKCAhwdHWsiBBERERERERG5gdjVRKc9evQgJSWl2HQbGxvq1asHQHR0NNnZ2dx3331l9ldQUEBqamq1x1ldrDm2m4Hyb1nKv2Up/5al/FuW8m9ZNZ1/o9FIQkICR44coXHjxvj7++Pi4mKebzKZuHjxIi4uLtjY3HzDuun4tzztA5Hrr0YKGKUxGo1MmjSJw4cPM23aNAwGQ5lt7Ozs8Pb2vg7RVVxqaqrVxnYzUP4tS/m3LOXfspR/y1L+LevK/GdkZLBz506SkpJITEwkKSmJS5cu4ePjQ6NGjfDx8aF+/fq4ubnh7u6Oq6srJ0+eJCkpiaSkJA4fPoyrqysNGjTAy8sLe3t7Nm7cyNq1azl9+rR5nQaDgcaNG1O3bl3S09NJS0sjNzeXQYMGMX/+fEulwiJ0/Fuete+DjIwMS4cgUiOuewHj7bffxsHBgenTp9+U1XIRERGR6mYymdizZw/79+/n0KFDHDx4kAsXLtCpUyfuv/9+mjZtWq4/GpUlPz+fgwcP8ssvv7B37142btzI7t27MZlMADg6OhIYGIiLiwt79uzh5MmT5nklcXBwwNfXl+zsbNLS0igoKADA29ubnj17cv/993P77bdz+PBh9u3bR0JCAhkZGbRs2ZL69euzYcMG1q9fX+XtEhGRf4brUsBYvnw52dnZ3HHHHSxevJh27drx5JNPAjB06FAeeOCB6xGGiIiIyD9Obm4u+/fvZ9++fQQEBNCmTZsixYiNGzfyxhtvsGnTJvO0+vXrm8ceg8vjk7Vu3RpbW9tKxZCXl8eBAwc4cOCAucjg4uJCcHAw77zzDh06dKB58+Y0atSoyB+o8vPzOXHiBGfOnCEzM9P8r0GDBjRt2hRfX19zTCaTiYyMDLKysvDx8SmyjW3bti0xrqlTp/Lf//6XkydPcsstt1Rq20RE5J+jxgoYPj4+LFy4EIDevXubp+/bt6+mVikiIiJyQzh//jzjxo3jhx9+IDExkcLCQvO8xo0b079/fzp37szMmTOJj4/H29ubadOm0alTJ/z8/HBzc8NkMnHo0CHWrFnD6tWr2b9/f6XjsbW1pXnz5vTr14/mzZvj5eVFSEgI9vb2pbazt7encePGNG7cuMx1GAwG6tSpQ506dcodV6tWrQDYtWuXChgiIjeB634LiYiIiIiUzGQy8d133/Hiiy9y6tQpevbsSf/+/bnjjjsICgpix44dxMXF8fnnnzNlyhQ8PDyYOHEiL774YpEBLuFyQSAgIICAgACeffbZao0zNTW1zOLF9XDXXXcBsHPnTnr06GHhaEREpKapgCEiIiJyFZPJRHJyMjt27CA7O5vu3bvj5eVVZJn9+/ezbNkyDAYDrVq1onXr1nh6epbZ765du1ixYgUrV64kKSmJ5s2bc+edd3LHHXewevVqli5dSqtWrVi2bBnt2rUr0r5169YMHz6c8+fPs3nzZtq3b1+hKxZuNHXq1KFx48bs3LnT0qFYjaysLM6ePUvDhg2xsyv6q/7Zs2dJTEykefPmeHh4WChCEZHKUwFDREREBCgsLGTBggV888037Nixg7NnzxaZ37ZtW8LCwjCZTMTFxfHXX38V6+PWW28t9YvhmTNnOHnyJAD33HMPffv2Zf/+/cyfP5/z58/j4uLCpEmTePnll4t9+bySu7s7oaGhldzSG0urVq3+kQUMk8lEXl4ely5d4tKlS2RnZ5t/zsnJwcXFBU9PT+rVq4eLiwt//vknv/76K7/++is7duygUaNGBAQEEBgYSO3atdm+fTu///47e/bswWg0YmdnR6NGjWjSpAmFhYXs27ePtLQ0AIYMGcLcuXMtnAERkYpTAUNERERq3Nq1a0lOTmbAgAG4urpaLI4DBw6wdu1a6tevz1133YWfnx8mk4kFCxbw3nvvsX//foKCgnjkkUdo3bo1rVu3xt7enh9++IFVq1Yxfvx4ALp06cJzzz1Hv379cHR0ZNeuXezcuZPdu3dz8eLFa67f2dmZkJAQevbsWWTMBpPJxPHjx3F2di7zKg4p6u+rVS5evEitWrWq3F96ejrbtm1j27ZtAHTt2pX27dvj4OBQZttLly6xatUqYmNj+e233wgKCqJdu3a0a9cOLy8vtm/fztatW9myZQtHjhzBaDSWKyYbGxvzst7e3tx+++2cO3eO+fPnmx+X6e7uzj333MNbb73FrbfeSnJyMocPH+bw4cPY2NjQu3dvmjdvzpo1a1i5ciUFBQWlFslERKyRzloiIiJSYy5dusSoUaP4/PPPAfjvf//L8OHDeeGFFwgICKi29eTk5LB161Y2bNjAxo0byc3NJTAwkKZNm9KkSRN2797N0qVL+fPPP4u0q1WrFu7u7pw4cYI777yTxYsX069fv2KPem/bti1vvfUW586dw2QyUbdu3SLzu3fvTvfu3Ssdv8FgwMfHp9Ltb2atW7fGZDKxd+9e2rdvX6G2GRkZbN++nT/++INt27bxxx9/kJycDGB+CorJZMLFxYX77ruPJk2amB8Le/X/mZmZ/Pjjj1y4cIEGDRrQrVs3Dhw4wMcff0x+fr55nT4+Ptxzzz0MGjQIFxcXnJ2dzf///c/JyYns7GzOnDnD6dOnycjIoEWLFnTs2JEmTZpw8uRJvL29gcu3hWRkZNCkSZNix21JmjRpwo8//sjmzZvp1KlThfIlImJpKmCIiIhIlfx9X/2pU6fw9/enadOmODk58ddffzFo0CD27NnDK6+8Qt++ffniiy+YNm0aU6dOpWHDhkUelVkRhYWFRR4JmpaWRl5eHgB33nkntWvXZvny5eZL5m1tbencuTPPPPMMPXv25Pz58+zevZvdu3eTnJzMkCFD6N+/f5lfAG/m8Sas1d9PItm5c2e5ChgXLlxg8eLFREVFsX79evP0gIAA7r33XkaMGEG7du1o06YNBQUF/PLLL/z888/8/PPP7N27F/j/ixtX/m9nZ8fAgQMZNGgQXbt2NV/dkJuby969ezl58iStW7emYcOG1bn51K1bt1hBrTQPPPAAdnZ2rFy5UgUMEfnHUQFDREREgMu3V2RlZXHHHXcUubT8zJkzxMbGsmTJEi5cuICtrS02NjYUFBRw6NAhTp8+XaQfGxsb/Pz8OHHiBK6ursTHx9OzZ08AOnXqxOTJk/n66685cuRIpWPNzs4u8tQNT09POnXqxH333Vfky1xmZiaHDx+mUaNGxb7k3X333ZVev1gPX19fPDw8yhwH48SJE7z++ussXryYS5cu0bRpU95++206duxI27Ztr1kE6Nu3L3379q10fI6OjrRt27bS7aubu7s7nTp1Ij4+nsjIyCLzTp8+zTPPPMPEiRNp1qyZhSKsGSaTidzcXC5cuEBWVhbnzp3j1KlT5n8AjRo1wtfXl0aNGpGens727dvZvn07f/75JxERERp3RsQKqIAhIiJyA7p06RLz589n1apV3HnnnXTp0oX27dvj5ORUbLnFixczc+ZMNm7cCICrqysdOnSgQ4cO7N69m/j4eAoKCrjtttvw9fXFaDSa78fv27cvQUFBBAUF4eXlxcGDB9m3bx8JCQnce++9TJw40Xyp+98aNmxIRERElbYvNTW1WL8lcXNzMz9qU25Mfz8FprQCxoYNGxg4cCAXLlxg6NChPPnkk3To0KHSVwD90/Xq1YuRI0eSnJyMr6+vefq0adP4/vvvyc3NJT4+3oIRFnXp0iV27txJcnIymZmZ5n+urq7ceuut3HrrrTRs2LDI+e3SpUts27aNzZs3s3nzZvbs2WO+SqsiPDw8yMvLY9asWSpgiFgBFTBERESus8zMTJKSkti/fz+JiYmkp6fTtm1bOnXqRGBgYLm+VB07dowNGzbw22+/4ezsTGBgIIGBgdSrV4+YmBi+/vprzp49i7e3N0uWLMFkMuHo6Mgdd9xRZDDChIQEMjIyCAwMZOLEifj4+LBp0yY2bdrEhAkT8PLy4uWXX+aJJ56gZcuWZcZ2zz33VDk/IhXVqlUrZsyYUezWIpPJxNSpUxk1ahQBAQGsXbuW22+/3YKRWoewsDBGjhxJfHw8//d//wdc/sL/xRdf4O7uzqpVq1i9ejUPPPBAie0LCwvJzMwkIyODS5cuYTKZMBqNmEwmjhw5wvbt2/nf//7Hzp07cXR0NF/Z4OPjg6OjY7njPHnyJFu3bmXXrl0UFBRUaltr1arFPffcw4gRI6hbty61a9fG1dUVd3d3brnlFry8vPDy8sJkMnHs2DGOHTtGcnIy7u7utG3bFj8/P/71r3+xdOlSjEZjucYZEZGaowKGiIhIDTGZTOzfv58ff/yRvXv3kpiYSGJiovkxmnD5r8eurq5Mnz4dgFtuuYW77rrrmk8HMJlMJCQkcPjwYQBq165Nfn4+OTk55mVsbW3p27cv//nPf+jcuTMZGRn8+uuvrF+/nr1795oHHQTo06cPw4YNo0uXLubixOOPPw5cvk3D0dGxyBdCEWvUqlUrsrOzSUpKonnz5sDlL9nh4eHMnz+ffv368e233+Lm5mbhSK1D8+bN8fPzY+XKleYCxrx580hPT2fVqlU8//zzvPrqq+zYsaPI+3/SpElMmDDB/OSTa7GxsaF58+Z06dKFwsJCkpOT+fnnnzl+/Hi5n7wCl89vd999NyNHjqR9+/Y0bdoUd3d33N3dqVWrFhcvXuT48eOkpKRw4sSJIoOl2tnZcddddxW7Ja40LVq0oEWLFsWmh4SE8M0337B7927zmCsiYhkqYIiIiFSRyWQiMzOTtLQ0Tp06RWpqKhs3bmTlypUcOnQIgPr16xMUFERYWBjNmjUz/wsICMDBwYF9+/axceNGNm7cyL59+0pd31133cWIESPo0qWL+aqIEydOkJSUREpKCl27dqVRo0bm5evUqUPv3r3p3bt3hbbryjEmRKzZlQN5/l3AiI6OZv78+YwbN46IiIib9naRkhgMBnr16sXXX39NTk4Ojo6OTJkyhVatWtGjRw8mTpzIwIED+fbbb/nXv/4FwJQpU3jttdcIDQ2lQ4cOuLu74+HhgbOzMwaDARsbGwwGA97e3tx1110lPtLWZDIVKaCWJ87S9lvt2rVp3ry5eZ/XlG7dugHw888/q4AhYmEGU0XOIhaSkJBQYjXUGpT3HlypGcq/ZSn/lqX8W8727duJjo4mNTWVpKQkDhw4wIULF4os4+zsTEhICL169SIsLIzGjRtbKNobk45/y7K2/Ofl5eHq6sorr7xCZGQk2dnZNGvWjFtvvZXff//9hiteVEf+f/jhB3r27MmqVaswGAyEhoYyZ84chg4dislkomPHjhw6dIikpCRiYmJ49tlnGTBgADExMeW+ouFGEhQURLNmzVi+fDlgfe+Bq1nz9yeRqrj5zj4iIiKVdOjQId566y0WLFiAra0tfn5+BAYG0rFjRxo3boyXlxcNGjSgQYMGBAUF4ezsbOmQRW4KDg4O3H777eaBPKdOncrx48eZP3/+DVe8qC5du3bF2dmZlStXkpSUxC233MKgQYOAy1c+fPTRRwQHB/Pwww+zfv16evXqxdy5c2/K4gVcvo1k3rx5FBQU3LQ5ELEGeveJiMg/nslkYuPGjfz+++84ODjg5OSEk5MTWVlZ5oEyExMTsbW1Nd+68fe91OW1bds2pk+fjr29PRERETzxxBM33GMGRf7JWrVqxapVq0hLSyMyMpI+ffrQqVMnS4dltZycnOjevTsxMTGcPXuW999/v8gAvx06dOCxxx4jNjaWkJAQFi9eXGT+zSYkJIQvv/yS7du30759e0uHI3LTUgFDRP6RCgoKOH78OEePHuXcuXP06tVLfxH5h8vOzmbz5s1kZWXh4eGBh4cH7u7upKenc/jwYQ4fPsyJEyfw9vYmMDCQpk2b4ujoSGxsLHPmzDEPanm12rVrExQURHBwMEajkcTERDZs2MDFixcrFJ+NjQ3/+te/GDt2LA0bNiQ1NbU6NltEqkmrVq349ttvef7558nOzmbixImWDsnq9erVixUrVuDk5MSzzz5bbP4nn3xCy5YtGTFiRLFHMN9sunbtClweB0MFDBHL0W/7Uq02btzIxYsXefDBB/WYKSm3vx+/VtaTDvLz84mOjubjjz9m3759FBYWmufFxsYycODAmg5VymAymcjOzi5x8LaSlt22bRvx8fGsW7eOzZs3FxlBviR/jzp/JYPBQEhICOPGjeOhhx7CYDCQk5NDTk4OTk5OeHl5FbuE3GQykZqaSnZ2drm3zc3NjQYNGpR7eRG5vv4eXHHJkiU899xzBAUFWTgi69erVy8MBgNDhw6lXr16xeZ7eXnx5ptvWiAy61O/fn3uvPNO1q1bx+uvv27pcERuWipg3IRycnJwcHCoVIEhLi6OmJgYIiIiuOuuu8zT8/Pzef311/n4448BaNasGS+99BJPPvlkub7IiPU7fPgwycnJBAcHV9slpEajkSVLljB+/Hj27dtHp06dCA0NJTQ0lNtuu838pTM/P585c+YwYcIEDh8+TJs2bXj99ddp3Lgxvr6+9OnThz/++EMFjOussLCQXbt2sWHDBvbu3UtCQgIJCQmcO3eO22+/nZ49exIWFsZ9991X5Jg5ePAg8+bNY968eSQmJmIwGGjTpg0vv/wy3bp1o0GDBmRkZJj/eXp64ufnR5MmTXB3d+fChQscOHCAAwcOcObMGcLCwvD19a1Q7AaDgYYNG1Z3SkTEgv7+vcTV1ZV33nnHwtH8f+3deXRU9f3/8ddMdggQQgKy7ygQEAIoFRAJUlQECkTCIspXtOK3aP2qFZAiKMhmRc9RqKVQl1IJiIBYFmU1RRCRRWQRlCWBEJUAARISssz9/cEvUwJZZpiZ3Jvh+TiHo7PcjDBj4AAAIABJREFUz7znfe/cO/PKXSqG+vXra+PGjYqNjTW7lAohLi5O8+bN0+XLl80uBbhpcRUSD1n9DMTXunjxotq3b6/IyEitXLlSt9xyi8vTLl++XA899JAcDodsNpueeuopTZkyRdnZ2UpISNCWLVv09NNP66677tLs2bO1Y8cOVa9eXR9//LF69uzpk/dT0frvbZcuXdKlS5eK/atJWQ4cOKA5c+aobdu2io+PV40aNYp9Xmpqql599VUtWLBABQUFqlKlinr37q2+ffs6T1h4I/bt26fp06fr4MGDuvXWW3Xvvfdq06ZNOnDggKSil04rvOxap06dNGnSJD3wwANF/qJ+xx13KDw8XBs3bryhWiqq8l7+DcPQ4cOHtWbNGm3cuFFJSUk6f/68pCt/mWrZsqVatmyp2rVr6z//+Y+SkpKUl5cnu91eZO+awr0s7rnnHg0fPlwDBw5UZGRkub0Pb7nZ1z9mo//msmr/hw4dqnvuuafYwyH8iVX77+9Wrlyp/v37KykpSc2aNbP0PLDy7yfAE+yB4YfS0tJ05swZxcTEXPfYhAkTdPToUZ06dUqdO3fWmjVrXFq5rV69WgkJCerUqZMWL16s119/XXPnztXixYtlt9uVmZmpjz76SEOHDpUkJSQkaOvWrfrd736nBQsW+CzAuNkYhqGDBw9q7dq1Wrt2rfMH4tChQzV+/Hi1bt26zDGysrI0ZcoUvfHGG5KunEtizJgx6t27twYMGFDkpIZff/213nnnHTkcDj311FOKi4vT2rVr9dlnn2np0qUev5+YmBglJiYqPj7e+QP3xIkT+vzzz5WcnFzkuV26dFHv3r2LPZt8bGysEhMTZRgGZ5u/AVu2bNHixYv1wgsvFHupz+3bt+ujjz7SqlWrdOTIEUlS8+bNlZCQoO7du6t79+6qW7fuddNdvHhRGzdu1I4dO+RwOJz3R0dHKz4+XvXr1/fdmwJwU1q0aJHZJcCP3X333bLb7dq4caOaNWtmdjnATYk9MDxklQS88Az8c+bM0bJlyyRJn376qR544AHnc7Zt26YuXbpozJgxevTRR/Xggw8qJydHy5YtU48ePUoce/369XrwwQfVunVrbdiwQREREZKk7777Tn/84x915swZJSYmFvvjuU+fPjpx4oT27t3r5Xd8hVX672sOh0OrV6/W9OnTtXXrVklSq1atdN9998kwDM2bN09ZWVkaOHCgBg8eXOLJLAvPMp6SkqKRI0dq1qxZOnnypBYtWqRFixbp5MmTRZ5vt9s1YsQITZ48WY0aNSpSz+7du7V3794b/st5RESEunXr5pVzpcybN09PPvmkjhw5oiZNmng8XkXhjeV/1apVio+PV05OjsLCwjR+/Hj96U9/UmhoqHbu3KmJEydqzZo1Cg0NVVxcnPr06aM+ffoUG3TcbG6W9Y9V0X9z0X9z0X/zdOrUSZUqVVJiYqKl54GVfz8BHjEqgAMHDphdQolOnTplGIZhZGVlGY0aNTL+/Oc/GwUFBeX2+g6Hw1iyZInRtm1bQ5IRERFhPPfcc0aHDh2M0NBQ4z//+Y9hGIaRk5NjtGzZ0qhfv75x4cIFwzAM4/jx40arVq2MoKAgo1OnTkbHjh2Njh07Gh06dDA6dOhgxMbGGrGxsUZoaKjRpk0bIz093e36xo4dawQFBRm5ublefd+FCvvvrwoKCoyFCxcaMTExhiSjYcOGxltvvWUkJycXeV56eroxceJEo1q1aoakUv/FxMQYSUlJxb7WwYMHje+//975LzU1tdT6rNL/HTt2GJKMjz/+2OxSypWn/U9MTDQCAwONDh06GLt27TIeeughQ5LRpEkTo1+/foYkIzIy0pg5c6Zx8eJFL1XtP6yy/N+s6L+56L+56L95XnzxRSMoKMj46aefzC6lVFb+/QR4gkNIvKRSpUrq1auXpk6dqj179mjhwoVFdsV3V25uroKCgkrdHX7r1q164YUXtG3bNrVq1Up///vfNWzYMFWqVEmnT59W165d9eCDD+rLL7/U8uXLdfDgQa1evVpVqlSRJDVs2FBfffWVXnzxRedf3gtf7+r/xsTEaNasWSWeI6E0bdq0UV5eng4dOlTsIS0o2enTp/Xoo49qzZo1atWqlT788EMNGTJEQUFB1z23Ro0aevXVV/Xiiy+WeClJ6coeFbfeemuxe2jY7XbddtttXn0P5SUmJkaBgYHatWuX4uPjzS6nQpg/f75+//vfq1u3bvrss89UtWpVLVmyRBs2bNDTTz+tzZs365VXXtGzzz6rqlWrml0uAACWEBcXp1mzZum7775T06ZNzS4HuOkQYHjR3/72N91+++169tlndeedd2rFihU39IPw7Nmzateunf7nf/5Hr7zyynWP5+Tk6NFHH9WSJUtUu3ZtzZ8/XyNHjixykrzo6GitW7dOXbp00W9/+1udO3dOw4cP1/33319krIiICM2bN8/9N+uiNm3aSJK+//57Agw3fPnllxo2bJjS09P1zjvv6KmnnnLpUIvw8HBnz28moaGhat26tXbt2nXdY4sWLdJbb72l9evXO8M7TxiGodTUVO3bt0/79u3TL7/8opiYGLVv314tW7a8LmDKy8vT3r17tXXrVm3fvl12u12NGzdW48aN1bBhQ1WqVMnl187MzNTx48d17NgxHT9+XOfOnVOdOnUUGRmpGjVqKCwsrMRp8/Ly9NNPP+nAgQM6ePCgfv31V91///1aunRpkRp69uyp/fv3u3RZWwAAbjZxcXF69dVX1aJFC7NLAW5KBBheZLPZ9Ic//EFt2rRRfHy87rzzTv34449uX6XhhRde0IkTJ7Ry5cpiA4xly5ZpyZIlGj9+vCZMmFDiZUobNGigL774Qt26dVO1atX01ltv3dD78sStt96qgIAA7du3r9xf26rOnj0rSdedO8IwDP300096//3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     },
     "metadata": {}
    }
   ],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "#     secondary_label = experiments.iloc[cc_idx]['string']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "        df = df[df.run == 1]  \n",
