Cournot_With_TF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From c:\\program files\\python\\python36\\lib\\site-packages\\tensorflow\\python\\util\\tf_should_use.py:118: initialize_all_variables (from tensorflow.python.ops.variables) is deprecated and will be removed after 2017-03-02.\n",
      "Instructions for updating:\n",
      "Use `tf.global_variables_initializer` instead.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a: [0 1 2 3 4]\n",
      "q1: [6.000435, 4.500052, 4.1249676, 4.0312147, 4.007847]\n",
      "q2: [2.9997888, 3.7499874, 3.9375, 3.9843755, 3.9960938]\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 3750x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "from IPython.core.pylabtools import figsize\n",
    "from matplotlib import pyplot as plt\n",
    "figsize (12.5, 4)\n",
    "plt.rcParams['savefig.dpi'] = 300\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "\n",
    "def disp(q1, q2):\n",
    "    c = max(len(q1), len(q2))\n",
    "    a = np.arange(c)\n",
    "    print ('a:', a)\n",
    "    print ('q1:', q1)\n",
    "    print ('q2:', q2)\n",
    "    plt.plot(a, q1, color='C0')\n",
    "    plt.plot(a, q2, color='C1')\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.ylabel(\"q\")\n",
    "    plt.xlabel(\"$z$\")\n",
    "    plt.title(\"Cournot\")\n",
    "    return\n",
    "\n",
    "def findq(q, v=14.0):\n",
    "    tf.reset_default_graph()\n",
    "    \n",
    "    _q = tf.Variable(tf.random_uniform(shape=[1], minval=0, maxval=v-q, dtype=tf.float32), dtype=tf.float32)\n",
    "    \n",
    "    # 1. /  _q * (v - (q + _q))\n",
    "    qa = tf.add(float(q), _q)\n",
    "    cond = tf.reduce_mean(v - qa)\n",
    "    up = tf.cond(cond > 0, lambda: tf.multiply(_q, tf.subtract(v, qa)), lambda: tf.div(1., 0.02))\n",
    "    uq = tf.div(1., up + 1.)\n",
    "    \n",
    "    loss = uq ##tf.square(uq)\n",
    "    opt = tf.train.GradientDescentOptimizer(1.)\n",
    "    train = opt.minimize(loss)\n",
    "    \n",
    "    with tf.Session() as sess:\n",
    "        init = tf.initialize_all_variables()\n",
    "        \n",
    "        sess.run(init)\n",
    "        \n",
    "        for step in range(6000):\n",
    "            sess.run(train)\n",
    "            #if step % 100 == 0:\n",
    "            #    print ('\\t', step, sess.run(_q), sess.run(uq), sess.run(up))\n",
    "        \n",
    "        return sess.run(_q), sess.run(up)\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    q1 = []\n",
    "    q2 = []\n",
    "    q,_ = findq(0, v=12.)\n",
    "    for i in range(10):\n",
    "        if i % 2 == 0:\n",
    "            q1.append(q[0])\n",
    "        else:\n",
    "            q2.append(q[0])\n",
    "        q,_ = findq(q, v=12.)\n",
    "    \n",
    "    disp(q1, q2)\n",
    "    \n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q3: [6.99964]\n",
      "q4: [2.500177]\n",
      "q3: [5.749773]\n",
      "q4: [3.1251206]\n",
      "q3: [5.437329]\n",
      "q4: [3.2813437]\n",
      "q3: [5.359223]\n",
      "q4: [3.3203802]\n",
      "q3: [5.339914]\n",
      "q4: [3.3300514]\n",
      "q3: [5.334871]\n",
      "q4: [3.332573]\n",
      "q3: [5.33361]\n",
      "q4: [3.3331864]\n",
      "q3: [5.333304]\n",
      "q4: [3.3333397]\n",
      "q3: [5.3332267]\n",
      "q4: [3.333395]\n",
      "q3: [5.3331995]\n",
      "q4: [3.3333917]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a: [0 1 2 3 4 5 6 7 8 9]\n",
