{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ergodicity economics\n",
    "\n",
    "An attempt to implement the simple game introduced by Ole Peters and collegues found in the [lecture notes](https://ergodicityeconomics.com/lecture-notes/).\n",
    "\n",
    "\n",
    "\n",
    "## The game\n",
    "\n",
    "The game is faily simple. \n",
    "\n",
    "- Flip a coin\n",
    "- If it lands *heads*, you increase your wealth with 50%\n",
    "- If it lands *tails*, you decrease your wealth with 40%\n",
    "\n",
    "Would you accept the game?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Playing the game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy.random as random\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (10, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we start the game with a wealth of 1\n",
    "inital_wealth = 1\n",
    "\n",
    "# our wealth at the start of the game is our inital wealth\n",
    "wealth = inital_wealth\n",
    "wealth_t = []\n",
    "\n",
    "# we play they game once a week, for a year\n",
    "for i in range(1,53):\n",
    "    # each flip has a 50/50 chance of either decreasing our wealth with 40%\n",
    "    # or increasing with 50%\n",
    "    coin_flip = random.choice([0.6, 1.5])\n",
    "    wealth = wealth*coin_flip\n",
    "    wealth_t.append(wealth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc3ae80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.step(range(1,53), wealth_t) \n",
    "plt.legend(\"wealth\", loc='upper left')\n",
    "plt.title(\"Wealth at t, for a single coin tosser\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This game shows a single trajectory for a game with a single player. This might not tell us that much about its statistical properties. Lets try running the game many times instead, to see if there is a clear trend of what outcome we can expect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "## just copy the above code\n",
    "\n",
    "wealths = []\n",
    "N = 100000\n",
    "\n",
    "for player in range(1,N):\n",
    "    # we start the game with a wealth of 1\n",
    "    inital_wealth = 1\n",
    "    # our wealth at the start of the game is our inital wealth\n",
    "    wealth = inital_wealth\n",
    "    # represents the history of wealths for a person at time t\n",
    "    wealth_t = []\n",
    "    \n",
    "    wealth_t.append(wealth)\n",
    "\n",
    "    # we play they game once a week, for a year\n",
    "    for game in range(1,52):\n",
    "        # each flip has a 50/50 chance of either decreasing our wealth with 40%\n",
    "        # or increasing with 50%\n",
    "        coin_flip = random.choice([0.6, 1.5])\n",
    "        wealth = wealth*coin_flip\n",
    "        \n",
    "        \"\"\"\n",
    "        print(player)\n",
    "        print(game)\n",
    "        print(coin_flip)\n",
    "        print(wealth)\n",
    "        print(\"****\")\n",
    "        \"\"\"\n",
    "        \n",
    "        wealth_t.append(wealth)\n",
    "    ## an array with the result for each player at time t\n",
    "    wealths.append(wealth_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# take the wealth at time t for each player, and average it\n",
    "arr_all = np.array(wealths)\n",
    "\n",
    "## select a random set of trajectories with different number of people\n",
    "random_rows_10 = random.randint(0, arr_all.shape[0], size=10)\n",
    "random_rows_1 = random.randint(0, arr_all.shape[0], size=1)\n",
    "random_rows_100 = random.randint(0, arr_all.shape[0], size=100)\n",
    "random_rows_1000 = random.randint(0, arr_all.shape[0], size=10000)\n",
    "\n",
    "## Compute the enseble average over each size of sample trajectories\n",
    "wealth_n_10_avg = arr_all[random_rows_10].mean(axis=0)\n",
    "wealth_n_1_avg = arr_all[random_rows_1].mean(axis=0)\n",
    "wealth_n_100_avg = arr_all[random_rows_100].mean(axis=0)\n",
    "wealth_n_1000_avg = arr_all[random_rows_1000].mean(axis=0)\n",
    "wealth_n_all_avg = arr_all.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11aabb5c0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9cce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2, figsize=(15,5))\n",
    "# plot a line for each sample size, normal scale\n",
    "ax[0].step(x=range(1,53), y=wealth_n_1_avg)\n",
    "ax[0].step(x=range(1,53), y=wealth_n_10_avg)\n",
    "ax[0].step(x=range(1,53), y=wealth_n_100_avg)\n",
    "ax[0].step(x=range(1,53), y=wealth_n_1000_avg)\n",
    "ax[0].step(x=range(1,53), y=wealth_n_all_avg, c='k')\n",
    "# format plot\n",
    "ax[0].legend(['n = 1', 'n = 10', 'n = 100', 'n = 100', 'n=10000'], loc='upper left')\n",
    "plt.ylim(0,10)\n",
    "plt.title(\"Ensemble average - Change in wealth for different sample sizes\")\n",
    "\n",
    "# log scale\n",
    "\n",
    "ax[1].step(x=range(1,53), y=log(wealth_n_1_avg))\n",
    "ax[1].step(x=range(1,53), y=log(wealth_n_10_avg))\n",
    "ax[1].step(x=range(1,53), y=log(wealth_n_100_avg))\n",
    "ax[1].step(x=range(1,53), y=log(wealth_n_1000_avg))\n",
    "ax[1].step(x=range(1,53), y=log(wealth_n_all_avg), c='k')\n",
    "\n",
    "plt.ylim(0,3)\n",
    "plt.legend(['n = 1', 'n = 10', 'n = 100', 'n = 100', 'n=10000'], loc='upper left')\n",
    "plt.title(\"Ensemble average - Log of wealth at time t \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that adding more observations over time reduced fluctuations in the time series, and we can observe that playing this game for some time is indeed a good outome.\n",
    "\n",
    "**BUT WAIT**\n",
    "\n",
    "There is a flaw in this type of average, since it reflects a reality where a *single person would have access to many paralell games*. It is not necessarily the case that *my* returns will be that over the average of the *\"market\"*. THis is illustrated in a different way: with the time average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "inital_wealth = 1\n",
    "# our wealth at the start of the game is our inital wealth\n",
    "wealth = inital_wealth\n",
    "# represents the history of wealths for a person at time t\n",
    "wealth_t = []\n",
    "\n",
    "wealth_t.append(wealth)\n",
    "\n",
    "# we play they game once a week, for a few year\n",
    "for game in range(1,1040):\n",
    "    # each flip has a 50/50 chance of either decreasing our wealth with 40%\n",
    "    # or increasing with 50%\n",
    "    coin_flip = random.choice([0.6, 1.5])\n",
    "    wealth = wealth*coin_flip\n",
    "\n",
    "    wealth_t.append(wealth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11b0d7e48>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad88e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, t_avg_plt = plt.subplots(1,2, figsize=(15,5))\n",
    "t_avg_plt[0].step(y=wealth_t, x=range(1,1041))\n",
    "t_avg_plt[0].set_title(\"Wealth at time t, with a single play\")\n",
    "t_avg_plt[1].step(y=log(wealth_t), x=range(1,1041))\n",
    "t_avg_plt[1].set_title(\"Log of wealth for single player, at time t\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, there is some discrepancy between what we can observe in the *enseble* and the *time* average. Depending on the one you choose to look at the situation, you either end up rich or end up bust."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}