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   "source": [
    "# Discussion of the Equilibrium Concept (6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "74cba7b6",
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     "start_time": "2022-06-09T13:29:18.815746Z"
    }
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from poisson_approval import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "87521eda",
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2022-06-09T13:29:20.001721Z"
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   "source": [
    "random_profile = RandProfileHistogramUniform(n_bins=1)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "id": "117c6f44",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "not_converge=524\n",
      "converge_ordinal=1168\n",
      "converge_cardinal_is_large_equilibrium=8308\n",
      "converge_cardinal_is_not_large_equilibrium=0\n"
     ]
    }
   ],
   "source": [
    "not_converge = 0\n",
    "converge_ordinal = 0\n",
    "converge_cardinal_is_large_equilibrium = 0\n",
    "converge_cardinal_is_not_large_equilibrium = 0\n",
    "for i in range(10000):\n",
    "    profile = random_profile()\n",
    "    result = profile.fictitious_play(\n",
    "        init='random_tau', \n",
    "        n_max_episodes=1000,\n",
    "        perception_update_ratio=one_over_log_t_plus_one,\n",
    "        ballot_update_ratio=one_over_log_t_plus_one\n",
    "    )\n",
    "    if not result['converges']:\n",
    "        not_converge += 1\n",
    "    elif result['tau'].focus == Focus.DIRECT:\n",
    "        converge_ordinal += 1\n",
    "    else:\n",
    "        is_stable = profile.is_equilibrium_stable(result['strategy'])\n",
    "        if is_stable:\n",
    "            converge_cardinal_is_large_equilibrium += 1\n",
    "        else:\n",
    "            converge_cardinal_is_not_large_equilibrium += 1\n",
    "            break\n",
    "print(f\"{not_converge=}\")\n",
    "print(f\"{converge_ordinal=}\")\n",
    "print(f\"{converge_cardinal_is_large_equilibrium=}\")\n",
    "print(f\"{converge_cardinal_is_not_large_equilibrium=}\")"
   ]
  },
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   "execution_count": null,
   "id": "bf09e2a9",
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