{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# CS579: Lecture 09 \n", "\n", "**Cascades II**\n", "\n", "*[Dr. Aron Culotta](http://cs.iit.edu/~culotta)* \n", "*[Illinois Institute of Technology](http://iit.edu)*\n", "\n", "With some figures from [Networks and Markets: Reasoning about a highly connected world](http://www.cs.cornell.edu/home/kleinber/networks-book/), David Easley and Jon Kleinberg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Last time...**\n", "- We defined cascades as happening when others' decisions dominate personal evidence\n", "- Surprising cascades can occur even assuming rationality.\n", "- Cascades can lead to sub-optimal outcomes.\n", "- Cascades are fragile\n", "\n", "This made several assumptions:\n", "



\n", "- rationality\n", "- everyone can observe everyone else's actions\n", "- everyone's actions have equal influence\n", "- everyone has same utility function (e.g., we all win the same if we guess the number of marbles in the urn)\n", "- my utility is independent of yours" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Today:**\n", "\n", "- Assume people make decisions in a social network\n", " - I can only view the actions of my neighbors\n", "- My utility is influenced by your decision" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Game-theoretic Diffusion Model\n", "\n", "Consider the following scenario:\n", "- Each node must choose between two possible behaviors $A$ and $B$\n", " - E.g., $A$= join Facebook; $B$= join MySpace\n", "- If nodes $v$ and $w$ are linked by an edge, they are incentivized to have same behavior\n", "- Payoff matrix:\n", "\n", "\n", "\n", "\n", "\n", "\n", "
      $w$
$v$$A$$B$
$A$a,a 0,0
$B$0,0 b,b
\n", "\n", "- Both do $A$: both get reward $a$.\n", "- Both do $B$: both get reward $b$.\n", "- Do opposite: both get reward $0$.\n", " \n", "**Each node plays this game with all neighbors.**\n", "\n", "- Payoff for a node is sum over all neighbors." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Suppose some of $v$'s neighbors choose $A$ and some choose $B$ \n", "**Which should $v$ choose?**\n", "\n", "




\n", "- E.g., if $a$ > $b$, then really I'd like to join Facebook\n", "- But, if most of my friends are on MySpace, then I should join MySpace instead.\n", "- This tradeoff is determined by difference in utility ($a-b$) and the proportion of my friends using MySpace\n", "\n", "\n", "