    "\n",
    "# MAKE A FOR LOOP or FUNCTION FOR ALL AGENTS\n",
    "        chosen_agents = df['chosen_agent'].tolist()\n",
    "        chosen_agents_private_prices = []\n",
    "        for agent in chosen_agents:\n",
    "            chosen_agents_private_prices.append(agent['agent_private_price'])\n",
    "        \n",
    "        df['private_price'] = chosen_agents_private_prices\n",
    "            \n",
    "        df['agent_1_private_price'] = df.agents.apply(lambda x: np.array(x['agent_private_price'][0]))\n",
    "        df['agent_2_private_price'] = df.agents.apply(lambda x: np.array(x['agent_private_price'][1]))\n",
    "        \n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Agent Private Price vs Global Price' \n",
    "        # + '\\n' + 'Scenario: ' + str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Price')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r', 'k' ]\n",
    "        \n",
    "        plt.hlines(y= max(df['agent_1_private_price']), xmin=0, xmax=max(df.timestep), label = 'Agent 1 Private Price',  color = colors[0])\n",
    "        plt.hlines(y= max(df['agent_2_private_price']), xmin=0, xmax=max(df.timestep), label = 'Agent 2 Private Price',  color = colors[1])\n",
    "\n",
    "        df.plot(x='timestep', y='private_price', label='Private Price at action', ax=ax, legend=True, kind= 'scatter')\n",
    "        df.plot(x='timestep', y='spot_price', label='Price', ax=ax, legend=True, color = colors[5])\n",
    "\n",
    "        ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inference \n",
    "\n",
    "Price converges as the agents bond and burn tokens over time. \n",
    "\n",
    "The system responds well to the agents' bond and burn actions, incorporating each action into the estimation of system Price. We conclude that the system is a good estimator of the token price.\n",
    "\n",
    "The plots below show how system Reserve and system Supply change as agents bond or burn tokens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {}
    }
   ],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "# config_labels = ['RULE 1,'RULE 2']\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "#     secondary_label = experiments.iloc[cc_idx]['string']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "#         df = df[df.run == 1]  \n",
    "        \n",
    "        df = df.groupby('timestep').agg({'reserve': ['min', 'mean', 'max']}).reset_index()\n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Reserve' + '\\n' + 'Scenario: ' \n",
    "        #+ str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Alpha Value')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r', 'k' ]\n",
    "\n",
    "        ax.plot(df.timestep, df[('reserve','mean')],label='reserve') \n",
    "\n",
    "        ax.fill_between(df.timestep, df[('reserve','min')], df[('reserve','max')])#, supply=0.3) \n",
    "\n",
    "        ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {}
    }
   ],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "# config_labels = ['RULE 1,'RULE 2']\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "#     secondary_label = experiments.iloc[cc_idx]['string']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "#         df = df[df.run == 1]  \n",
    "        \n",
    "        df = df.groupby('timestep').agg({'supply': ['min', 'mean', 'max']}).reset_index()\n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Supply' + '\\n' + 'Scenario: ' \n",
    "        #+ str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Alpha Value')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r', 'k' ]\n",
    "\n",
    "        ax.plot(df.timestep, df[('supply','mean')],label='supply') \n",
    "\n",
    "        ax.fill_between(df.timestep, df[('supply','min')], df[('supply','max')])#, supply=0.3) \n",
    "\n",
    "        ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Correlation of agents' payouts to their beliefs\n",
    "\n",
    "### Introduction\n",
    "Agents take actions based on their private beilef of Alpha and Price. If they believe Alpha is higher than the current system Alpha, then they will make a positive attestation and vice versa. Likewise, if an agent believes the price to be higher than the current system price, they will make a bond action and vice versa.\n",
    "For more information on agent behaviour heuristics, see [AgentBehaviourModel - Heuristic](Math_Specification/4a_AgentBehaviourModel - Heuristic.ipynb)\n",
    "\n",
    "Agents participate in the prediction market motivated by the ability to increase their final payout once the bond has completed its execution. An agent with $n$ supply tokens can choose to keep the tokens as is (as $s_{free}$), or use them to make positive attestations ($s_1$) or negative attestations ($s_0$) in the hope of increasing their expected future payout.\n",
    "\n",
    "The payout $\\Theta_a$ of an agent comprises of their share of payout corresponding to their holdings of $s_{free}$, $s_1$ and $s_0$. \n",
