{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Economics Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a simulation of an economic marketplace in which there is a *population* of actors, each of which has a level of wealth.  On each time step two actors (chosen by an *interaction function*) engage in a transaction that exchanges wealth between them (according to a *transaction function*).  The idea is to understand the evolution of the population's wealth over time.  I heard about the problem when I visited the Bard College Computer Science Department. \n",
    "\n",
    "<img src=\"money.png\" width=200>\n",
    "\n",
    "Why is this interesting? \n",
    "- It is an example of using simulation to model the world. The model is simple but captures some aspects of a complex world.\n",
    "- Many students will have preconceptions about how economies work that will be challenged by the results shown here.\n",
    "- It reveals subtle differences between computational thinking, mathematical thinking, and statistical thinking."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Population Distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will model a population as a list of `N` numbers, each number being one actor's wealth. We'll start with a Gaussian distribution (also known as a *normal* distribution or *bell-shaped curve*), with a mean wealth of 100 [simoleons](http://en.wiktionary.org/wiki/simoleon) and a standard deviation of 1/5 the mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "N  = 5000 # Default size of the population\n",
    "MU = 100. # Default mean of the population\n",
    "\n",
    "population = [random.gauss(mu=MU, sigma=MU/5) for actor in range(N)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Population Statistics and Visualization\n",
    "\n",
    "How evenly is the wealth in a population distributed?  The traditional measure is the [Gini coefficient](http://en.wikipedia.org/wiki/Gini_coefficient), which Wikipedia says is computed by this formula (which assumes the *y* values are sorted):\n",
    "\n",
    "![Gini](https://upload.wikimedia.org/math/b/b/5/bb50601acc135c45a24bb0493f7555b4.png)\n",
    "\n",
    "A Gini index of 0 means total equality (everyone has the same amount), and values closer to 1 mean more inequality (most of the money in the hands of a few individuals).  Here's a table of Gini coefficients for several countries:\n",
    "\n",
    "<table>\n",
    "<tr><td>Sweden <td> 0.250\n",
    "<tr><td>Canada <td> 0.326\n",
    "<tr><td>Switzerland <td> 0.337\n",
    "<tr><td>United States<td> 0.408\n",
    "<tr><td>Chile <td> 0.521\n",
    "<tr><td>South Africe <td> 0.631\n",
    "</table>\n",
    "\n",
    "\n",
    "The Gini coefficient is traditionally computed over *income*, but we will be dealing with *wealth*. Here is the computation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def gini(y):\n",
    "    \"Compute the Gini coefficient (a measure of equality/inequality) in a population, y.\"\n",
    "    y = sorted(y)\n",
    "    n = len(y)\n",
    "    numer = 2 * sum((i+1) * y[i] for i in range(n))\n",
    "    denom = n * sum(y)\n",
    "    return (numer / denom) - (n + 1) / n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll define the function `hist` to plot a histogram of a population. Our `hist` wraps `plt.hist`, but with some specific keyword values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def hist(population, label='pop', **kwargs):\n",
    "    \"A custom version of `hist` with better defaults.\"\n",
    "    label = label + ': G=' + str(round(gini(population), 2))\n",
    "    h = plt.hist(list(population), bins=30, alpha=0.5, label=label, **kwargs)\n",
    "    plt.xlabel('wealth'); plt.ylabel('count'); plt.grid(True)\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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cAEwHVpnZce7uReaUuLq7tw3ZswdYvXp+8WFExrjCW1Lu/u/JzXdQLVAOnAncksy/Bah9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\nRFJRwRARkVT+P3v6rPLtu8ibAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104702240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a transaction, two actors come together and exchange some of their wealth. For now we will use a wealth-conserving transaction function in which all the wealth from both actors is put into a pot, which is then split randomly and uniformly between the two actors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def random_split(A, B):\n",
    "    \"Take all the money uin the pot and divide it randomly between the two actors.\"\n",
    "    pot = A + B\n",
    "    share = random.uniform(0, pot)\n",
    "    return share, pot - share"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(95.3251239711815, 104.6748760288185)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_split(100, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we decide which parties interact with each other?  We will define an interaction function that, given the size of the population, randomly selects any two actors in the populations (denoted by their index numbers in the list). We'll call this function `anyone`, meaning that any actor can interact with any other actor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def anyone(N): return random.sample(range(N), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3405, 116]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anyone(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `simulate` takes an initial population, calls an interaction function to select two actors, and a transaction function to split their wealth, and repeats this T times. After each transaction, we yield the population, so `simulate` yields the complete history of the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def simulate(population, T, transaction=random_split, interaction=anyone):\n",
    "    \"Run simulation on population for T transactions; yield (t, pop) at each time step.\"\n",
    "    population = population.copy()\n",
    "    yield population\n",
    "    for t in range(1, T + 1):\n",
    "        i, j = interaction(len(population))\n",
    "        population[i], population[j] = transaction(population[i], population[j]) \n",
    "        yield population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a simple example of simulating a population of 4 actors for 8 time steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100, 100, 100, 100]\n",
      "[100, 139.34514344135886, 100, 60.65485655864116]\n",
      "[170.2563182135521, 139.34514344135886, 29.743681786447894, 60.65485655864116]\n",
      "[105.13376035310705, 139.34514344135886, 29.743681786447894, 125.7774144190862]\n",
      "[105.13376035310705, 222.24697868451042, 29.743681786447894, 42.875579175934625]\n",
      "[105.13376035310705, 222.24697868451042, 53.493944819559275, 19.125316142823255]\n",
      "[105.13376035310705, 182.09114633291017, 53.493944819559275, 59.28114849442351]\n",
      "[105.13376035310705, 221.7092394595479, 53.493944819559275, 19.663055367785798]\n",
      "[264.84710771935215, 61.995892093302835, 53.493944819559275, 19.663055367785798]\n"
     ]
    }
   ],
   "source": [
    "for pop in simulate([100] * 4, 8):\n",
    "    print(pop)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SImulation Visualization\n",
    "\n",
    "If we want to do larger simulations we'll need a better way to visualize the results.\n",
    "The function `show` does that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import statistics\n",
    "\n",
    "def show(population, k=40, percentiles=(1, 10, 50, 90, 99), **kwargs):\n",
    "    \"Run a simulation for k*N steps, printing statistics and displaying a plot and histogram.\"\n",
    "    N = len(population)\n",
    "    start = list(population)\n",