      "q1: [6.99964, 5.749773, 5.437329, 5.359223, 5.339914, 5.334871, 5.33361, 5.333304, 5.3332267, 5.3331995]\n",
      "q2: [2.500177, 3.1251206, 3.2813437, 3.3203802, 3.3300514, 3.332573, 3.3331864, 3.3333397, 3.333395, 3.3333917]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3750x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "from IPython.core.pylabtools import figsize\n",
    "from matplotlib import pyplot as plt\n",
    "figsize (12.5, 4)\n",
    "plt.rcParams['savefig.dpi'] = 300\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "\n",
    "def disp(q1, q2):\n",
    "    c = max(len(q1), len(q2))\n",
    "    a = np.arange(c)\n",
    "    print ('a:', a)\n",
    "    print ('q1:', q1)\n",
    "    print ('q2:', q2)\n",
    "    plt.plot(a, q1, color='C0')\n",
    "    plt.plot(a, q2, color='C1')\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.ylabel(\"q\")\n",
    "    plt.xlabel(\"$z$\")\n",
    "    plt.title(\"Cournot\")\n",
    "    return\n",
    "\n",
    "def findq(q, v=14.0):\n",
    "    tf.reset_default_graph()\n",
    "    \n",
    "    _q = tf.Variable(tf.random_uniform(shape=[1], minval=0, maxval=v-q, dtype=tf.float32), dtype=tf.float32)\n",
    "    \n",
    "    # 1. /  _q * (v - (q + _q))\n",
    "    qa = tf.add(float(q), _q)\n",
    "    cond = tf.reduce_mean(v - qa)\n",
    "    up = tf.cond(cond > 0, lambda: tf.multiply(_q, tf.subtract(v, qa)), lambda: tf.div(1., 0.02))\n",
    "    uq = tf.div(1., up + 1.)\n",
    "    \n",
    "    loss = uq ##tf.square(uq)\n",
    "    opt = tf.train.GradientDescentOptimizer(1.)\n",
    "    train = opt.minimize(loss)\n",
    "    \n",
    "    with tf.Session() as sess:\n",
    "        init = tf.initialize_all_variables()\n",
    "        \n",
    "        sess.run(init)\n",
    "        \n",
    "        for step in range(10000):\n",
    "            sess.run(train)\n",
    "            #if step % 1000 == 0:\n",
    "            #    print ('\\t', step, sess.run(_q), sess.run(uq), sess.run(up))\n",
    "        \n",
    "        return sess.run(_q), sess.run(up)\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    q3 = []\n",
    "    q4 = []\n",
    "    v1 = 14.\n",
    "    v2 = 12.\n",
    "    q,_ = findq(0, v=v1)\n",
    "    for i in range(20):\n",
    "        if i % 2 == 0:\n",
    "            q3.append(q[0])\n",
    "            print ('q3:', q)\n",
    "            q,_ = findq(q, v=v2)\n",
    "        else:\n",
    "            q4.append(q[0])\n",
    "            print ('q4:', q)\n",
    "            q,_ = findq(q, v=v1)\n",
    "    \n",
    "    disp(q3, q4)\n",
    "    \n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    # considered the before result.\n",
    "    #\n",
    "    #u1 = (12 - (q1 + q2))q1 + (14 - (q3 + q4))q3 - f\n",
    "    #u2 = (12 - (q1 + q2))q2 + (12 - (q3 + q4))q4\n",
    "    #u1 = u2\n",
    "    #(14 - 26/3)*16/3 - (12 - 26/3)*10/3 = f\n",
    "    #(256/9) - 100/9 = f\n",
    "    # f = 156/9\n",
    "    \n",
    "    #(14 - (q1 + q2))q1 + (14 - (q3 + q4))q3 - (12 - (q1 + q2))q2 - (12 - (q3 + q4))q4 = f\n",
    "    # f = 8 + (16/3)(16/3) - (10/3)(10/3)\n",
    "    #   = 72/9 + 256/9 - 100/9 = 168/9\n",
    "    \n",
    "    #\n",
    "    ## compare before and after.\n",
    "    #\n",
    "    #(14 - (q3 + q4))q3 - f = (12 - (q1 + q2))q1 = 16\n",
    "    # f = (42/3 - 26/3) * 16/3 - 144/9 = 112/9\n",
    "    "
   ]
  }
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