    "$$\\Theta_a = \\frac{s_{free}}{s} (\\alpha_t C+R) + \\alpha_t \\frac{q_1}{Q_1} \\frac{s_1}{s} (C+R) + (1-\\alpha_t) \\frac{q_0}{Q_0} \\frac{s_0}{s} (R)$$\n",
    "\n",
    "### Hypothesis\n",
    "The agent that has the closest prediction of final system Alpha - i.e. their private belief of Alpha - obtains the largest final payout.\n",
    " \n",
    "### Experiment set up\n",
    "We set up a 21-agent system. Each agent is initialized with equidistant private beliefs of Alpha. <br/>\n",
    "Agent 1's private belief of Alpha = 0.00 <br/>\n",
    "Agent 2's private belief of Alpha = 0.05 <br/>\n",
    "Agent 3's private belief of Alpha = 0.10 <br/>\n",
    ". . . <br/>\n",
    "Agent 21's private belief of Alpha = 1.0 <br/>\n",
    "\n",
    "All agents have the same private belief of Price, which remains constant throughout the system execution.\n",
    "\n",
    "Other agent parameters are initialized equally for all agents. They start out with the same reserve as well as same amount of supply tokens in all pools, with initial values as the following:\n",
    "\n",
    "\n",
    "| Agent Variable Name -> | agent_attestations_1 | agent_attestations_0 | agent_reserve | agent_supply_1 | agent_supply_0 | agent_supply_free |\n",
    "|:-----------------------|:--------------------:|:--------------------:|:--------------------:|:--------------------:|:--------------------:|:-------------:|\n",
    "|Brief Description ->    | Claim on Pos. Attest. | Claim on Neg. Attest. | Reserve funds | Pos. Attest Tokens |  Neg. Attest Tokens  |  Unattested Tokens  |\n",
    "|Initial Value ->        | 0  | 0 | 100   | 3 | 3 | 44 |\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Agents vs their Positive Attestations\n",
    "#### The table below is a snapshot at one timeslice during the simulation of the all of the agents current positions. We observe that agents with low beliefs of alpha have attested negatively (agent_attestations_0). Agents with alpha beliefs closer to 1 have only attested positively (agent_attestations_1). Importantly, agents within the range of alphas and their own threshold values during the simulation (alpha = 0.5 and 0.55) have attested both positively and negatively.\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "    id  agent_attestations_1  agent_attestations_0  agent_reserve  \\\n0  0.0              0.000000               0.29059          100.0   \n1  1.0              0.605875               0.00000          100.0   \n\n   agent_supply_1  agent_supply_0  agent_supply_free  agent_private_alpha  \\\n0        3.000000       60.783782           6.216218                  0.3   \n1      122.496561        3.000000           4.503439                  0.7   \n\n   agent_private_price  \n0                  0.5  \n1                  1.5  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>id</th>\n      <th>agent_attestations_1</th>\n      <th>agent_attestations_0</th>\n      <th>agent_reserve</th>\n      <th>agent_supply_1</th>\n      <th>agent_supply_0</th>\n      <th>agent_supply_free</th>\n      <th>agent_private_alpha</th>\n      <th>agent_private_price</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.0</td>\n      <td>0.000000</td>\n      <td>0.29059</td>\n      <td>100.0</td>\n      <td>3.000000</td>\n      <td>60.783782</td>\n      <td>6.216218</td>\n      <td>0.3</td>\n      <td>0.5</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.0</td>\n      <td>0.605875</td>\n      <td>0.00000</td>\n      <td>100.0</td>\n      <td>122.496561</td>\n      <td>3.000000</td>\n      <td>4.503439</td>\n      <td>0.7</td>\n      <td>1.5</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "t = 1601\n",
    "\n",
    "experiments.dataset[0].agents[t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "KeyError",
     "evalue": "2",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-14-610d19f81498>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     25\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_1_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     26\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_2_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_3_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     28\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_4_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_5_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36mapply\u001b[1;34m(self, func, convert_dtype, args, **kwds)\u001b[0m\n\u001b[0;32m   3846\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3847\u001b[0m                 \u001b[0mvalues\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobject\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3848\u001b[1;33m                 \u001b[0mmapped\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmap_infer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mconvert\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mconvert_dtype\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3849\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3850\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmapped\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmapped\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mSeries\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\lib.pyx\u001b[0m in \u001b[0;36mpandas._libs.lib.map_infer\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32m<ipython-input-14-610d19f81498>\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(x)\u001b[0m\n\u001b[0;32m     25\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_1_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     26\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_2_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_3_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     28\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_4_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m         \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_5_attest_1'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'agent_attestations_1'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m__getitem__\u001b[1;34m(self, key)\u001b[0m\n\u001b[0;32m    869\u001b[0m         \u001b[0mkey\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply_if_callable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    870\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 871\u001b[1;33m             \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    872\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    873\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mis_scalar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_value\u001b[1;34m(self, series, key)\u001b[0m\n\u001b[0;32m   4403\u001b[0m         \u001b[0mk\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_convert_scalar_indexer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkind\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"getitem\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4404\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4405\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtz\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mseries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"tz\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4406\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4407\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mholds_integer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_boolean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.Int64HashTable.get_item\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.Int64HashTable.get_item\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 2"
     ]
    }
   ],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "# config_labels = ['RULE 1,'RULE 2']\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "        df = df[df.run == 1]  \n",
    "        \n",
    "\n",
    "# MAKE A FOR LOOP or FUNCTION FOR ALL AGENTS\n",
    "        df['agent_1_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][0]))\n",
    "        df['agent_2_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][1]))\n",
    "        df['agent_3_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][2]))\n",
    "        df['agent_4_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][3]))\n",
    "        df['agent_5_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][4]))\n",
    "        df['agent_6_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][5]))\n",
    "        df['agent_7_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][6]))\n",
    "        df['agent_8_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][7]))\n",
    "        df['agent_9_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][8]))\n",
    "        df['agent_10_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][9]))\n",
    "        df['agent_11_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][10]))\n",
    "        df['agent_12_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][11]))\n",
    "        df['agent_13_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][12]))\n",
    "        df['agent_14_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][13]))\n",
    "        df['agent_15_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][14]))\n",
    "        df['agent_16_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][15]))\n",
    "        df['agent_17_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][16]))\n",
    "        df['agent_18_attest_1'] = df.agents.apply(lambda x: np.array(x['agent_attestations_1'][17]))\n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Agents vs. their Positive Attestations' + '\\n' \n",
    "        # + 'Scenario: ' + str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Amount')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r']\n",
    "\n",