    "    results = [(t, sorted(pop)) # Sort results so that percentiles work\n",
    "               for (t, pop) in enumerate(simulate(population, k * N, **kwargs))\n",
    "               if t % (N / 10) == 0]\n",
    "    times = [t for (t, pop) in results]\n",
    "    # Printout:\n",
    "    print('   t    Gini stdev' + (' {:3d}%' * len(percentiles)).format(*percentiles))\n",
    "    print('------- ---- -----' + ' ----' * len(percentiles))\n",
    "    fmt = '{:7,d} {:.2f} {:5.1f}' + ' {:4.0f}' * len(percentiles)\n",
    "    for (t, pop) in results:\n",
    "        if t % (4 * N) == 0:\n",
    "            data = [percent(pct, pop) for pct in percentiles]\n",
    "            print(fmt.format(t, gini(pop), statistics.stdev(pop), *data))\n",
    "    # Plot:\n",
    "    plt.hold(True); plt.xlabel('wealth'); plt.ylabel('time'); plt.grid(True)\n",
    "    for pct in percentiles:\n",
    "        line = [percent(pct, pop) for (t, pop) in results]\n",
    "        plt.plot(line, times)\n",
    "    plt.show()\n",
    "    # Histogram:\n",
    "    R = (min(pop+start), max(pop+start))\n",
    "    hist(start, 'start', range=R)\n",
    "    hist(pop, 'end', range=R)\n",
    "                \n",
    "def percent(pct, items):\n",
    "    \"The item that is pct percent through the sorted list of items.\"\n",
    "    return items[min(len(items)-1, len(items) * pct // 100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  19.7   55   74  100  125  145\n",
      " 20,000 0.50  98.2    1   11   70  230  440\n",
      " 40,000 0.51 102.6    1   10   69  232  489\n",
      " 60,000 0.50  98.2    1   11   70  232  453\n",
      " 80,000 0.50  99.1    1   11   68  230  459\n",
      "100,000 0.50  99.6    1   11   69  227  472\n",
      "120,000 0.49  98.3    1   11   71  224  459\n",
      "140,000 0.50  99.7    1   11   69  229  469\n",
      "160,000 0.50 101.1    1   11   68  228  484\n",
      "180,000 0.50 100.4    1   10   68  230  465\n",
      "200,000 0.50  99.8    1   10   69  230  456\n"
     ]
    },
    {
     "data": {
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7BlTbW2tM9xvAxo1wwQV6S6FIALMQXFRQwL319XT7/SlpgBT6M/W5qXhqPQzvHMa9083w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\ne+DYf9KPd7cX7x4vPUd6zOI1kenKvJV5zPj5jHG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MEaCHHoKrroJvfQu+8Q1z+czFcNlc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f000d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BXTU4nS5vdO+kmFcNLi8vD+4XSoiZIMxc+cjU2C+qETeOKPjRXGXTyvbYr6amhv79+3Pp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\nREREcvb/AW30R4ihFCL1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1100700f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three parts to this output:\n",
    "\n",
    "**The printout:** For the starting population and for every 10,000 transactions along the way, we \n",
    "print the Gini coefficient and standard deviation of the population, and the wealths at five percentile points in the population: the 1%, 10%, 50% (median), 90% and 99% marks.\n",
    "\n",
    "**The plot:** This shows the same information as the printout (except for the Gini index), but with more data points along the way. The leftmost (blue) line is the 1% mark, the rightmost (purple) is the 99% mark, and the inner lines are the 10%, 50% and 90% marks, respectively. For the plot, time goes from bottom to top rather than top to bottom. So, the 99% (purple) line starts at around 150, and over time increases to over 400, indicating that the richest 1% are getting richer. The fact that the lines are going more or less straight up after about 50,000 transactions suggests that the system has converged.\n",
    "\n",
    "**The histogram:** The starting and ending populations are plotted as histograms. \n",
    "\n",
    "The results show that income inequality is increasing over time. How can you tell? Because  the Gini coefficient is increasing over time, the standard deviation is increasing, and the 1% and 10% marks are decreasing (the blue and olive lines are moving left as time increases) while the 90% and 99% marks are increasing (the aqua and purple lines are moving right as time increases).\n",
    "\n",
    "Would the population continue to change if we let the simulation run longer? It looks like only the 1% line is changing, the other lines remain pretty much in one place from about T=15,000 to T=25,000. This suggests that running the simulation longer would not have too much effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Effect of Starting Population\n",
    "\n",
    "What happens to the final result if we vary the starting population? I'll introduce the function `samples` to sample from a distribution function `n` times, normalizing the result to have the specified mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def samples(distribution, *args, n=N, mu=MU):\n",
    "    \"Sample from the distribution n times, then normalize results to have mean mu.\"\n",
    "    numbers = [distribution(*args) for _ in range(N)]\n",
    "    return normalize(numbers, mu)\n",
    "\n",
    "def normalize(numbers, mu):\n",
    "    \"Make the numbers non-negative, and scale them so they have mean mu.\"\n",
    "    numbers = [max(0, n) for n in numbers]\n",
    "    factor = len(numbers) * mu / sum(numbers)\n",
    "    return [x * factor for x in numbers]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can easily make an initial population from a distribution function. I'll start with a uniform distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.34  58.7    2   20   99  182  199\n",
      " 20,000 0.49  95.7    1   11   72  228  443\n",
      " 40,000 0.50 100.5    1   10   69  231  460\n",
      " 60,000 0.50  99.3    1   11   70  232  465\n",
      " 80,000 0.50 100.1    1   11   69  229  464\n",
      "100,000 0.50  99.1    1   11   71  233  465\n",
      "120,000 0.50 100.8    1   11   68  236  471\n",
      "140,000 0.50 101.1    1   11   67  228  479\n",
      "160,000 0.50  99.5    1   10   69  230  455\n",
      "180,000 0.51 102.3    1   11   67  233  475\n",
      "200,000 0.50  98.7    1   10   71  227  455\n"
     ]
    },
    {
     "data": {
      "image/png": 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dNp1deSWUlsIvfxn/e48wMt5/nw/nzmWKU20uVBwbDb9roOrmKsy5ZjLPziTr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\nUkopW2gBUkopZQstQEoppWzx/24Q7NWDAs7oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bf98898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OiomIiORMxSQBmjOJJ8RMEGYuZYpHmZKjYiIiIjlTMUmA5kziCTEThJlLmeJR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\nkjMVExERyZmKiYiI5Oz/A/Nvkc3R0Q0qAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105d2b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(samples(random.uniform, 0, 200))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And try a constant distribution, where everyone starts out the same:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.00   0.0  100  100  100  100  100\n",
      " 20,000 0.49  94.7    1   12   71  228  425\n",
      " 40,000 0.50 100.0    1   11   70  226  457\n",
      " 60,000 0.50 100.5    1   11   69  230  458\n",
      " 80,000 0.50  99.6    1   11   70  229  450\n",
      "100,000 0.49  99.3    1   11   70  231  445\n",
      "120,000 0.50  98.8    1   11   71  231  461\n",
      "140,000 0.51 101.7    1   10   69  231  472\n",
      "160,000 0.50  99.0    1   11   68  232  458\n",
      "180,000 0.50  99.4    1   11   70  229  460\n",
      "200,000 0.49  99.0    1   12   69  229  449\n"
     ]
    },
    {
     "data": {
