{
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   "cell_type": "markdown",
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   "source": [
    "$nCycles$ - number of simulation cycles\n",
    "\n",
    "$nBuyers$  - number of the buyers\n",
    "\n",
    "$nSellers$ - number of the sellers\n",
    "\n",
    "$seed$ - the seed of the random numbers\n",
    "\n",
    "$d_{1a}$ - the lower bound for random uniform numbers, for the buyers\n",
    "\n",
    "$d_{1b}$ - the upper bound for random uniform numbers for the buyers\n",
    "\n",
    "$d_{2a}$ - the lower bound for random uniform numbers, for the sellers\n",
    "\n",
    "$d_{2b}$ - the upper bound for random uniform numbers for the sellers\n",
    "\n",
    "initial buyer $i$ reservation price, different for each buyer: $p_{b,i}=\\frac{1} {1 + u_i}$ with $u_i\\sim\\mathcal{U}(d_{1a},d_{1b})$\n",
    "\n",
    "initial seller j reservation price, different for each seller: $p_{s,j}=1 + u_j$ with $u_j\\sim\\mathcal{U}(d_{2a},d_{2b})$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "levels of gray\n",
    "https://en.wikipedia.org/wiki/Shades_of_gray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "%pylab inline\n",
    "import numpy as np\n",
    "import pylab as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def plotCurves(d1a,d1b,d2a,d2b):\n",
    "\n",
    "    nBuyers= 10000\n",
    "    nSellers=10\n",
    "\n",
    "\n",
    "    seed=111\n",
    "    np.random.seed(seed)\n",
    "\n",
    "    buyerPriceList=[]\n",
    "    sellerPriceList=[]\n",
    "\n",
    "    for i in range(nBuyers):\n",
    "        eps=np.random.uniform(d1a,d1b)\n",
    "        if eps < 0:\n",
    "            buyerPriceList.append(1/(1+abs(eps)))\n",
    "        else:\n",
    "            buyerPriceList.append(1+eps)\n",
    "    for j in range(nSellers):\n",
    "        eps=np.random.uniform(d2a,d2b)\n",
    "        if eps < 0:\n",
    "            sellerPriceList.append(1/(1+abs(eps)))\n",
    "        else:\n",
    "            sellerPriceList.append(1+eps)\n",
    "    \n",
    "    fig =plt.figure(0)\n",
    "    ax1 = fig.add_subplot(111)\n",
    "    ax1.plot(sorted(buyerPriceList,reverse=True),color=\"black\");\n",
    "    plt.title(\"Demand curve in black, offer curve in gray\",y=1.1)\n",
    "    xlabel(\"the agents (buyers in the bottom scale, sellers in the top one)\");\n",
    "    ylabel(\"agents' reservation prices\");    \n",
    "    ax2 = ax1.twiny()\n",
    "    ax2.plot(sorted(sellerPriceList),\"silver\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "plotCurves(-0.09,0.01,-0.01,0.09)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotCurves(-0.11,-0.01,0.01,0.11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotCurves(-0.05,0.05,-0.05,0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotCurves(-0.10,0.10,-0.10,0.10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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