    "        df.plot(x='timestep', y='agent_1_attest_1', label='agent_1', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_2_attest_1', label='agent_2', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_3_attest_1', label='agent_3', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_4_attest_1', label='agent_4', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_5_attest_1', label='agent_5', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_6_attest_1', label='agent_6', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_7_attest_1', label='agent_7', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_8_attest_1', label='agent_8', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_9_attest_1', label='agent_9', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_10_attest_1', label='agent_10', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_11_attest_1', label='agent_11', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_12_attest_1', label='agent_12', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_13_attest_1', label='agent_13', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_14_attest_1', label='agent_14', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_15_attest_1', label='agent_15', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_16_attest_1', label='agent_16', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_17_attest_1', label='agent_17', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_18_attest_1', label='agent_18', ax=ax, legend=True)\n",
    "\n",
    "        ax.legend()\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()\n",
    "#plt.title(\"AGENTS VS THEIR POSITIVE ATTESTATIONS\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "# config_labels = ['RULE 1,'RULE 2']\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "        df = df[df.run == 1]  \n",
    "        \n",
    "\n",
    "# MAKE A FOR LOOP or FUNCTION FOR ALL AGENTS\n",
    "        df['agent_1_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][0]))\n",
    "        df['agent_2_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][1]))\n",
    "        df['agent_3_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][2]))\n",
    "        df['agent_4_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][3]))\n",
    "        df['agent_5_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][4]))\n",
    "        df['agent_6_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][5]))\n",
    "        df['agent_7_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][6]))\n",
    "        df['agent_8_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][7]))\n",
    "        df['agent_9_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][8]))\n",
    "        df['agent_10_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][9]))\n",
    "        df['agent_11_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][10]))\n",
    "        df['agent_12_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][11]))\n",
    "        df['agent_13_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][12]))\n",
    "        df['agent_14_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][13]))\n",
    "        df['agent_15_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][14]))\n",
    "        df['agent_16_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][15]))\n",
    "        df['agent_17_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][16]))\n",
    "        df['agent_18_attest_0'] = df.agents.apply(lambda x: np.array(x['agent_attestations_0'][17]))\n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Agents vs their Negative Attestations' + '\\n' \n",
    "        # + 'Scenario: ' + str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Amount')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r']\n",
    "        \n",
    "\n",
    "        df.plot(x='timestep', y='agent_1_attest_0', label='agent_1', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_2_attest_0', label='agent_2', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_3_attest_0', label='agent_3', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_4_attest_0', label='agent_4', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_5_attest_0', label='agent_5', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_6_attest_0', label='agent_6', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_7_attest_0', label='agent_7', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_8_attest_0', label='agent_8', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_9_attest_0', label='agent_9', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_10_attest_0', label='agent_10', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_11_attest_0', label='agent_11', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_12_attest_0', label='agent_12', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_13_attest_0', label='agent_13', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_14_attest_0', label='agent_14', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_15_attest_0', label='agent_15', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_16_attest_0', label='agent_16', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_17_attest_0', label='agent_17', ax=ax, legend=True)\n",