      "image/png": 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FDKPbYuedO+l+rRt7hZ3CqwupfqSa9NnpugcbjIZyQMR3QA1dDcbdkK6iAv75\nT71VKI6DNLOZL5aVUZuWxuMtLez1epnocOgtS3GCUPNEDZ2vdOLe5KZ/RT8HfnMAxyQHOefkUHh1\nIRnzMwy1CFrNARF/CM5qshozCwJAfT2con2IeCqOb48X42ULkxBcWVjIg1VVACxtbR3jCv1R7SKG\n0W1hL7NTdksZJ/3iJOYum8sZXWdw0q9PwpxuZu2CtXS/qu0uyh8W5YCI3wOqza9la8fW5ItJhP/8\nJ9ILUqQs+3w+AJyjpWJXKDTAZDWRuSCTirsrcJ7kZNMlm1g5fSWe3caY31ZDcMR3QDu6d1CdW518\nMYlw++3w9NNw7bWaVmv08e1kMt62eLunhzMyM7m9bNSNeg2DahcxUskW27+wnZbHW0aUD9UP4d3l\nxVnl1EHV4ajbL+I7oJq8GrZ3bk++mERoaYFZI/b3U6QQC7Oy8ITDuMxmvaUoTlAmfnMiGfMP38ts\nYfNClsgl5JyTo5Oqw1EOiPgOKMeZgydojG7qCBobYepUzas1+vh2MhlvWxRYrTT5fARG24zKQKh2\nESOVbNG3vC+yG9owNpy/QR8xo6CG4IjvgAZ8A2TYDLgTalsbvPkmfOUreitRfAgmORy0BwJcsHEj\n/5w9G7OBIpMUqUtwMMj+H+6n770+et/upeJrFUz+6WQclQ5sRTaEyVjtTDkg4kfBOa1OhgKj7FSn\nJzt3Qn4+zJmjedWpNL493oyXLba63fy1s/PQWqChUIiQlIZ2QKpdxDC6LWRQ4m/142/zY3Ka6Pp7\nFwOrBw4lILUWWTFZTZTeUorZpf/wr3JAxHdAGbYMer299Hp7yXbonzPpEPPmQU8PrFkzLqHYivFh\nKBTi1DVr6A0G+URBAY9UV3NWVhYWFQWn0BBrtpWaJyJJlIN9Qbz7vQTaAoec0u7/2U3YEyZ7STYZ\np+g/wqNaPzApznrTfX37KMkoIdOemXxBR8Nuh6oqiN5Ba0kqjW+PN1rbwgQ0eDx8pbycawsLWZKd\nnTLOR7WLGKlkC0uWhfQZ6eSck0PRtUVU3FVB5X2VAKyZt4Z3c99l1exVbLp0E979+mTlUD0gIN7e\nYBKJw+Iw3o6oPp/aAygFcZjN/GHqVK6qrwdg3SmnMCdD/ztQxYmNZ7eHVdNXEfaEMbkiv2Vp09Nw\nVDiwV9ixT7DjmODAmqfPBolCSjn2WScwQgj55S9LfvKTw8vdfjclj5aw5bYtVGQZbNHnpz8NU6bA\nAw/orUTGfDWIAAAgAElEQVSRIB1+P1fV15NjsfDrk06i0BY/Xb5CcTyEfWF8B3z4mn34mnz4m/34\nmn0MrB6g752+Q+ed2Xcmlkxt+h1CCKSUH2ryUvWARsFmtjEpZxIrm1cazwHdcw+ccw5ceSWobMop\ngTsUYsfQEHdXVCjno/hQSCkJtAfw7vPS/Wo3zb9oJtgXxFZsw15mjxzldmxlNkpvLaXqwSrsZXZs\npTbMTv0DD4ajHNAo7OrZRetgK5fWXKq3lJHMmgUPPQS33qrpcJwe+90bFa1tUWCz0RMMUpaCO6Kq\ndhFDT1tsvWErbc/Gds90zXThmu5i7vtzcU5yGi7EOhGUAxqFovQi3AE3VrM+Y6NjcuWVcNdd4PeD\nuqM2LFJKPt/QwHPt7UxwOLiysFBvSYoUpfxL5YS9YYa2Rvb4Gdo6hL/Vj7veja3ERtqUNHLOyyH7\nY9lY0lPjpz01VOqA0+LEG/QipTRU+vJDmEyR+HENU7mou9wYWtnCGw5T19vLYCjEtSnqfFS7iKGn\nLTJOzmD6c9MPvZYhib/Dj78lcvSv7GfrtVsJDYaoXVpL8fXFumlNFIOFeOlDvHVAg/5BHBYH8shc\nFkZh926YMEFTB6TQHpMQXFlQAMBjzc06q1GcSAizwF5sJ2NuBq6ZLvY9vI/QYCStS/c/jbXtwmgo\nBwQMxUl4kJeWh81so2uoK/mCEsFuj2zLrSGptMZhvNHKFnaTiYcmTeJrFRVUpujGc6pdxDCqLRwV\nDk6tP5Wi6yPbbYe9xs8xCGoIDoDRdkauyKygsaeRAldBcgUlQnk5dHXB3r0wcaLeahSjMBQK8a+e\nHkJSUu926y1HcYIRHAyy+dLNuLe4CbRHbkgrvlFB9Q8MupXMEage0FGwmCy0DbaNfaIepKfDokXw\nj39oVqUa64+hlS1e6+7m0/X1/LipibtSdBNB1S5iGM0WMijJvSgX10zXobLh636MjuoBjYIv6GND\n2wYumHyB3lLi88QTUFcHTz6ptxLFUfhkQQGlNhunr1vHxbm5estRnCCE/WG237ydzr924qh0YJ9g\np/TWUuwT7GQvMlDuyjFQPaBRsFvs1OTVsKltk95S4rN1K1xyCRRoNzxo1PFtPdDKFi93dnLxpk1c\nU1jIrPR0TepMNqpdxDCKLYa2DdH1chc1T9Yw9XdTqX2qlik/m8LEeyaSdXqW3vISRvWAiL+MZm/v\nXtrcbUwt0H7jN01YuBC++129VSiOwpqBAS7bvJlrCwt5dPJktfupQjNsJTbyLsuj5cmWSKbrFj/B\n3iAmh4myL5cx6cE4GZYNiHJARJbUHMmm9k2cUnIK6TaD3rX+4Q9wzTWaVmm08W090cIWs10u/jJ9\nOi90dDBh+XJmp6ezMgW30FDtIoZRbGErsDF1aeTmeHDzIINrBxlYO0Dr0tYRu6AaGeWAAE+cnbfX\nHFjD3OK5yReTKMuWwaOP6q1CcRQsJhNXFBRwRUEB7/b2ctb69Tzb2sr1xcZfIKgwHmFfmEBngEBP\ngGBPkGBPEO8+Lzvv2HnonMrvVjLxf1InKlbNARF/HZDEoBkQDjJrFmzQdn93o4xvGwGtbXFmdjZb\n5s/n9oYGujVevzXeqHYRQ09bLHMuY3n5clbPXM2ue3Zx4PEDDKwYoOyOMkpuLiH34lyKrys29u/W\nESgHRHwHdGnNpTyx9onki0mUU06BFSv0VqFIkLCU/LmjAyGEobffVhgXYYm1G2uBFXtpZD8fZ7WT\nouuKmPWPWTgmptZiZ7UfkBDyrLMky5YdXh6WYSzftRD4dgCzyYCTx+eeC9deC5/9rN5KFAngC4dx\nLFvGQ1VV3KsWDiuOg+BAEP8BP/4OP4H2AP52P97dXtyb3HS/1s28jfNIn5m8OWu1H5BGxFugbhIm\nJuVMYl3rOuaVzku+qLG44Qb49a+VA0oR7CYTVxUU8Kf2duWAFMeFJcPC7l/upn95P4GOAP42Pwiw\nFdlIPzkdky31BrRST/E4EArFLz+78mxe2f5KcsUkypVXwsaN0NqqWZVqrD+G1rZ4saODf/f0cEdZ\nmab1JgPVLmLobYvmnzZTeX8ls/81m9PbT2eRexGn7TqNeWvmkVaTpqu240H1gIDRFqhn2DNwWAw6\npmq3RwIR1q2Diy7SW41iFP7fvn280dPDWz09vDVnDouzU2eVusJ4uGa62PLJLVhyLFiyLSMePQ0e\nSj5fQuGnUmPrD+WAiL8dA8DErInUd9QnV0yieDyRbAi1tZpVaZQ1DkZAK1t0BYP0BoM4TCb2j5b1\n1uCodhFDb1vM2zCPsCccCcPuDUZCsnsjIdnbrtsGQFptmnJAqURmZvxyiSQYDiZXTKK8917E+VRV\n6a1EcRQenjSJe4JBztuwgYZ4C84UimNACIE5zYw5zYy97PDt3XM+lsPub++m7Q9t9L3TR94leeSc\nl4Oj0oGt2GbIOSLjKdKB0RzQzu6dzCqalVwxiZKXB/v3j76XxHGg9/i2kdDSFiv6+9nkdnN3imbD\nVu0ihpFtYS+zU/t0Lae3nc7kn00mHAjT+PVGPpj0Acvsy3iv6D1Wz13Nxks24tljjJuhMR2QEOIk\nIcS/hRCbo69nCSH+Z/ylJY+MjPjl27u2Mzl3cnLFJMrcuTB7Njz+uN5KFGPQ7vczw+VSueAUScFk\nMZF9ZjbVP6hm0vcnQTTISlgEabVp5P1XHrbCOAkwdSCRHtATwL1AAEBKuRHQNgmZzsTLBQdQmVXJ\nzu6d8d/Um+5uWLMGpkzRrEq9x7eNhFa2GAgG2eP1ssXtJpiia+5Uu4iRarZIn5tO1YNVlNxUgmu6\ni4G1AzTe1cjK2pVsOH8DG87fgK/Zp5u+ROaA0qSUK49I72DQiZHjo7c3frndYscTNEZXdQT19ZGu\n24UX6q1EMQr/6u7mvI0buTA3l3/Ono19tDsdhWKcsOZamfityLqzQHeAjj934N7spuvvXfT8sweI\nLHC1Yz9aNeNGIn8RnUKIaqI5VoUQnwJaxlVVkmloiF9+4eQLeX3n68kVkyhOZ2QOyKfd3YuRx7eT\njRa28ITD5FutrBsY4IWODg5o+H+VTFS7iJHKtuj8WycNtzTg3e9lyq+msLB5IUvkEly1rrEvHicS\ncUC3A78BaoUQzcBXgFsTqVwI8ZQQok0IsXFYWY4Q4k0hxHYhxBtCiKxh790rhNghhNgqhDh/WPnJ\nQoiNQogGIcRPhpXbhBDPRa9ZLoSYMOy966PnbxdCXHdUI4xihc6hTkoyShL5qsnn0UfhiivAYdB1\nSgo+np9Pxxln8O7cufykqYlfHzigtyTFRxD3Njd7vreH5p83A+Dd5SXvwjzspfr0eoYzpgOSUu6S\nUp4LFAC1UsozpZR7Eqz/GeDIPa3vAf4lpawB3iIyv4QQYhpwFTAVuAj4pYiN+/0K+JyU8iTgJCHE\nwTo/B3RLKacAPwF+FK0rB/gOMB9YANw33NEdyWgOaF/fPiZkToj/pt6sXQsaj0en2vj2eKKlLR5v\naaHMZuPrKRoFp9pFjFS0xaqpq9jznT0Mrh0kY0EGGadk0PlKp96ygATmgIQQ2cB1QCVgOegTpJRf\nGutaKeW7QogjE19dBiyOPn8WqCPilC4FnpNSBoE9QogdwKlCiL1AhpRyVfSa3wKXA29E67ovWv4C\n8LPo8wuAN6WUfdHv8CZwIfB/8XSOFpzU4e5gUo5BdxYcHNTcASnGhxKbjVa/nx0eD3NHC7lUKMZA\nhiWBjgC+Fh/+luguqH1BwkNhQkOhUR8z5mUQ6Arg3e1lYMUAAysGCPvD5H88X++vlFAQwqvAB8Am\nYJScAcdEoZSyDUBK2SqEOLhktwxYPuy85mhZEGgaVt4ULT94zf5oXSEhRJ8QInd4+RF1xWXUKLjs\nSvb17UvsWyWb6mp4+WW46y7Nqqyrq0vJO7zxQEtb3FlRwVA4zCe3bGHXaadpUmcyUe0ihh62cG91\ns2pa5P7bmm/FVmLDVmrDXmLHkmPB5DRhTjNjzbdiTjNjSjMd/dFpwpxujCUBiTggh5RSu1+5kWgZ\nm3pcqcF37LiB+++vBCA7O5s5c+awZMkSnFYnu9btos4Ra3QHJyF1f/2lL8EDD1B38snG0HOCvT6I\nVvXdvWgRP2lq4oGXXmJxdrbu3+9YXq9fv95QevR8vX79+qR/fqAvQPbMbIa2DrHetJ4p357C+Vee\nn3h9blgy/8PrqaurY+nSpQBUVlaiBWPuBySEuBMYBP4OHArjkVJ2J/QBkSG4V6SUs6KvtwJLpJRt\nQohi4G0p5VQhxD2RauUPo+e9TmR4be/Bc6Ll1wCLpZS3HjxHSrlCCGEGWqSUhdFzlkgpb4le8+to\nHSOG4IQQcsECyQcfjNT+9LqneWffOzxz2TOJfNXk0tgIp50GL74IZ52ltxrFKGxzu3m+o4Pn29sZ\nCIV4c/ZsatJSL2uxQj/8nX4abm6g560eQv0hFuxegLPSqbcsTfYDSiQKzg88QmR4bE30WH0MnyE4\nvGfyMnBD9Pn1wN+GlV8TjWyrAiYDK6WUrUCfEOLUaFDCdUdcc330+ZVEghogMj90nhAiKxqQcF60\nLC5dXfHL2wbbyHfqP04al+pqeOQR+OEP9VaiGIWhUIjT1q7lvj17OCs7mx0LFijnozhmvHu89P6n\nl+pHqlnYstAQzkcrEnFAXwUmSykrpZRV0SOhmXkhxB+B94lEru0TQnwW+AER57AdOCf6GillPfA8\nUE9k3uk2Geue3Q48BTQAO6SUBxfnPAXkRwMWvkIkmAEpZQ/wPSKOcgXwgJRylOWmMGfOyLKwDPNK\nwyvMLp6dyFdNPlLCsmXg0i6G/8jhp48yWtgizWymaeFCHps8mV8fOMBXdho0q8YYqHYRQw9bpNWm\nUfL5Ejr+3MGq6at4v/R9Nl6ykd3f3o2n0aAL5RMkkTmgncDQ8VQupfz0KG+dO8r5DwMPxylfA8yM\nU+4jErodr66lwNJEdKbH2cXWH/KztmUtl9ZcmkgVyScchvXr4cYb9VaiOArpFgunRCPffjDJoBGV\nCkMT6gvh2enB3+5H+iXhcBj/AT9uuxvfAR/O6tTtESXigNzAeiHE2xw+BzRmGHaqMBTHvTosDjLt\nmQz4Bsi0j5IuW0/MZrjmGti2TbMqD048KrS1Rb3bzZz0dDItqbn7iWoXMfSwRd97fXT+JbJux5Jn\nIevMLDLmZUSOk1M7rD+Rv4iXoscJy2hxGIWuQloGWyjLNOg2ym++CZcatIemOESB1UqaSeWBUxwf\nhVcVUnhVIeFAGE+jB/dGNwNrBtj2mW0U31BM9SPVeks8bhLJhPBsvCMZ4pLFwED88hmFM9jRtSO5\nYhKltxeWL4fzzx/73ARRY/0xtLTFqoEBThtt06kUQLWLGHrawmQ14ap1UXhVIVUPVjHx2xM58Hhq\np3catQckhHheSnmVEGITI9fqSCmlQWfnjx37KCmRvEEvZpMxFmyNoLERioqgpkZvJYoxmOZy8bjK\nA6fQAO9eL61LW2n+eTP2CXYm/SC15xVHXQckhCiRUrYIIZ4Hvjb8LeBHUsq4k/+phhBCXn215Lnn\nDi+XUlLwSAHrb1lPeWa5PuKORlcXlJXBN74BDzygtxrFUThvwwZmulz8eLJBNzdUpAQrZ6xkaEtk\nwjr/k/lkL8nG7DKTf1k+1lxr0vVosQ5o1B6QlPLglguTpZR7j/jg2g/zoUYj3q7Wvd5ehgJDlGaU\nJl9QIuTlwdlng4qsMjzZFgsBKfGHw9jUXJDiOJn5t5kMbRvC3+7H1+xj5x2RsH7ry1ZD5HU7Hkb9\naxBC3BodfquJboVw8NgNbBztulTE7x9ZluXIojSjlLUta5MvKBF274bVq+ETn9CsSjXWH0NLWzhM\nJn7e3Mzy/n7N6kwmql3E0NMWzmonuRfnkn95PtmLswGwl9tT1vnA0aPg/gi8RmRdzj3DygcSTcOT\nKuTH+f8LhUPs7dvL5FyDDpvk5ESiJ5ypuwbgo0Jdby9P1tSwODtbbykKgxL2hdly1RZ8TT4cEx2Y\nnCaCfUFC/SGC/UFCfdHH/hAmh4m06WkUfaaIzAWpG9wCRx+C6wP6gP8veXL0ISdnZJnVbCXdlo4/\nFKd7ZASys6GgADZvhrlzNalSrfeIoZUtOv1+mnw+0kfb8yMFUO0ixnjYIjgYZGD1AF0vR3KCDa4d\nBGDG32ZgybJgzjRjyYw9muwnzjBuaq6M05h4Q3AQScdjFgb+4cjMjD+BpTAM+TYbkxwOgmMk/VV8\n9HBvcbPpsk14GyN/w9ZCK+VfKidjfgbpc9OxFdh0Vjj+nDiu9EMwWhj2xKyJ7O7dnVwxx8KnPgUP\nj8hcdNyosf4YWtnid62t7PJ6OT9eNztFUO0ihpa2cNY4qflNDVN+MYWyL5UR7A7iqHKQe37uR8L5\ngOoBAfFzwQH0+fpwWBzJFXMsXHQR/OMfeqtQHIWF0QWoL3Z28oVSg0ZUKnTBZDGRc04OOedEbk4G\nVg7Q+ttWAh0BLHkWrHnWQ4cl14Ily4IwfaioZ8OhHBAQDMYvr86ppnWwlRmFM5IrKFE6OuJPYB0n\naqw/hla2mJyWxq2lpXQHAprUpweqXcQYT1tUfreS/vf78TR6CKwMEOgKEOyKzA8d5PS207EWWIns\nTJP6KAcE9PTELy/NKOXAgIFXsNfXq3VAKcDUtDSeamnh3okT9ZaiMDC55+WSe17uiPKWZ1pouKWB\ntNo0Vk5bSdgbxl5qj/SMhvWULDkWAl0BMudnUnRtkQ7f4NhRDojRHZDFZGHAN0qiOCPw+uvwJe2S\nktfpsN+9UdHKFn3BIP+zezc3l5R8eFE6odpFDD1sUfLZEko+G2s/gd4A/lY/wa4g/g4/TY820fbb\ntkPv987oTRkHpIIQAMco0zzv7HuHMyackVwxiVJfD1u3apqMVKE9mWYzD1ZV8YsDB/CGQnrLUZwA\nWLOtuGpdZJ2Rhb3MTt+7fQDMfns2S+QS5m+ar7PCxFE9IEaPgpNSYhIG9dE7dkTmf0YTfxyou9wY\nWtlCCIFfSq4pLMSRomuBVLuIYQRbSCkJD4UJdAdYuzCWqWXD2RsAKLymkGl/mqaXvGNCOSAg3nxe\nt6eb1sFWphUY9D/y0kvhi1+E116Dj39cbzWKo/DL5maeVFnLFceJDEsCHQF8zT58zT623bCNYHcQ\nW5kN1zQXliwLYW+YkDtEaDCEfYJ2N6XjjXJAxB+C63B3kJeWZ9wekBBw553wzDOaOSA11h9DK1v0\nBgI0+3wpvRBVtYsYybRFyBviHec7cd8r+UIJjgmOQ9kRbMU2cs7LSbnoOOWAiD+KVZFVQa+3l9bB\nVuNmxF62DK64Qm8ViqOwy+tFCMEMl0tvKYoUw+wwM2/jPEIDIcK+cCwvXH+I7je6aX26FRmQCLsg\n59zoeqIUG+VVDoj4W3L/veHvzCudR0m6QaOXfD7Yvz+Sjkcj1F1uDK1scXJGBsU2G691d3NdURGW\nFNyOQbWLGMm2RfrMkavkfa0+dn51J+V3lZNzbg5ZZ2RhdqaY54mSen8N40C8XHBOi5NQOGTcLu1L\nL0WG4dT8j6Fp8flYlJXF57Zv56XOTr3lKE4AZFBicpjIXJCJs9qJyZG6P+Opq1xD4mVCWFK5hOVN\nywmFDRo6u20bnH46aBhZpXJ+xdDCFk+3tFC6fDm/bWujyuFI2e0YVLuIYQRbhAZChPpCbLliCysm\nrWDjRam7PZsagiO+A9rTu4ccRw5mk0G7tkKMnsROYQhuKC7mjKws1g0McHdjIz9tbuZ7VVV6y1Kk\nOIGOw9M69bzRw/sl72Mvt2OvsB96tBXZyLskT5ftuhNFOSDidyLe3/8+iysXJ19MophMoHF+MTXW\nH0MLW5iEoCYtjWyLhWa/nwf37uWT+fnMycj48AKTiGoXMYxgi+xF2SyRMR3hYJhAWwDvfi++Jh++\n/T68e7zs+vouzOlmij9XjDXfetjhnOTEMUH/RMvKAQHxFqifXHIyv17z6+SLSZTsbNi3T28VigT4\n+KZNADxcVcVJaWk6q1GcaJgsJuxlduxlh4fz5l+ej6/JR6AzQKAzwOC6QQIdATr/GpmLrLy/cmTW\n7TwLtgIbZldyRn6UAyL+nm7Lm5ZTllGWfDGJ8uabsGiRplWq9R4xtMwFt2FwkLo5c1J6Dki1iwip\nZIucsw/PlB/2hQl0BSi8ppCWJ1voeKGDoR1DSN/IMODhPazxRDkgwOMZWWY322kZbEFKacxIuL17\n4bTT9FahGIMf7dvHgszMlHU+itRGSsmue3bR/ItmpF8e2lvImmvFUe0gY34GllwL9lI7ruku0qan\njehJjSdCpvAKbS0QQsjLL5f89a+Hl0spyfxBJvvv3E+2w4A/Hjk58O67MH263koUoyCl5Kr6elb0\n97Nv4UK95Sg+grT9qY3tN29nwY4F2Iptmt5MCyGQUn6oClUYNvHn8kMyhFmY8QV9yRc0FuEwWCya\nByEotKU3GOSFjg72+3yIujp61f+XIsn0r+gn7A6zvHQ5noY4Qz06oxwQ8ZORvrfvPSZkTaDQVZh8\nQWPR1BRxPrNna1qtEdY4GAUtbJFjteJftIg0k4k0kwlnimbDVu0iRirYItgfZM2CNayoXUHL4y24\nZrso+UKJIZOUKgdEpDNxJFU5VbQMthCW4eQLGoutW6G2Nr7nVBgKq8nEzgULODMri683NuotR/ER\nwOQw4Wv24dnuweQ0IUwC3z4fO27fwa57d9H8q2Z63u7Bd8CH3lMwag5ICPnJT0peeOHwciklju87\n6Pp6F+k2gy349Pth4sRIMtIpU/RWo0iAd3t7uXDjRpbW1vKpQgP2qhUpT//qftwb3JFtGdwhgj1B\nvLu9eBo9eBo9hPrjZ3U5s/dMLFnHHo+mxRyQioIjfg9ICEFpRint7nbjOSCbDc46C955RzmgFOGM\nrCy+Ul7OzQ0NygEpNENKiXuTm5137sS7y0v2kmxMLhPmdDPmDDOZCzPJOTcHc7o5Uu4yR470yKMp\nzXRczkcrlAMiElAWj0AogFkYdNz+v/4LXnkFbrxRsypTaY3DeKO1LS7ZtInVAwP8fupUzepMFqpd\nxNDbFu56N4MbB3FvduPe4KZveR+WTAtlt5dR9uUyTJbUmlVRDohIVpsj2du7F3/IT3lmefIFJcKU\nKbB8OfT2RrIiKAzJXTt38peODvb5fLQsXEixhluoKz5aeBo9rJq+CkeVg+Lriym+oZiTfnMS9tLU\nbVPKAQFDQyPLhBAIIYy7I2pXVyQIQcMfNHWXG0MLW7zT28v/NjVxS2kpv5gyBVOKBo2odhFDT1s4\nJjmY9Mgkmn/ezP5H92MrtR1KwWMrtZF7Qe6I7AdGRzkgYGBgZJnFZKHP24c36MVpdSZf1Fj09sLC\nheA0oDYFAH+N7v9jhpR1PgrjIIRgwt0TqPhqBaH+EC1PttD5t07aftcGwNDWoZRzQAa9vU8ufX0j\ny0rSS1g0cREv1L8w8k0j0N4ef+zwQ5AKaxyShRa28IfDWIVgh8fDP7u7P7wonVDtIoYRbCGEwJJl\nofHuRoa2D1H9v9XMXT6XaX+cpre0Y0Y5IOInFBBCUOgqxBcyYCYEgD/8Ac48U28ViqPwsylT+NuM\nGWx2uzl/40YCYQOuKVOkLHPq5pAxL4M9397Dtuu30fJMi96Sjhm1DkgIuXixJN6NzT3/ugerycr3\nPva9pOsakwsvjMwBvfaa3koUo7B2YIAz1q3DG3U8nWecQZ7VuJuDKVKTcDBM2+/a2H7jdlyzXeR8\nLIcJ907AVmAb189VueA0YrTh+WA4iNVs0B8MkwnOOENvFYqjcHJGBv1nnslZWVkAhxyRQqElJouJ\nks+WsKBxAe5Nbpr+t4lNH9+kt6yEUA4IGO2m9JWGV7h4ysXJFZMov/oVPPJIZFsGjTDC+LZR0MoW\nVpOJ12bN4pT0dL63Z4/uqU+OB9UuYhjZFiF3CKL3OMHeIOvOWsfGSzZS/+l6Gm5toPGeRvY+tJfm\nXzTT+rtWBjcP6isYFQUHQHqcRAeBUIADAweoyq5KvqBEsNkie4kXF+utRDEGDpOJaqeT//T14ZcS\nu4qIU4wD6TPTWSKX4GvxEWgPsHrO6hHnCIsgbVoa1jwreV15pM/QN8uLckBARsbIMospYhrDrgPa\nvz+yBkjDHzO13iOGlrb4fVsbz3d00HDqqdg1jlxMBqpdxEgFW9hL7NhL7FhyLAR7goe9V35XOdU/\nrNZJ2UhS769hHIg3BCeEoDi9mJZBg0aWbN4MkyePPn6oMAyLsrK4uaSEM9atw6/mgRRJouCTBYcX\niMi23EZCOSDAFyfSOizD7OndQ3WOce4WDtHbC/feGzk07AEZeXw72Whpiyqnk69WVKRsEIJqFzFS\nyRYyHJtvdM1wUXJTCfYSO62/baXrtS76V/fj3eslNBQ/S3Yy0G0ITgixB+gjMm0WkFKeKoTIAf4P\nmAjsAa6SUvZFz78XuBEIAl+WUr4ZLT8ZWAo4gFellF+JltuA3wKnAJ3A1VLKffG0DMaZixMIphdM\n583GN/l4zce1+dJa8ctfwgUXwMUGDZBQHMYL7e18oaGBR6ursaXgEJwiNal5vIaq71bha/JFjmYf\nvv0+3Jvd+Dv8BDoCBDoC+Nv9CLPAVmSj5KYSSm4qwVY4viHcB9FtHZAQYhdwipSyZ1jZD4EuKeWP\nhBDfAHKklPcIIaYBfwDmA+XAv4ApUkophFgBfFFKuUoI8SrwmJTyDSHErcBMKeVtQoirgU9IKa+J\no0Nefrnkr38dqfGOV+9gUs4k7lx4p/YGOF6kjAQe/PvfMGOG3moUCbBo3TpuKinhOhUwojAgUkpC\ngyG8u73se3gfXa914ZzkJK0mLZJvrtR+6NE124U1OzLsn+r7AQlGDgFeBiyOPn8WqAPuAS4FnpNS\nBoE9QogdwKlCiL1AhpRyVfSa3wKXA29E67ovWv4C8PPRhOTlxS/v9fWS7TBYpmkhImOG+fl6K1Ek\nyMAq04wAAB74SURBVIW5uXy1sZHzc3JUNmyF4RBCYMmwkD4rnWl/msbAugF23LaD9ufaYyeZwFZs\no+KuCiq+WqHZZ+vpgCTwTyFECPiNlPJJoEhK2QYgpWwVQhzcuasMWD7s2uZoWRBoGlbeFC0/eM3+\naF0hIUSvECJXSjkiKVe8VDwA5RnlNA80H+fXGyfc7siOqGlpmlet914nRkIrW3xn925+1tzMbaWl\nZMXb+TAFUO0iRqrbIuwLExwIEuoPEewPEhoIRZ5Hyzw7Pex/ZD8Tvz2RCd+ccKj3Yyu0IczaLx/Q\n8y/iDCllixCiAHhTCLGdiFMajpbjg6Nar67uBu6/vxKA7Oxs5syZw5IlS3AH3PRu66UuHGt0Bych\ndX8dndA2jJ4T7PVBPmx979bVkeHx8F8zZ+I0mw3z/Y7l9fr16w2lR8/X69evN5SeeK97/tPDtAPT\nEGbBuxvfJdARYObgTAKdAdaF1mF2mZmfOx9zppl14XWY08ycVnkalkwLq3tXY7vDxpLvDqt/Oywp\nWUJdXR1Lly4FoLKyEi0wRC44IcR9wCBwE7BEStkmhCgG3pZSThVC3ANIKeUPo+e/TmR4be/Bc6Ll\n1wCLpZS3HjxHSrlCCGEGWqSUI/ZCFkLIhQsl778/Utd/v/jfLJ64mJtPuXlcvvdxc8MNUFUF9903\n5qkKfQmEw1yxZQu1aWk8Um3AiErFCcfWz2yl7fdtWHIt1DxRE9kvqMyGNd+KyW5CaBQ5m7K54IQQ\naUKI9OhzF3A+sAl4Gbghetr1wN+iz18GrhFC2IQQVcBkYKWUshXoE0KcKiJWve6Ia66PPr8SeGs0\nPaNtqbPqwCoWViw8nq84vphMkWAEheGxmkzs83pxh0K0+/16y1F8BJj0g0mU31lOsDuIOd1M5oJM\nHOUOzA6zZs5HK/SKCS0C3hVCrAM+AF6JhlX/EDgvOhx3DvADACllPfA8UA+8CtwmY12324GngAZg\nh5Ty9Wj5U0B+NGDhK0SCGeISLwwboGuoi/w0A072CzEuDujI4aePMlra4unaWoZCIYref587duzQ\nrN5kodpFjFSwxYYLNuDZ4WHSjyaRMS9OmhcDocsckJRyNzAnTnk3cO4o1zwMPBynfA0wM065D7gq\nET3xghA63B2EZIgiV1EiVSSXhgb49Kf1VqFIkFMyMlg6der/396Zh8lRXYf+d3qdmW7Nqtk0Qhti\ntAspEpaEEBIWm/HDEJZAzPNCDE6ebTAmwQKTgMEkgXzE8YKJSQgY8MPgxDEICM8CgT4QSICQRjtC\nsvZZNWtrZnq6u7ru+6N61DPStDRCPVM13ff3ffXVrVvVpVNHd+rUvffcc2g1DI7oXpDmDKl9vJZ9\n9+7DFXDhznPjynNBHGJtMYxWA1xw7qpz8Y9xvsflyHTLSTNjxpxYdyh0yHku2AB1dbB1K8yYkfZb\n905katKvi5hpsjsc5pfV1Wm973Cg20USJ+gifjSO0W5A+4nnfFU+fKU+tv/ZdtwBN+6AZaB6y8cf\nF19ejL/KPkOlDRBWUOnjGVcwjiNdR5yXE6igwBp+6+jQkbAdjlKKVW1tvNnWxqstLUzOzeXCRG4g\njeazMm7FOMatGNevzggZGCEDs8sk3hU/tpndyePec0aHQbQuSu1j1hKTsi+X4av04a+0XK7zpuYx\nau7wDN1pA4Q1p388OZ4cRIRIPOIsAxQIwL33wgMPwPPPp/XWa0b4God0kg5dhOJxLt+yhVsrK/m3\n6mouKChw3CTwYNDtIolTdeHJ9+DJP/nr3DRMorVRunZ20b29m5KrSmh9rZWm560Fp648F/4qP8G5\nQWa8mP4RloHQBoiBDVDQF2RG6Qw21G1g2YRlwy7TSZk3D155xW4pNKdgW1cXAN+orGRBfr7N0miy\njdCHIQ7/7DCRgxF6DvQQrY/iLfOSNyWPwIwAJV8ooeo7Vfir/PjH+HHnD7+XnDZAJ2Fe5TzWHVrn\nPAMUCqX2HT8DnPhlZxfp0MWT9fWM9/up8A1PYMehQreLJCNJF54CDyqiCK0LUbCkgPkb5+MtcdBo\nDtoAAak9mhWKfL8Dv1xnz4aNG2HXLpgyxW5pNAMQM02eb2ykZv58xufk2C2OJoPpOdBDaH2IWHPM\n8oRrM45tsbYYnhIP7W+3c/TjoxRfWmy3uP3QBgiIp0iH8d6h97hm2jXDK8xgOPtsWLEC7roLVq5M\n222dOr5tB+nQRaXPR4dhnPpCh6PbRRIn6SLaFOX98hNDuORMyiH37FxyJ+dS8RcV+Mf68RZ78Y9z\nnlu2NkCkNkATCidwpOvI8AozWG66CR55xG4pNClYFwpxIBJhb08PU/PyKNSZazVpxlvqZdars1CG\nsno+LQax1hixFms9UOvrrcSPxpn6zFTE5UznF22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FeL+jg3WhEHvDYZYUFvK18nIuKipK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\nNBqNLWgDpNFoNBpb+P9iXd+FDST+lwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f03d588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LS0oBqr+/23JpcWa5YFiNy2VlpRQXF1f/NlPVh83V8tSpUxk0aFCTvV9TLmf3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9957b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def constant(mu=MU): return mu\n",
    "\n",
    "show(samples(constant))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting histogram looks different, but only because the starting distribution is so narrow and tall; the end distribution has a Gini coefficient of about 1/2 and standard deviation of about 100, just like we get from the other starting distributions.\n",