\n", "- Suppose fraction $p$ of $v$'s neighbors choose $A$; $1-p$ choose $B$.\n", "- Let $d$ be the number of neighbors of $v$.\n", "- Then, $pd$ choose $A$ and $(1-p)d$ choose $B$\n", "- If $v$ chooses $A$, payoff=?\n", "- If $v$ chooses $B$, payoff=?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Suppose some of $v$'s neighbors choose $A$ and some choose $B$ \n", "**Which should $v$ choose?**\n", "\n", "- Suppose fraction $p$ of $v$'s neighbors choose $A$; $1-p$ choose $B$.\n", "- Let $d$ be the number of neighbors of $v$.\n", "- Then, $pd$ choose $A$ and $(1-p)d$ choose $B$\n", "- If $v$ chooses $A$, payoff=$\\mathbf{pda}$\n", "- If $v$ chooses $B$, payoff=$\\mathbf{(1-p)db}$\n", "- $A$ should be chosen iff\n", "\n", "$$\n", "pda \\ge (1-p)db\n", "$$\n", "\n", "equivalently\n", "\n", "$$\n", "p \\ge \\frac{b}{a+b}\n", "$$\n", "\n", "Let $q=\\frac{b}{a+b}$\n", "\n", "- Small $q \\rightarrow$ $A$ much more appealing; only need a few neighbors choosing $A$ to choose $A$.\n", "- Large $q \\rightarrow$ $B$ much more appealing; need many neighbors choosing $A$ to choose $A$.\n", "- We'll arbitrarily break ties by choosing $A$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "E.g., \n", "- if utility of Facebook is 6 and utility of MySpace is 4\n", "- if 8 of my 10 friends are on MySpace, which should I join?\n", "\n", "$q = \\frac{b}{a+b} = \\frac{4}{10}$\n", "\n", "$p = \\frac{2}{10}$\n", "\n", "if $p \\ge q$, choose Facebook\n", "- but, $\\frac{2}{10} < \\frac{4}{10}$, so stick with MySpace\n", "\n", "How many of my friends have to switch to Facebook before I will switch?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "These decisions are made in a network, which means that order matters.\n", "\n", "What if half my friends switch to Facebook?\n", "\n", "When does this stop?\n", "\n", "


\n", "\n", "# What are states of equilibria?\n", "\n", "



\n", "\n", "- All adopt $A$\n", "- All adopt $B$\n", "- Some adopt $A$ and some adopt $B$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Simulation\n", "\n", "- Assume all nodes select $B$ at time $0$\n", "- Select some nodes to adopt $A$ (\"initial adopters\")\n", "- What is resulting equilibria?\n", " - All adopt $A$?\n", " - Some adopt $A$?\n", " - Assume we cannot switch back from $A$ to $B$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import networkx as nx\n", "graph = nx.Graph()\n", "graph.add_edges_from([('v', 'w'), ('v', 'r'), ('v', 't'),\n", " ('w', 'r'), ('w', 's'), ('w', 'u'),\n", " ('w', 't'), ('r', 's'), ('t', 'u'), ('s', 'u')])\n", "# Initialize every node to choice 'B'\n", "nx.set_node_attributes(graph, 'choice', 'B')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'r': {'choice': 'B'},\n", " 's': {'choice': 'B'},\n", " 't': {'choice': 'B'},\n", " 'u': {'choice': 'B'},\n", " 'v': {'choice': 'B'},\n", " 'w': {'choice': 'B'}}" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph.node" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "layout = nx.spring_layout(graph)\n", "def draw_graph(graph):\n", " plt.figure()\n", " nodes = graph.nodes()\n", " colors = ['r' if graph.node[n]['choice'] == 'A' else 'b'\n", " for n in graph]\n", " plt.axis('off')\n", " nx.draw_networkx(graph, nodelist=nodes, with_labels=True,\n", " width=1, node_color=colors,alpha=.5,\n", " pos=layout) \n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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F4OFeIGHRzjQqrLe9I7ICficVNIIXkVnYG/8D4VxaZ+ZiW0dfFLuQNPJwL5zTga0V0K/c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\nevwcLjkKwzZiB6T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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make v, w \"early adopters\"\n", "graph.node['w']['choice'] = 'A'\n", "graph.node['v']['choice'] = 'A'\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "['v', 'w', 'r', 't', 's', 'u']" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[v for v in graph]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def simulate(graph, a, b, verbose=False):\n", " \"\"\" For each node, set new choice based on payoffs a/b and\n", " choices of neighbors. \"\"\"\n", " for v in graph:\n", " if graph.node[v]['choice'] == 'B': # see if v wants to switch to action 'A'\n", " a_neighbors = [w for w in graph.neighbors(v)\n", " if graph.node[w]['choice'] == 'A']\n", " b_neighbors = [w for w in graph.neighbors(v)\n", " if graph.node[w]['choice'] == 'B']\n", " p = len(a_neighbors) / (len(a_neighbors) + len(b_neighbors))\n", " q = b / (a + b)\n", " if verbose:\n", " print('node %s p=%.3f q=%.3f' % (v, p, q))\n", " if p >= q:\n", " graph.node[v]['choice'] = 'A'\n", " else:\n", " graph.node[v]['choice'] = 'B'" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "node r p=0.667 q=0.400\n", "node t p=0.667 q=0.400\n", "node s p=0.667 q=0.400\n", "node u p=1.000 q=0.400\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make first step of simulation.\n", "simulate(graph, 3, 2, verbose=True)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make second step of simulation.\n", "simulate(graph, 3, 2, verbose=True)\n", "draw_graph(graph)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "So, all adopt $A$ after 2 steps." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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dXtxbwB2552DWn0+r6qY2Pi84y/9HV+ZMexKOF4B7iZii+fM/w79eDXPnQyAF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\nJupZWFhyo3ct7The3KPLZsyIi+arAm/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Consider a larger network. (Fig 19.4 in book)\n", "def create_large_graph():\n", " graph = nx.Graph()\n", " graph.add_edges_from([(1,2), (1,3), (2,3), (2,6),\n", " (6,4), (6,9), (4,7), (4,5),\n", " (9,7), (5,7), (9,11), (5,8),\n", " (7,8), (7,10), (9,10), (8,10),\n", " (11,12), (11,15), (10,12), (8,14),\n", " (15,16), (12,16), (14,13), (12,13),\n", " (14,17), (13,16), (15,16), (17,16)])\n", " nx.set_node_attributes(graph, 