    "        df.plot(x='timestep', y='agent_18_attest_0', label='agent_18', ax=ax, legend=True)\n",
    "\n",
    "        ax.legend()\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Agents' Belief of Alpha vs their Payout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "KeyError",
     "evalue": "2",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-18-b1d3b5bc80e2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[1;32min\u001b[0m \u001b[0magents_id\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m     \u001b[1;31m#print(a)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 12\u001b[1;33m     \u001b[0mq1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexperiments\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdataset\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magent_attestations_1\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     13\u001b[0m     \u001b[0mq0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexperiments\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdataset\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magents\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0magent_attestations_0\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m__getitem__\u001b[1;34m(self, key)\u001b[0m\n\u001b[0;32m    869\u001b[0m         \u001b[0mkey\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply_if_callable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    870\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 871\u001b[1;33m             \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    872\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    873\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mis_scalar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_value\u001b[1;34m(self, series, key)\u001b[0m\n\u001b[0;32m   4403\u001b[0m         \u001b[0mk\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_convert_scalar_indexer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkind\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"getitem\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4404\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4405\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtz\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mseries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"tz\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4406\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4407\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mholds_integer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_boolean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.Int64HashTable.get_item\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.Int64HashTable.get_item\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 2"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "S_free = experiments.dataset[0].supply_free[t]\n",
    "S_0 = experiments.dataset[0].supply_0[t]\n",
    "S_1 = experiments.dataset[0].supply_1[t]\n",
    "\n",
    "agents_id = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]\n",
    "payout_list = []\n",
    "\n",
    "for a in agents_id:\n",
    "    #print(a)\n",
    "    q1 = experiments.dataset[0].agents[t].agent_attestations_1[a]\n",
    "    q0 = experiments.dataset[0].agents[t].agent_attestations_0[a]\n",
    "    \n",
    "    s_free = experiments.dataset[0].agents[t].agent_supply_free[a]\n",
    "    s1 = experiments.dataset[0].agents[t].agent_supply_1[a]\n",
    "    s0 = experiments.dataset[0].agents[t].agent_supply_0[a]\n",
    "    s = s_free + s1 + s0\n",
    "    \n",
    "    agent_private_alpha = experiments.dataset[0].agents[t].agent_private_alpha[a]\n",
    "\n",
    "    Q0 = experiments.dataset[0].attestations_0[t]\n",
    "    Q1 = experiments.dataset[0].attestations_1[t]\n",
    "\n",
    "    R = experiments.dataset[0].reserve[t]\n",
    "    S = experiments.dataset[0].supply[t]\n",
    "\n",
    "    C = experiments.C\n",
    "    alpha = experiments.dataset[0].alpha[t]\n",
    "\n",
    "    T1 = (s_free/s)*(alpha*C + R)\n",
    "    T2 = (s1/s)*(q1/Q1)*alpha*(C+R)\n",
    "    T3 = (s0/s)*(q0/Q0)*(1-alpha)*(R)\n",
    "\n",
    "    agent_payout = T1+T2+T3\n",
    "    payout_list.append(agent_payout)\n",
    "    #print(a, \"'s Payout = \", agent_payout, \"| Private Alpha = \", agent_private_alpha)\n",
    "\n",
    "#plt.plot(payout_list)\n",
    "\n",
    "arr2d = np.array(payout_list)\n",
    "\n",
    "arr1d = arr2d.flatten()\n",
    "\n",
    "x = agents_id\n",
    "payouts = arr1d\n",
    "\n",
    "x_pos = [i for i, _ in enumerate(x)]\n",
    "\n",
    "plt.bar(x_pos, payouts, color='green')\n",
    "plt.xlabel(\"Agent ID\")\n",
    "plt.ylabel(\"Payout amount (tokens)\")\n",
    "plt.title(\"Agent and their Payouts\")\n",
    "\n",