    "\n",
    "Here is one that statisticians call the [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) (with carefully chosen parameters):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.50  99.2    1   10   69  236  430\n",
      " 20,000 0.50  99.8    1   11   68  230  467\n",
      " 40,000 0.50 101.2    1   11   70  228  490\n",
      " 60,000 0.49  96.4    1   11   70  230  433\n",
      " 80,000 0.50  99.8    1   10   70  227  469\n",
      "100,000 0.50  98.6    1   10   69  232  459\n",
      "120,000 0.49  96.3    1   11   71  228  443\n",
      "140,000 0.50  99.3    1   11   69  232  447\n",
      "160,000 0.50 101.2    1   10   69  234  460\n",
      "180,000 0.50  98.6    1   10   69  235  444\n",
      "200,000 0.50  99.2    1   11   69  230  467\n"
     ]
    },
    {
     "data": {
      "image/png": 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Pe2t76V/Zj2enh2B3LBnpdrazWC7WT/DDoAwQkKhCckVWhTH3Ab3xxqiEYBvB\nv20URkMX091u7quu5stbt7Jp3jzN+x8t1LiIoacuzC4zZlds9uxr9tG3rI9AZ4Dh7cO0PNRCwacK\nyF4YcbvtezjHJ7jDNgDKAAE98SoWAVn2LPp9cYoF6U1JCfzpT5EkpGnmzvkoMhgM8nZfH690dfF0\nezt3jh2rt0iKE4At126h5z8H/nhZciLrQNZ8K7YSG/YxdmzFNp0kPDJqDYjEla2z7dn0+friv6gn\n998Pvb2waZOm3SpffwwtdBGWkgebmxm7YgU/bWyk1G5n/dy5/PeYMccvYApR4yKGkXQx641ZLJaL\nmf7P6eR/PB97hZ3WR1ppuLuBrddtZcP5G1g9ZTVr563VW9SEqBkQkCjOwG1z0zzQnFphksFiAZcL\nVq7UPBRboR0/a2zktl27+HlNDd9KM6OjSB9MdhO2chtu3FgLrfiafQTaAwiLIGNKBs7xTrZ/fTu2\nMhuuqS4KLjFOWZBRrwdkdIQQ8otflDzyyKGv/Xz5z2keaOYXF/wi9YIdiR/9CJYvh5df1lsSRQI8\noRDfr6/n101N+BYt0lscxUeIvvf6WHfGOgiDKcOEvdyOvdyOa7qLCb+ZoMl7pEs9IMOTKDmx2WTG\nFzTgRlSAbdvgoov0lkJxGJxmMy0+H59S+34UKWZw/SCEofTLpWRMzsBWZsNWasNekThTth6oNSAS\nG6D63noKMowzXT2ATZtgzhxNuzSSf1tvtNBFXzDIq93dXF9aevwC6YgaFzHSRRcFlxYw/oHxhP1h\nWh9rZfNVm/ngrA9YNWEVgxsH9RZvP2oGRGID5LA4CEkD5oIbHobt22HiRL0lURwGuxAszsnh+/X1\nPOl0plUROoWx8bX4aPlTC8GeIIHuAMGu6N/u2F+Ty4S91I6t1EbRVUX7Z0BGCstWa0BCyKuukjz1\n1KGvnfXYWdx2+m1cOP7C1At2OP79b7jzTlhr3OgWRYSwlNyxaxf3Nzbyn1mzOCc3V2+RFCcAfcv7\nWHf6uliDCZw1Tpw1Tix5FoRJ4JruYsyto5d1Xa0BaUSiGVCPp4dsuwF3rDc1QZq7dT4qmITgvpoa\n1g4M8NvmZlr9fq4qKkqbUgwKY5J9WjYLmhcQ6AgQ6Ang2e5h21e34dk+Ij+kGcb8vzFg4K2Cag2I\nxBlt3DY33Z7u1AqTDCefDOvXQ5+2e5TSxb+dCrTWxWNTpvBCZyef37yZ9kT1PwyKGhcxjKQLe5kd\n9yw3HX8ML/LuAAAgAElEQVTtYO/v9x7w2tyNc1kcXIwwG/tGR82AgP4EyQ56vb2MyTbg/o05c+DS\nS+Haa+GFF/SWRnEEnmxt5Z6GBi7IzeWlGTOwmdR9n+LYCfvDdP6jk96lvQTaA3Q83xHnpNTLdSwo\nAwRs3hy/XQiBwKB3EIWF0K3t7Ezl/IqhpS4CUtIZCPDazJlpaXzUuIihhy6klAR7gwQ6AwQ6A2z6\n9Cb8LX7yL8mn+LPFlN1YhrXQiq3QhiXfgsmSPmNMGSBg585D28IyTENvA+VZ5akXKBn27AH1w5AW\nfLG0lA8GB/n0pk08NGkSJ2dm6i2SIg0YWDvA2rmxQCNroRVHtQPXNBfBniClXy6l4OMG3SaSJMoA\nAUVFh7Y19TfhsrnIc+alXqBkcLlGZQ1I3e1G0FoX91ZXc++ePfy/nTt5a/ZszfpNBWpcxBgNXQxu\nHMSzw4O/xY9vrw//3shf7y7vAefNenMW7hluTd9bb5QBIn5CabvZjjfoRUppzIiliy+Gz38+UpZB\n1QUyPE6zGbMQlNiMm5lYkXr63utj3WmxcOqMyRm4Z7vJPSuXrDuyyJyXidlp4DC240TtAxJCLlgg\nWb78wPawDHPKH0/h1tNu5YrpV+gj3OFoaICqqogrTiW6NDT+cJjLN21im8fDyzNmMC5RBUTFR45A\nT4COv3YQ6Ajgb/fT8qcWwsOxCIJFoUX7K5saDbUPSCPiRcWahIn/mvBf1HXUpV6gIyElXHBBZA0o\nK0tvaRSHQUrJxqEh3uzt5bYxY5TxURyANddK2VfL9h8XXFLAps9s2l/RdKl5KXNWzMGSa9n/SKcg\ngyNx4nyS48CXIN/o7t7dlLhLUitMMoRCkTWg4mLQsLSzkfY46I0WupBSYlq6lLlr13JTWVnalmRQ\n4yLGaOsi9+xczug6g8LLCsEMmfMy2X7zdjZ8bAMrJ6zkbevb1IpaakUtw1uHR1WWVKBmQECioKQt\nnVu4ce6NqRUmGSwWePppOPtsCAYjxwrD0RMM4jSZ+FJJCT+pqdFbHEUaMe2v0/Y/l2FJyx9bqL+7\nHuc4J9lnZpN9RjbOiek/m1a/XMQ3QFJKTMLEoN84mWMPYMIEmD4dvvlN+M1vQINACRXpFEMLXWRb\nLEzNyGDLcHrfqapxESPVuhhYN0Dd5XWYXCZmvDKDzNknVgi/csEBXV2Htq1oWkHHUAdnVJ6ReoGS\nQQi47TZ48MFIbSCF4Xivr4+1g4O82dvL75oNWFlXYXhsxTaC/UFkUJ5wxgeUAQIgXmRssbuY4cAw\ndouxCjgdwHvvweWXw6RJmnSnfP0xtNDFGTk5rIrWbGrweo9wtnFR4yJGqnWx45YdmOwmKm+tTOn7\npgplgIC8OHtNi13F9Pn6CIUNWA9oH4WFiVN5KwzBcDhMvsXCLRUVeouiSEP63u3DkmtheMswrU+2\nEuhJr0S2R0KtARFZxz8Ys8mMlBKr2Zp6gZKloCBSnE4jlK8/hla6WJSTww3l5UxZtYrPFBXx85oa\nstIsaESNixha68K314ev2UdoIERoMLT/b3AgSGgwRPbp2fQs6WHPvXsAqPllDWO+mZ7RlPFIr2/C\nKBEvCMFhiVSv9Aa9+58bDpcLOjv1lkJxBO4ZN45rS0oYv3Il5+bmckW83E+KjyRbv7KVvnf6CA0c\n6mkxZ5nJmJRB/sfycU5ykjE5g9yzT6yChsoFl4B9sx9v0MC++yeegHPO0aw75euPobUu3GYzNiGo\n93oJpJnbVI2LGFrrYubLM1nYv5Az+s9g3pZ5TPvbNMq/Xo5rhotQf4iB1QO0PdlG/ffq6XmtB2ue\ngT0yx4CaARE/lZpE4gl4cFldqRcoGXbsgL//HVR0VVpQbLOxed48bti2jfcHBnh22rQjX6T4yGDJ\ntPDB1R8wXDeMc6KTjKkZFFxSgHOCM3I8IQNr/ollfEAZICB+NhuTMJHtyKbH20ORy4Auk+efhyuv\nhJwczbpUvv4Yo6GLaqeT2yoruWPXLs37Hk3UuIgxGroY2jTEru/sYmDVAAuaF2AvM3DkrcYoA0T8\nXHDeoJdB/6BxyzF87GNw4YWRPEL2j86ATWe8oRA3bNvGbZUnZkit4thoe7qNrpcimxFXVK3A5DBh\nLYoUmLOV2nDPcuM+2Y1rmgtroRWzy2zMDP3HgDJARFKrHUz7UDv5znwsJoOqaObMSGnuX/wC7rhD\nky5V3ZcYWuvind5ePrd5M6dkZvKl0lLN+k0FalzEGA1dVP+wmuofVgPR6qd9QQLtAQIdAXzNPgbX\nD9L8m2aGNw8T6AoggxJrvhWz20ygI0CwN4jZbWb+zvnYitKr3IdBf11TSzwDVN9bT4Y1w7j1gADO\nPx/eektvKRRHwBMK8XxHB4OhEM+rtR/FYRBCYM2xYs2xwsRIW9HlBy4BhLwhgl1B3qt4L3KNReCe\n7cbkTL+YMlUPSAh5882S3/zmwPZQOMT0303noY8/xMKxC/UR7nB0d8PEibBkSWQ2pDAkHwwOMnvN\nGiZnZPD18nJuLDdoiXdFWuHd42XF2BVkTM3AXmHHWmjFWhBx21kLreSek4uzZnSTlap6QBoRbwZk\nEia6hruMWY4BIlFwY8Yo42NwJjmdfLKggFe6uuiLt+NZoTgGHJUOTm08FX+rn0BHYP9jqG6I3Xfu\npuKbFYz/5Xi9xTwi6TdnGwXi/S4MBYYY8A8wIX9C6gVKhra2SCYEDVH7PWJopQuH2cwL06fz4+pq\nPhg0aGb1I6DGRQwj6cJWbIMQeLZ56H61m+bfNtPxtw4KryhkzG3pkS3hiAZICDFRCPGmEOLD6PFM\nIcSdoy9a6og3A3JYHITCIYb8Q6kXKBl+9zu47DK9pVAkyfm5uSzp7eUnDQ16i6JIc8LBMBsu2sA7\n7nfYev1WhjYPkXteLjNensEZ3Wcw7Zlp2EvSIzL2iGtAQoilwLeBP0gpT4q2fSilnJ4C+UYdIYS8\n5hrJo48e2O4Nesn+STa+OxOUS9Wbr30tkorn5z/XWxJFkjT7fExauZLt8+dTqkLnFceIDEuWmpeS\n97E8Zr6snwteizWgZFxwGVLKVQe1nVDO7P7+Q9vsZjtSSnxBgxqgm26CRx6Jv4lJYUhu2raN6S4X\nZqNGVSrSAn+7H3O2malPT9VblOMmGQPUKYSoASSAEOIyoGVUpUoxvjg2xhfyYTaZUy9MskyfHrGc\nGmbDNpJ/W2+01kVISv7Z1UXt7NkUxStAZWDUuIhhBF10/bML90w3lqz0jyFLxgDdBPwBmCyEaAa+\nCdyQTOdCiIeFEG1CiA0j2nKFEK8LIbYKIV4TQmSPeO0OIcR2IcRmIcT5I9rnCCE2CCG2CSEeGNFu\nE0I8E73mPSFE5YjXromev1UIcfXh5CwsPLStub+ZwoxC4xakEwJqauDZZ/WWRJEEZiFwmEz4P+Lb\nHhRHT7A/SP/qftqfbafhJw20P92OvdKgv0tHyRENkJRyl5TyXKAQmCylPENKWZ9k/38GLjio7Xbg\nP1LKScAS4A4AIcRU4HJgCnAR8KCI7QD9HXCdlHIiMFEIsa/P64BuKeUE4AHg/mhfucD3gVOA+cBd\nIw3dwcQLTlrfup6phQaf4ub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peBTGZPMXNtP2ZKSgmclpIu+CPMq+WkbhZYVYi6yYrMae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\nMo+vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3a13c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ak+5+OLAQmAAQ3PP++0B/YDhwm5mFckMaEREJVySFxcy6ACe6+z0A7l7j7tXA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11062c0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def beta(): return random.betavariate(0.9, 12)\n",
    "    \n",
    "show(samples(beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Surprise:** We can confirm that the starting population doesn't matter much. I thought it would make a real difference, but we showed that three very different starting populations&mdash;Gaussian, uniform, and beta&mdash;all ended up with very similar final populations; all with G around 1/2 and standard deviation around 100. The final distribution in all three cases looks similar to the normalized beta(0.9, 12) distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Effect of Transaction Function\n",
    "\n",
    "Does the transaction function have an effect on the outcome? So far we've only used the `random_split` transaction function; we'll now compare that to the `winner_take_all` function, in which the wealth from both actors is thrown into a pot, and one of them takes all of it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def winner_take_all(A, B): return random.choice(([A + B, 0], [0, A + B]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  19.7   55   74  100  125  145\n",
      " 20,000 0.89 282.9    0    0    0  374 1411\n",
      " 40,000 0.94 403.7    0    0    0  111 1946\n",
      " 60,000 0.96 473.6    0    0    0    0 2627\n",
      " 80,000 0.97 555.7    0    0    0    0 2986\n",
      "100,000 0.97 611.4    0    0    0    0 3485\n",
      "120,000 0.98 694.3    0    0    0    0 3592\n",
      "140,000 0.98 762.0    0    0    0    0 3670\n",
      "160,000 0.98 799.5    0    0    0    0 3603\n",
      "180,000 0.99 844.0    0    0    0    0 3603\n",
      "200,000 0.99 890.0    0    0    0    0 3677\n"
     ]
    },
    {
     "data": {
      "image/png": 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Zwvd37OC+PXtYcuAAL7W2kkmDVFzmkZUzXCebc+1719LT3MPIK0f2y0CU7f3Z\nn+KQMR00SQzMKymhvquLjW1tPNXYyJ6uLjZ3dHB2SQm3Tp7M1KKiqCOKvIb3Oj0He+je1/3qraGb\nnn09dDd0s/+R/bz54JvJKYz2YnYifaVpumNM07X19vLVrVv5aV0dt06axCfHjIkgnQwknbs72f2z\n3clT7wSn20k99U7qqXkS7Qlyh+aSNzyP3OHJr4duucNzKXtLGWVvKYv6I0kWU80oZMerGS1vauL9\n69axbsECyvJ0HIakh7uz4aMbOLjkIGM/PZbc0lxySnLIKc0htySXnNIcckpS7hfnqA4kkVLNqJ8t\nLC3l/SNH8qEXX6Q7kYgsR1zmkZXzxHjC2fdf+9jw0Q00/LGBBWsXUHVzFWOvH0vl1ZWsL1tP+VvL\nKV1QSvGMYgrGFpBbkptxA1Gm9OfxxCFnHDKmgwajPvj2aafRlUjwoRdf5Ac7dvDkgQM09vREHUuy\nQEt1C2vfvZbiM4qZv3I+ecO19y0Dk6bp+ri0e3dnJ7/du5f1ra2sbW1lb3c3y+fN09Sd9FmiO0HX\nri46tnfQuaOTzu2d7P39XsoWlXHa10+LOp7ICVHNKGQnc5yRu3PjK6/wQEMD/z5tGm8rLz+lU6lI\n9tv9q91s+tQmcstyKRxfSMH4AgrGFzDkjCFU/HVFxk27iRyPakYZwMy4fcoUvnHaadz4yiu8aeVK\nVjc3p/U94zKPrJyvl+hOUPulWuY8OIfzdpzHvKXzmH3fbKZ8awqV11S+4UCk/gxXHHLGIWM6aDA6\nBR8YOZI1Z53FFydM4LI1a7hvz56oI0kG6dzVSd1dday7Yh05JTmULdJSa5Fj0TRdSKcDWtXczLvW\nrGFGURFfnjSJC8v0i2eg6t7fzYEnDlBzfQ0FYwuo/Hglw98znMETB0cdTSQ0qhmFLMxz03UlEty3\nZw83bd7MX1VU8InKSmYU62JlA8mBJw7w4l+9SMlZJZRfXM7o/zWa3BKd6ESyj2pGGSx/0CA+VlnJ\n8vnzae/t5eIXXuC2bdtCee24zCMP5Jx7frOHlxa/xIyfzeCM/zqD8Z8ff8oD0UDuz3SIQ844ZEwH\nDUZpMKaggB9Mm8Y9M2fy6/p6egf43mc2c3c6tnew5749bPvmNsZcO4bh7xoedSyR2NE0XRovIZFw\n511r1zI2P587ZsxIy3tIdNZfuZ4Dfz7AoIJBDJk3hFEfHsXID43UyUllQFDNKGTpvp5RfVcXp69Y\nwT0zZ3LWzHxWAAAPR0lEQVTJsGFpex/pX+7O08VPs2D9AgZP0sIEGXhUM4qZivx8fjR1Ku9au5YP\nrFvHqpM8Hiku88jZlLP7YDf7/nsftV+uZeP/2sjay9eyauEqllYt5anBT5FblkvB2ILIc2YC5QxP\nHDKmg5b59IMPjhrFhWVl/Hz3bq7esIEXzjqL3EH6OyCT7fjeDrb84xZKFpRQek4pJfNLyK/MJ68i\nL3np7op8cgZrOk4kLJqm68fLjrs7i6qrOW/oUL42aZJOIZSh2mraeH7h88xfPV/HBokcg6bpYszM\n+M2sWTx54AA3vvJK1HHkKPY/tp+VZ66k8m8qNRCJ9CMNRv2ssqCAn0yfzv0NDZzIHllc5pHjnLOz\nrpOaz9Qw+WuTmfKtKf0f6iji3J+ZKA4545AxHVQzisCc4mKKBg3ifw4eZFF5edRxBix3p+X5Fvb8\ndg9NS5toeb6F8V8cz7jPjIs6msiAo5pRP9aMUn1r+3Y2tbXx4+nT+/29BbzX2XTdJvbet5exN4xl\n6FuGUrKghLwyXZ9KpC/CrhlpzygiEwsLebaxMeoYA1Lr+lZWX7iawvGFnPnsmRTP0vkDRaKmmlFE\nZhYV8cSBA2zv6OjT8+Myj5zJORPdCV647AVWLVjFtnds46zVZ2X8QJTJ/ZlKOcMTh4zpoD2jiIzI\ny6MtkaB7gE+TpktvR2/y0t7bkpf37tjWwYHHD9C5q5PzG87n6eVPRx1RRFKoZhRRzQjg0hde4MZx\n43j7cJ1Y81QlehLU313PwScP0vx8M+2vtFMwpoCCCQXJy3xPKKB4djEjrxzJoDxNCIicKtWMskRT\nTw/Lm5qYqesdnZREd4LWNa00PddE03NNHHz6IIMnDabiYxWM+/w4imcVMyhfg45IXOinNSK5ZnS5\n09zT06fnx2UeOV05PeG0rGth2ze3sXrRap4pf4aXFr9ES3ULZYvKmPPQHN70xJsY/YnRlMwtOe5A\nNND7M2zKGZ44ZEwH7RlFZFNbGxX5+UwtKoo6Skbr3JU8EPXgkwfJHZpL+aXlTPiHCQy9YCi5pfrv\nK5ItVDOKqGb0xIED/GttLUvOPLPf3zsO2l5uY/MXN3PgTwcY97lxjPm7MRSMSe8ZskWk71QzyhIV\n+fns6OyMOkZk3J3uvd10bOmgfUs7HVs6krfa5NfOXZ1M/OeJTL9jOnnlOhBVJNupZhSRpp4ehuf1\n/ZdsXOaRj8zp7ux/fD/bv72dmk/XsObda1g+ezlPD3ma5bOWU3NDDQ1/aKDnQA9DzhzCuBvHMeeh\nOZy/73wmfHFC2gaiuPZnplLO8MQhYzpozygiG9vaqCosjDpG2vS09NDwhwZ2/3w3XXu6KL+knMFT\nBlP+tnIKJxVSOLFQNR8ROUw1owhqRr/Zs4frN23iP2bNyspLkdf9vI5X/uEVhp43lFF/NYqRHxip\nZdYiWSbsmpEGo34ejHrdKXvmGZ4980zOGDKk3943Xdydrt1dtFS30LK6hX0P7aNjSwdv+tObKJ6t\nY6hEspUurhdz2zs6KMvNPeGBKFPmkXuaejjw5wNs/dpW1l6xlqVjlrJizgq2f2s73fu62X75ds7Z\ndk7GD0SZ0p/Ho5zhikPOOGRMB03a97OdXV0My41Xt3fv66bhgQZ2/XAXrRtaGTJ3CKVnl1Lx0Qqm\nfm8qBRMKDl9CfceSHTrdjoicME3T9eM0XU8iwTnPP8/iykpuGJeZF3DzhNNe007TiiaalzfTtLSJ\ntk1tlC0qY8y1Yyh/a7kGGxHRcUZxduu2bZTn5XH92LFRRwGS9Z7OnZ00r2hODjwrmmhe2UxeeR4l\nC0ooWVjCaVeeRunZpVqAICJppd8w/eShhgZ+tns3d06ffnhK60SEMY+c6EnQ+FwjW28N6j1jl7Lq\nzFXU3VGHFRjjbxzP2ZvO5pwt5zD7vtlM+MIEyi4oO6GBKC7z3coZLuUMTxwypoP2jPrB1o4O/nbT\nJn41cyYT+unYokRXgraNbbSuaaX5+WaaVzbTsrqFwkmFlF1URsVHK5jy3SkUVhWe1OAoIhIm1YzM\n3N/xDpg4MXmbNAnOPhsmTAjl9Te0tvKONWv4wvjxaakTuTud2zppXd9K69pWWta00Lq2lfaadgon\nFlI8p5gh84ZQclYJJfNKyBumU+uIyKnTcUYhMzP3Bx+E2lrYsgU2b4ZnnoExY+AHP4ALLjip113T\n0sL3d+7kD3v38n9PO42Pjx59ylm7D3TTvLw5OfAEt7YX28gZkkPx7GKKzyhmyBlDKJ5TTNHMInIG\n55zye4qIHI0GoxNkZm8HvkOyPnanu992xPdfv5qutxceegg++Ul44YXkwNQHve48ceAAP6mr49nG\nRq4bM4a/GzOGkfn5J5Xd3emo7aB5RTOP//Zxqp6sYsicIRSfXkzx6cUUzS6ieHZxRp1IdMmSJSxa\ntCjqGMelnOFSzvDEISNoNd0JMbNBwA+AtwK7gBVmdr+7v/SGG+bkwBVXwLJlcMst8NOfHve91rS0\ncM1LL2HANZWV3DVjBsU5J7Zn0lkXrGxb2Xz4q+UZJQtK2Ni9kff95X0UTcvs6x9VV1fH4gdJOcOl\nnOGJQ8Z0yOrBCFgI1Lj7VgAzuxe4AnjjweiQz34Wpk1LTtcVHP1aOm29vXx7+3a+u3Mn35g8mcWV\nlcdcEJDoTtC5vZOOrR2HL5nQvqWdjs0dtG9ux7s8uaR6QQljPjWGkgUlh6/h8/t/+X3GD0QABw8e\njDpCnyhnuJQzPHHImA7ZPhiNBbanPN5BcoB6jbfecTnTK6uYPKyKqqFVzB8zn8nlk6GiAqqqYN06\nmD+fvV1dPNXYyJb2drZ0dLClo4NVzc1cUFzKiolnUNGWS8vzLXTv76ZzWzDo1L5666rvIr8yn8KJ\nhRRWFVI4uZBhlwyjcHIhhZMKKRhboJVtIjIgZftg1Cdr7/4b/iexlcKKrRRULKVn9A1Mr6zit1f+\nlqqqKti5k5+MHs1Nmzfzb7cOYtIemN0MBc0JcpoSeNs+dgxtZHdZLrllueSW51IwvoDCiYWUXVyW\nHHwmJgebkz17QW1tbbgfOk2UM1zKGa445IxDxnTI6gUMZnYO8C/u/vbg8U2Apy5iMLPs7QARkTTS\naro+MrMcYCPJBQx1wHLgr9x9Q6TBRETkNbJ6ms7de83sBuAxXl3arYFIRCTDZPWekYiIxMOAPlGq\nmb3dzF4ys01m9sUMyFNrZi+Y2WozWx60lZvZY2a20cweNbOhKc+/2cxqzGyDmV2axlx3mlm9ma1J\naTvhXGY2z8zWBP39nX7IeIuZ7TCz54Pb26PMGLz+ODN7wszWm9laM/tM0J5p/Xlkzk8H7RnVp2ZW\nYGbLgp+ZtWZ2S9CeMf35Bhkzqi9T3mNQkOeB4HH/9KW7D8gbyYH4ZaAKyAOqgRkRZ9oMlB/Rdhvw\nv4P7XwS+HtyfBawmOdU6MfgslqZcbwbmAmtOJRewDFgQ3H8YuCzNGW8BbjzKc2dGkTF4zUpgbnB/\nCMma5owM7M9j5czEPi0KvuYAz5E8fCPT+vNoGTOuL4PX/XvgV8ADweN+6cuBvGd0+IBYd+8GDh0Q\nGyXj9XurVwC/CO7/AnhvcP9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3a1518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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srCz75trTKYtAWQTKIjAz3N12vWTDNEW7zJKfak8Dlye3hwBP5YxfZGZ7mdlB\nwCHAK0lLbaOZ9U8OBLgsZx2pg/7xBMoiUBaBsogvarvMzB4FTgG6mtkKMnsmdwL/Y2Y/IrOXcgGA\nuy82syeAxUAVcJ2H3ayhwESgLTDd3WfGnLeIiDSO2EeXXezu+7v73u5e7O4PunuFu3/X3Q9399Pc\nfUPO8ne4+yHu3sfdZ+eMv+ruX3f3Q939xphzTpPczyP2dMoiUBaBsohP3/gXEZFoVGRSTP3mQFkE\nyiJQFvGpyIiISDQqMimmfnOgLAJlESiL+FRkREQkGhWZFFO/OVAWgbIIlEV8KjIiIhKNikyKqd8c\nKItAWQTKIj4VGRERiUZFJsXUbw6URaAsAmURn4qMiIhEoyKTYuo3B8oiUBaBsohPRUZERKJRkUkx\n9ZsDZREoi0BZxKciIyIi0ajIpJj6zYGyCJRFoCziU5EREZFoVGRSTP3mQFkEyiJQFvGpyIiISDQq\nMimmfnOgLAJlESiL+FRkREQkGhWZFFO/OVAWgbIIlEV8KjIiIhKNikyKqd8cKItAWQTKIj4VGRER\niUZFJsXUbw6URaAsAmURn4qMiIhEoyKTYuo3B8oiUBaBsohPRUZERKJRkUkx9ZsDZREoi0BZxKci\nIyIi0ajIpJj6zYGyCJRFoCziU5EREZFoVGRSTP3mQFkEyiJQFvGpyIiISDQtqsiY2elm9o6ZLTWz\nW5p7PvlO/eZAWQTKIlAW8bWYImNmBcB/AQOAI4Hvm9kRzTur/LZw4cLmnkLeUBaBsgiURXwtpsgA\n/YFl7r7c3auAx4HBzTynvLZhw4bmnkLeUBaBsgiURXwtqcj0BD7Mub8yGRMRkTzVurknEMNHL5fV\n+bht3cZd999FxRcVu9zW+8vep/ehvXd7meZY7oXZL1C+oZziomJuG3HbLreXZuXl5c09hbyhLAJl\nEZ+5e3PPoV7M7P8AY9z99OT+cMDdfdxOy7WMFyQikmfc3Rp7my2pyLQC3gW+A6wGXgG+7+5LmnVi\nIiJSqxbTLnP3bWb278BsMp8l/V4FRkQkv7WYPRkREWl5WtLRZXXaU76oaWblZvaGmb1uZq8kY4Vm\nNtvM3jWzWWbWKWf5EWa2zMyWmNlpOePHmNmiJK8JzfFaGsrMfm9ma81sUc5Yo712M9vLzB5P1nnJ\nzIqb7tU1TC1ZjDazlWb2WvJzes5jqczCzHqZ2Vwze9vM3jSzG5LxPe59UUMW1yfjzfu+cPcW/0Om\nWL4HHAgIhdf1AAAE0klEQVS0ARYCRzT3vCK91veBwp3GxgE3J7dvAe5MbvcFXifTFi1JMqree/0b\n8K3k9nRgQHO/tnq89hOBo4FFMV47cC1wb3L7QuDx5n7NDcxiNDCshmX7pDULoAdwdHK7PZnPbY/Y\nE98XdWTRrO+LtOzJ7Elf1DS+ugc6GJiU3J4EnJXcHkTmTbDV3cuBZUB/M+sBdHD3+clyk3PWyVvu\n/gKw83Hnjfnac7f1RzIHmeSlWrKAzPtjZ4NJaRbuvsbdFya3PwOWAL3YA98XtWRR/V3CZntfpKXI\n7Elf1HRgjpnNN7Mrk7Eid18LmTca0D0Z3zmXVclYTzIZVWvJeXVvxNeeXcfdtwEbzKxLvKlH8e9m\nttDMfpfTItojsjCzEjJ7dy/TuP8mWnIWf0uGmu19kZYisycpdfdjgDOAoWZ2EpnCk2tPPpqjMV97\no39nILJ7gd7ufjSwBvhlI247r7Mws/Zk/rK+MfkrPua/iZaWRbO+L9JSZFYBuR9A9UrGUsfdVyf/\nXQdMJdMqXGtmRQDJru7HyeKrgANyVq/OpbbxlqgxX3v2Mct8L6uju6+PN/XG5e7rPGmWA78l896A\nlGdhZq3J/FJ9yN2fSob3yPdFTVk09/siLUVmPnCImR1oZnsBFwFPN/OcGp2ZtUv+SsHM9gVOA94k\n81ovTxYbAlT/Q3sauCg5IuQg4BDglaR9sNHM+puZAZflrJPvjB3/emrM1/50sg2A84G50V5F49gh\ni+SXabVzgLeS22nP4gFgsbvfnTO2p74vvpJFs78vmvuIiEY8suJ0MkdTLAOGN/d8Ir3Gg8gcOfc6\nmeIyPBnvAvwlef2zgc4564wgc9TIEuC0nPFjk20sA+5u7tdWz9f/KPARsAVYAfwQKGys1w7sDTyR\njL8MlDT3a25gFpOBRcl7ZCqZzyVSnQVQCmzL+XfxWvK7oNH+TaQgi2Z9X+jLmCIiEk1a2mUiIpKH\nVGRERCQaFRkREYlGRUZERKJRkRERkWhUZEREJBoVGZFmYmYPmtk5ye0bzaxtzmObm29mIo1HRUYk\nP9wE7JtzX19gk1RQkRGpJzP7sWUuAY6Z3WVmzyS3TzWzh83se2b2opktMLM/mFm75PFbzexvyUWg\n7q9hu9cD+wNzq7eZGbafJ2fOfdHMujXRyxRpVCoyIvX3PHBScvtYYN/kJIEnkTltx0+B77j7N4FX\ngf+bLHuPux/n7kcB7czsX3M36u73kDlFzCnuXn19jn2BFz1z5tzngasivi6RaFRkROrvVeBYM+tA\n5pxhLwHfIlNk/kHmqovzzOx1MicVrD4z+HfM7GXLXCr5VODIWrafe+LPLe4+Ped5SxrzhYg0ldbN\nPQGRlsLdt5pZOZmz+84js/dyKnAwmctiz3b3H+SuY2Z7A78BjnH3j8xsNNCWXavKub0N/VuVFkp7\nMiIN8zzwY+CvwAvANWTOePs3oNTMDobsZRkOJVNQHPg0uUzDebVsdxPQMed+Xl8YS6S+VGREGuZ5\noAfwkrt/TKZN9ld3/4TMHs5jZvYG8CJwuLtvBH4HvA3MAF7J2VbuEWS/BWbmfPCvo8skFXSqfxER\niUZ7MiIiEo2KjIiIRKMiIyIi0ajIiIhINCoyIiISjYqMiIhEoyIjIiLRqMiIiEg0/x/I1eGeYja6\nQgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11024cd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population, transaction=winner_take_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the