    "plt.xticks(x_pos, x)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that Agent 10 has the highest payout. <br>\n",
    "\n",
    "We know that Agent 10's private belief of Alpha is 0.50. To verify if this is close to the final system Alpha, we plot Alpha. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "experiments = experiments.sort_values(by =['rules_price']).reset_index(drop=True)\n",
    "\n",
    "cols = 1\n",
    "rows = 1\n",
    "cc_idx = 0\n",
    "\n",
    "\n",
    "while cc_idx<len(experiments):\n",
    "    cc = experiments.iloc[cc_idx]['rules_price']\n",
    "    cc_label = experiments.iloc[cc_idx]['rules_price']\n",
    "#     secondary_label = experiments.iloc[cc_idx]['string']\n",
    "    sub_experiments = experiments[experiments['rules_price']==cc]\n",
    "    cc_idx += len(sub_experiments)\n",
    "    fig, axs = plt.subplots(ncols=cols, nrows=rows, figsize=(15*cols,7*rows))\n",
    "    sub_experiments.reset_index(drop=False)\n",
    "    for i, experiment in sub_experiments.iterrows():\n",
    "        df = experiment['dataset'].copy()\n",
    "        # filter out starting point\n",
    "        df = df[df.timestep > 0] \n",
    "        # FIRST RUN ONLY\n",
    "        df = df[df.run == 1]  \n",
    "\n",
    "# MAKE A FOR LOOP or FUNCTION FOR ALL AGENTS\n",
    "        chosen_agents = df['chosen_agent'].tolist()\n",
    "        chosen_agents_private_alphas = []\n",
    "        for agent in chosen_agents:\n",
    "            chosen_agents_private_alphas.append(agent['agent_private_alpha'])\n",
    "        \n",
    "        df['private_alpha'] = chosen_agents_private_alphas\n",
    "            \n",
    "        df['agent_1_private_alpha'] = df.agents.apply(lambda x: np.array(x['agent_private_alpha'][0]))\n",
    "        df['agent_2_private_alpha'] = df.agents.apply(lambda x: np.array(x['agent_private_alpha'][1]))\n",
    "        \n",
    "\n",
    "        plot_label = experiment['rules_price']\n",
    "        ax = axs\n",
    "        title = 'Agent Private Alpha vs Global Alpha' \n",
    "        # + '\\n' + 'Scenario: ' + str(cc_label)  + ' rules_price'\n",
    "        ax.set_title(title)\n",
    "        ax.set_ylabel('Alpha Value')\n",
    "        colors = ['b','orange', 'g', 'magenta', 'r', 'k' ]\n",
    "        \n",
    "        #plt.hlines(y= max(df['agent_1_private_alpha']), xmin=0, xmax=max(df.timestep), label = 'Agent 1 Private Alpha',  color = colors[0])\n",
    "        #plt.hlines(y= max(df['agent_2_private_alpha']), xmin=0, xmax=max(df.timestep), label = 'Agent 2 Private Alpha',  color = colors[1])\n",
    "\n",
    "        df.plot(x='timestep', y='private_alpha', label='Private Alpha', ax=ax, legend=True, kind= 'scatter')\n",
    "        df.plot(x='timestep', y='alpha', label='Alpha', ax=ax, legend=True, color = colors[5])\n",
    "\n",
    "        ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "\n",
    "        ax.set_xlabel('Timesteps')\n",
    "        ax.grid(color='0.9', linestyle='-', linewidth=1)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        \n",
    "fig.tight_layout(rect=[0, 0, 1, .97])\n",
    "fig.patch.set_alpha(1)\n",
    "display(fig)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.6300419112564714"
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "source": [
    "experiments.dataset[0].alpha[t]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system's final Alpha is 0.4977. <br/>\n",
    "Agent 10 with alpha belief 0.50 has the higest payout. \n",
    "\n",
    "Notice that jaggedness of the agent payout surface. It's not necessarily true that an agent with the closer belief of Alpha *always* and *strictly* gets a higher payout.\n",
    "\n",
    "Consider Agent 17 with a Alpha belief of 0.85 and a payout of 33.94. \n",
    "$$\\hat\\alpha_{17} = 0.85$$\n",
    "$$\\Theta_{17} = 33.94$$\n",
    "Agent 18 with an Alpha belief 0.9 - which is farther away from the final system Alpha -  obtained a much larger payout of 334.86.  \n",
    "$$\\hat\\alpha_{18} = 0.90$$\n",
    "$$\\Theta_{18} = 334.86$$\n",
    "\n",
    "This could be explained due to a possible large action that either agent took early on in the system when system Alpha was quite volatile. If said large action was in the right direction towards final system Alpha, this move acted in their advantage. If it was in the wrong direction to system Alpha, this resulted in their disadvantage. \n",
    "\n",
    "In this case, Agent 18 placed a risky bet towards the correct direction of system Alpha very early on. \n",
    "\n",
    "This indicates that the process has path dependence. This is a system property by design.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inference\n",
    "The agent with the highest payout has an alpha belief of 0.50, which is close to the final system Alpha. We conclude that the agent with the closest prediction of Alpha generally obtains the largest final payout.  "
   ]
  }
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