results look **very** different: most of the wealth goes to the 99th percentile (purple line on the far right of  the plot), with everybody else getting wiped out (although the 90th percentile holds out until around 50,000 transactions). The Gini coefficient is all the way up to 0.99 and the standard deviation is over 800, and still rising.\n",
    "\n",
    "That makes sense: any time two actors with non-zero wealth interact, one of them will end up with zero&mdash;the number of actors with zero wealth increases monotonically until all the wealth is with one actor, and from then on the wealth just gets swapped around.\n",
    "\n",
    "At the other end of the spectrum, let's try a transaction function, `redistribute`, that taxes both parties 31% (the average income tax rate in the US) and splits that tax revenue evenly among the two parties; the non-taxed part is split with `random_split`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def redistribute(A, B, rate=0.31):\n",
    "    \"Tax both parties at rate; split the tax revenue evenly, and randomly split the rest.\"\n",
    "    tax = rate * (A + B)\n",
    "    Arand, Brand = random_split(A + B - tax, 0)\n",
    "    return tax / 2 + Arand, tax / 2 + Brand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  19.7   55   74  100  125  145\n",
      " 20,000 0.33  60.2   17   36   86  182  288\n",
      " 40,000 0.33  62.2   17   35   86  186  302\n",
      " 60,000 0.33  60.7   17   35   87  185  289\n",
      " 80,000 0.33  61.8   17   35   86  183  291\n",
      "100,000 0.33  61.0   18   35   85  182  293\n",
      "120,000 0.33  61.1   17   34   87  185  288\n",
      "140,000 0.33  60.8   17   35   86  183  295\n",
      "160,000 0.33  61.4   16   34   86  185  297\n",
      "180,000 0.33  61.4   17   36   86  184  292\n",
      "200,000 0.33  61.9   18   34   85  187  288\n"
     ]
    },
    {
     "data": {
      "image/png": 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F7L1wLztX7KTw1EI6t2hHrkTN084Jsqr2kUQZIAO8/LJWdSbVwBae4MBgYkNi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\n/3ltgOzqq+HgQVr7UT11MOiKRvmws5PqYJCDweAZj03hMEV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11186d470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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q13g5lvLycsqib9mSkhIGDRrU8OHVT34VYnnC5AnMf3M+AL379gagZlXNXssb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\nIiIieVMxERGRvKmYiIhI3v4/0BVJuawHhpMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11185d2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population, transaction=redistribute)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Another surprise:** This transaction function does indeed lead to less inequality than `split_randomly` or `winner_take_all`, but surpprisingly (to me) it still increases inequality compared to the initial (Gaussian) population.\n",
    "\n",
    "Here's one more interaction function, `status_quo`, in which both actors keep half of their wealth out of the transaction, and the other half is randomly split using a triangular distribution in such a way that the most likely outcome is that each actor keeps what they started with, but from there probability falls off on either side, making larger and larger deviations from the status quo less and less likely:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def status_quo(A, B):\n",
    "    \"A transaction that is most likely to leave things unchanged, but could move any amount of wealth around.\"\n",
    "    a = random.triangular(0, (A + B) / 2, A / 2)\n",
    "    return (A / 2 + a), (A + B) - (A / 2 + a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  19.7   55   74  100  125  145\n",
      " 20,000 0.21  38.5   33   55   95  151  209\n",
      " 40,000 0.22  40.3   31   53   94  154  219\n",
      " 60,000 0.22  40.3   31   53   94  154  214\n",
      " 80,000 0.23  41.0   31   52   94  155  220\n",
      "100,000 0.23  40.8   30   52   94  156  216\n",
      "120,000 0.23  40.9   31   53   94  154  220\n",
      "140,000 0.23  41.3   31   52   95  153  223\n",
      "160,000 0.22  40.5   32   53   95  153  213\n",
      "180,000 0.22  40.3   32   53   94  155  213\n",
      "200,000 0.23  40.9   32   52   94  156  216\n"
     ]
    },
    {
     "data": {
      "image/png": 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cnBEezsb6erYNoDNB7l4X4aeFM61wGjPqZjD+q/H4D/Fn3bB17LhkB22VbW6V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\nscB/AHeKyBVYQclXJM9SieRrfwYYbIzJAY4AT9pcnqARkST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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1101ef7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NY9GJdHO5+xh37+XuBwPDgRfdfQTwJFAaNbsEmB49fwIYbma7mVlvoA8wezvH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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bfa39e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population, transaction=status_quo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `status_quo` transaction increases inequality from the initial population, but not as much as the other transaction functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Effect of Interaction Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have been using `anyone` as our interaction function: anyone can enter into a transaction with anyone else. Suppose that transactions are constrained to be *local*&mdash;that you can only do business with your close neighbors.  Will that make income more equitable, because there will be no large, global conglomorates?  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def neighborhood(n, width=5): \n",
    "    \"Choose two agents in the same neighborhood\"\n",
    "    i = random.randrange(n - width)\n",
    "    return random.sample(range(i, i + width + 1), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  19.7   55   74  100  125  145\n",
      " 20,000 0.48  93.2    1   11   72  224  415\n",
      " 40,000 0.48  93.6    1   11   71  227  423\n",
      " 60,000 0.49  95.7    1   11   72  225  432\n",
      " 80,000 0.49  96.2    1   11   71  226  442\n",
      "100,000 0.49  95.4    1   12   71  229  430\n",
      "120,000 0.49  96.0    1   10   70  229  432\n",
      "140,000 0.50  97.5    1   11   70  235  430\n",
      "160,000 0.50  97.5    1   11   70  234  448\n",
      "180,000 0.50  98.3    1   11   71  232  453\n",
      "200,000 0.49  96.5    1   11   71  229  442\n"
     ]
    },
    {
     "data": {
      "image/png": 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zkjI1hWn/nqazwoGj9gENIUIIvAEvVpNBa3dNnw5/+UtoE5PDobcaRQxcfj+v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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ad918d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f01d978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population, interaction=neighborhood)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Surprise:** The `neighborhood` interaction is not too different from the `anyone` interaction.  \n",
    "\n",
    "Let's get even more local, allowing trade only with your immediate neighbor (to either side):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  19.7   55   74  100  125  145\n",
      " 20,000 0.45  84.0    1   13   79  217  364\n",
      " 40,000 0.47  90.1    1   11   75  223  399\n",
      " 60,000 0.47  90.8    1   12   74  226  401\n",
      " 80,000 0.49  94.9    1   11   72  229  437\n",
      "100,000 0.48  93.0    1   12   73  222  431\n",
      "120,000 0.48  93.0    1   12   73  228  424\n",
      "140,000 0.48  93.3    1   10   73  228  421\n",
      "160,000 0.48  94.2    1   11   72  226  430\n",
      "180,000 0.49  93.2    1   11   72  231  416\n",
      "200,000 0.48  92.7    1   11   72  225  412\n"
     ]
    },
    {
     "data": {
      "image/png": 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mxnuBO0VYMTE2lgtSU8mLiqLWbCbXaAy2JEUYceS1I+y5dM9XxpLOTiLjvzIY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\n6u0N5t7jHhgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f63c320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yyvfYhMcYecfIOvv9avR9fHHU2Dr7vTltOv81urjG1/a9OdZjjw1n5MiZda4z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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f43acc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def adjacent(n): return neighborhood(n, 1)\n",
    "    \n",
    "show(population, interaction=adjacent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is still surprising that we still have no efect from restricting trade."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# United States Distribution\n",
    "\n",
    "We've drawn from mathematical distributions; let's look at the actual distribution of family income in the United States. Each row in the following table is a tuple giving the lower bound and upper bound (in thousands of dollars of income), followed by the cumulative percentage of families in the row or a previous row. The table I got this from actually had \"\\$250,000 or above\" as the final row; I had to cut it off somewhere, and arbitrarily chose \\$300,000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "USA_table = [  \n",
    "  (0,    10,  7.63),\n",
    "  (10,   20, 19.20),\n",
    "  (20,   30, 30.50),\n",
    "  (30,   40, 41.08),\n",
    "  (40,   50, 49.95),\n",
    "  (50,   60, 57.73),\n",
    "  (60,   70, 64.56),\n",
    "  (70,   80, 70.39),\n",
    "  (80,   90, 75.02),\n",
    "  (90,  100, 79.02),\n",
    "  (100, 110, 82.57),\n",
    "  (110, 120, 85.29),\n",
    "  (120, 130, 87.60),\n",
    "  (130, 140, 89.36),\n",
    "  (140, 150, 90.95),\n",
    "  (150, 160, 92.52),\n",
    "  (160, 170, 93.60),\n",
    "  (170, 180, 94.55),\n",
    "  (180, 190, 95.23),\n",
    "  (190, 200, 95.80),\n",
    "  (200, 250, 97.70),\n",
    "  (250, 300, 100.0)]\n",
    "\n",
    "def USA():\n",
    "    \"Sample from the USA distribution.\"\n",
    "    p = random.uniform(0, 100)\n",
    "    for (lo, hi, cum_pct) in USA_table:\n",
    "        if p <= cum_pct:\n",
    "            return random.uniform(lo, hi) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let's see what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S32FpujS2UNoDqDZdEtJ+27aN3dqX2nRtv23bxk73++5p+a2tKznrrCYAGhqKP197e6Hi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\nU1YD2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2ab048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(samples(USA), label='USA')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hey&mdash;that looks like the beta distribution. Let's compare:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2C0ZrM6tWOWVlo7Jua9x0mUhk368QpdplQ6X88VL+sMV9n4mIiGwFVEwKTCJR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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2af828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(samples(beta), label='beta')\n",
    "hist(samples(USA), label='USA')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.46  89.5    2   17   74  219  422\n",
      " 20,000 0.50 100.0    1   11   69  227  478\n",
      " 40,000 0.50  99.9    1   11   69  229  463\n",
      " 60,000 0.50 101.5    1   11   68  232  465\n",
      " 80,000 0.50  99.7    1   11   69  230  463\n",
      "100,000 0.50 101.0    1   10   70  228  472\n",
      "120,000 0.50 100.0    1   11   68  236  448\n",
      "140,000 0.50 100.7    1   10   70  233  479\n",
      "160,000 0.50 100.7    1   11   69  228  455\n",
      "180,000 0.50 100.3    1   10   69  233  457\n",
      "200,000 0.50 100.3    1   11   69  228  468\n"
     ]
    },
    {
     "data": {
      "image/png": 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Tz9RfZVa1XbUGRLSw6Ml0+bqwGC3oMlv40qXRYnQvvpjUbpWvP06qdHFHSQmfLCykORjk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\ntAAppZRyxP8HSNlZa3IhPRsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f723240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lVTsDa8SIEQwfPpwDDzyQP/zhD5u0efPNN2PfTKuQJ5ZWVFQwadIkgLqxoVwU/Ax4M0sB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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111b6a5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(samples(USA))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The USA distribution is indeed similar to the beta(0.9, 12) distribution, and to the stationary ending distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
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    "# A Mathematician, a Statistician, and a Programmer walk into a problem ..."
   ]
  },
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    "In 2013, mathematician George Andrew's editorial *[Drowning in the Data Deluge](http://www.ams.org/notices/201207/rtx120700933p.pdf)* complains of an \"overblown enthusiasm for data analysis.\" The tone was that this new fad for \"big data\" was taking away from traditional mathematics.\n",
    "\n",
    "Two Stanford professors, mathematician Persi Diaconis and \n",
    "statistician Susan Holmes, were more accepting of new ideas. The three of us got to discussing Andrew's editorial and the differences between mathematical, statistical, and computational thinking. At the time, I had just heard about the economics problem covered in this notebook, and I suggested the three of us work on it, and compare approaches and results.\n",
    "In the end, all three of us found similar results, in that we all identified the shape of the final distribution. But there were differences in how we got there:\n",
    "\n",
    "**Mathematical thinking** (Persi):\n",
    "\n",
    "- **Tool:** Paper and pencil.\n",
    "- **Notes:** The process can be modeled by a Markov chain, using the same techniques as in [this paper](http://statweb.stanford.edu/~cgates/PERSI/papers/kac10.pdf). In the limit, there is a difference between the continuous case (where money is a real number, and the distribution is stationary), and the discrete case (where money comes in integer amounts and the distribution is not ergodic as there is an absorbing state). \n",
    "\n",
    "**Statistical thinking** (Susan):\n",
    "\n",
    "- **Tool:** Simulation in `R`, with N=10 actors for T=1,000 transactions.\n",
    "- **Notes**: this is extremely similar to what happens for random genetic drift in generations, that also gives clumping (and extinction of some of the alleles).\n",
    "\n",
    "**Computational thinking** (Peter):\n",
    "\n",
    "- **Tool:** Simulation in `IPython`, with N=5000 actors for T=200,000 transactions.\n",
    "- **Notes**: Results are very similar to Susan's, but with more variations explored and more pretty pictures."
   ]
  }
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