'choice', 'B')\n", " return graph\n", "\n", "graph = create_large_graph()\n", "# Initialize every node to choice 'B'\n", "layout = nx.spring_layout(graph)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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1KOaZ2DJMUl51e3FvAXfmno1Zfz6tqpuifFxwlv+PTs2Z9iQbLwD3ESFF8+fw\n53+Fa+fAvACkjYd9v4Tz9RC5UJNrtgQvv6r6aPB2l4lV6LYiLHurCMgXkZM0FvzjwIluEsaJKiwj\nInnA+7HMml+FTdwazdqTDS/uzeC+NDdii2E/V9W2eLxcBexR1Z2dMjhPsrIRW9hs0kTiJjh6E/wK\nYCcUvg3DJzVtzZgLPB96g5s8HCTMvM0VEvXFhL4I8zAqwqwbTtNY8EuA4yng15MNDDoBeVdDv79D\nf0QONVf05dxaPwRsApZGyAjy4p6oiNAbuAiLpfXGVrnLgTeB5cChSD0ORWQw8F5gB/BYW2Y6Lhwz\nFh+O8YSjWoPIYuBWrEI1YqraaDi+A4bvhKKxJrxgwnwEiCr7w81Aj7rtPK56tw8Noj8WuBjo6yya\nQwU/KPqJbVpmYdP5WA1ARi6k/ztMyIb/AEqc+doaVMsbHiIjse/4ElVd18yRvbgnGiIUYDHyue6m\nkzRY6mZi2S5XAztE+JMqu+1xIsAc4FJgsapuadvzng/HPOXDMZ5meB4ztboIS6VtOrkAJsHujTB2\nNBwPmBjXAz+gg4Zorno3KNwNz2n5+71pEP1hWGZYkYhU0zi8EzwBxLcNo8XKb8W+z/VYXnt1OeSe\ntNewH6tJuB34ICIPo/qmiFyIuXH+VVX3tPAMXtwTCREGAp/DMgoO0TSb4BwNxSmDgC+J8COQbdii\nSk8sDNMeg6ZFWDhmR7sG70l9VOsQ+TmWQjefhmKnRgyD0t2gR2DaYNgFfAfVo+H7xW5YWk+DZcP5\nClg34emJiWUh5nEzxf2NiIQLfglWpdu5om/Cfhe2JraPEDuHKshIt0bVYLH0s0COwv3fFlnn9n1E\nW3fZTGpxT6kiJjdjfwCLabZUMRpKLpQOhw/vgsXLsMu0Ni84ucu8m7BiJT9r97SMzZRnYLa/o7BJ\nSDUNfu6ZJSA/hOob4fOz2rbm0+mEdOIqCtsKsYrZ8PBOCebLE5sMHpEPYVffTWbeu6HvHhh0pa1x\nAFADgZUwJR/65cB941UjNbYOewp5F3BAo9g3EUk1cf8kMA3uGgKLp8ORfjBnE7z2hO3xbBF87CY4\nXmB/DzsC/7oOhhXCpP0w+CPtqSxzxkp3Y4VNb8fsBXlSHxPJoZjQ98GE/SzmTbJRrFJyh6quav4g\niYXz4g9m7xSF/J6HXRmEh3hOtsl/3/ol/DdwgJAZexZ8MbgHQA2kXQmrH4cXl8PkPDh3CRxNt05X\nX6Z1Z8lEwEJuAAAgAElEQVQPAauT9TudMmEZEfpiMcKDMKQX3L0Mloy2tlhBJp2FRx+FOafgTCbc\nfT08sAi2PQS9+mOXm2+24+kXAfuS9UPgiSMmMPvd1hSRpcAHRWRdstgGuAXYA247j5sEBYW+EKvy\nLAJ6icgpImfwRHrN8zFRb3QVUAXfAHgLhhyGHu+Cm98Fu5fCjMFwZAbsc74+w7F1j9Z6KuSTxGGZ\nlBF3bMVfgXp4wGUUrBkExSHiPqzStsM9YcUFZtlxIhd6VWJn8+tEWBspg6Y5RGQEMAGfHePpBFT1\niIgcwBZgX4v3eDqCS7U87LbzuCKivjQI/3hMwPuIyFlCBH8WnH4drslowRSsGtL/DoPz4Nxg6Dse\ndo5vvH8Vtgjbmrgndcw9lcR9Ic20bGtAgfXD4JIPQ1UaIPD+l9ydpVjss2/rxzHcTORdWHZMYqeL\neZKZl4A7ROTNVFzPcWtcxW47j8vgKaAhvDMyD8a9ATNP2KysogeU50NFbygvgIo8qKmGjBdgwlw4\nfhFsHmyNWUI5iV01NEtI39XwWoOkISXE3bXE6k1YIUdjagPw4jQT+KP/C1X18JXpMOpUyE71WFww\n2l6Vi4D9Phzj6UxUtUREdmBXpy+1tn+q4BZfgyZs2wAQGacw5gwcP2mePHmnIP8g9K+w7y5bYOhu\nKHwI/hZB2MEyaXIRkRbi7rnAuYTuxdsKgXgPIEYI9lpaCKdUpsPOCyCjFuoD0K8GfrAGvnyT9Ug8\nT1pUT2jhmIlAeFNcj6czeAW4yJXLd2fqBOgFlSPh5HQ4MB+2Xwvr5sH6NKhbAVkj4PhVYQVcIQSA\nulYWVJM6JAMpIu6q1GPl3C1cifSohumroLQAXp4Br4+FU5lQkwFb891OQhRmQz4c4+lqXN3FRiwW\n3Z0pJ0y36kHWwbDXYdoE2L0K8udDyVkrWIxENtZEpSW8uCcQb2HxcqAyAKfS7SRfL/Z7ZQDW1MGO\nTBi+D06nw80fgpwamFeK/cMriC4//kos/7VLe1l6uj3Lgeki0jPeA4kjxVj4tTfAach+AaaVQJ8r\n4M2VkHka8m+FTTusj2kk+tK0y1U4SS/uKRFzd7yIZRQAt10Gf1nQcFfBVLjlFZh0DP5vEnxlLqRX\nw8jD8LVXYMVMmF4F/X+mmtNiupmIDAcmAf/Xaa/E44mAqp4VkbVYN6CnWts/JVFVRBYr3LUdsrbC\nmJGwfyocDID+CqbNhK0zYf9KmDwd9gcah2uDYdc3Ihw9FC/uCcRO7KzeEx59mWbN9L+yBdYOhxO9\nYdEGi8SU5Fsa7LVTRLYfADZEqqRzTnvvwnxnfDjGEw9eA+4Vkdfb6FSaMnwJtr8XBpZC+jxYH9r4\n5KWQk14WVO+FPqMad8UaCKxENZqwTKTF2KQhZcIyLu7+R+ySq7lYm2P6fqhLg42DAYGiQpj6EGz/\nLdbo+G4RmeBKrEO5Ejikqtti/wo8ntZR1Qps1nl5nIcSF0Rk9Dfgzl/CYwvgUL8WOlENh8O7rTlK\nkCIsDfLPUTxVUhcwQQqJO4AqGzBP7CFYDL0ZAgpztsKekVA2Hut/+DdV3Q88gjVVuAK404Vhgk1z\nL8Aa4Ho88WQlMFqsDL9bICIZInIdduX8xA9VH06DHwL9OL/W1pgxcOws5J+yFMkh2GLst1GNZkae\n9GGZlPKWCSLCHOAjWNjpJE3/SZlAfzhYBH8rhlP3qP57TeNjSACzI1jojjEE83b3s3ZP3HGNm4eq\najSz0KTGtbm8GasybZyhJjIGs/0djTltnnA/Bch+Gy4QqB8LfwX+FqWwIyL3AX+MwjkyYUlJcQcQ\noQfWpfx6rKw5NIZeDSyB8lehxyLIKobKtdhsvxYoV6XCjiPpwD2Yb83fgZfaaQfs8cQMt/5zH/Bn\nVT3U2v7JiJtgXeK2Z4GNEa2ELXw6mIYG1z2w7/GpzbD2WrjgIPxXG5vufAH4bjJXBKesuAcRIYD9\n4/OwMNQ54LAqVSLkw/5LYdu/wuyjUFCGc5QD1gAvQkEVnLoF+Dn2wZmDpV0u05DOLh5PVyMis4CJ\nqvrbeI8l1ohIb8xCW4EntPUF0JaOdRuwTlU3troz50+c/wZ8Pa7NSDpIKmXLRMQttIa50xEQ4Ubg\nnTAsDXQXvDoIrtkBmXXYSWAq1M6BPw6EZ76p+v1TwMsishpLRbtXRFYBrydrd3RP0rMOmCciI1R1\nb7wHEwtcEsNU4BosM2hFDDzg12CTsqjEHRdvT2ZhhxRbUI0GEdKAO7H+icXAfhh+AHqfgtWj3W71\ndt+badCvHr7/ARHGAKhquao+AzyMFVLcJyJzXfjG4+kynO/Jy8AVETK7kg4RycXaY84DfqOqr8Wo\nucd2zGEy2gXopF9MhW4o7tjCzKVYB5eQGNxFO+FEH9jjVt4P94Qj/WH8Wqxy9TMiDAjuraqlqvo4\n8FvMTfJeEZnm4oQeT1exEcgBm3wkKyIyGmubdwZ4WGPYUtCdBNdia3DRkBLi3q1mm66/6vVwTz/4\nx1WNOzVl1cErCrfcjc3cA6AKNVfBow/DLYqdGBpVpqpqMfAHlzK5CLtMXoJ1z0nqyzpP4qOq9WIN\nPa4QkZ3J9plz8e1FmAnfE6ramsd6e1kL3CUiS5yvfEt4cU9C5gF1MOhM5E5N334D3l8Cu0fAgKPw\nVCY8chm85wh2lTNLhD6qNKkMVNV9IvJLYBz2YZ3vPkiRO+x4PLFjG3Y1OgnYHOexRE1YiuNDnVn1\nraqnRWQf0XVbSwlx7zYhBBGyMdE9Zp2avrgNekf4MA06AacLoeAMPDkNrtzg3qZg7O/i5p5Dje3A\nT7CZwntE5APdqdjE0/W42fpSYGEyhAVFJCAi84EPY2Zof+0iO481wKwo1ieSvjoVupG4A8Ow5sMt\nXJLVBmD9eJj9BiwbDzuHw6c2hOxwElt1bxFVrVfV9VgF3V7gdhG5yaV3eTydwS6sArPFDkPxxn0H\nbsfWCB5W1be6MJS0C6tlGdzKfn7mnmTktL7L5kGQVQUz9sHSXBh5Ei4OrWirwf7xUaGqtaq6AvgB\n5h/9CRG51jdc8MQaJ5AvApcnYuaWGNOAjwNvY9kw7c5dbw/uPVpD6wurPYCznT+izqU7iXsUs4Os\nGqjMguo0WD4CLt8PG4a2/ThhD1CtUtWXgB9j7/knRWSBa/rh8cQEt75TAsyI91hC6cQUx/awHpgg\nIi1N9vzMPcmIIqY3vhh6n4b/mQdn8uHzL8PeoXAsOFvPogNndFUtU9WngZ9hlgj3i8hFIhJVaz+P\nJwqWApe6LJS405kpju3BVZW/jVWbN8HF4/NI4sbYQbqTuO/DBD67+U5NAly8A54eBRfuh7FnYOJO\nWD3R4vH0Bl7t6EBcjvzfgN9h2TX3isjUVChE8cQXVT2CVWRfFM9xhLs4quqzbfF26WRaWljNAaoT\naKztptuIuyrVwHNAkXVqKvgSPDkfVk6132+7zPYsC8C6AbDgJOwstNl8bgWsHY1lzKyK3Zj0qKr+\nDjMkuwjLwx3rRd7TQV4CLhGRFmyvOw+X4vhxLLzxUCfmrreXA5gP/IgI96VESAa6gXFYKCIUAv8D\nHMEWR1vgaD6smArz1ltz7fVXQq/HVC/4n84ZmwgwAWsIUg4sUdUDLT/K44mMiLwbOO3WerrqOaNz\ncUwARGQ2MFJVHw27fRRwqar+Oj4jix3dZuYOoMpx4FFgKA29FJthwFmYtANWToFAHxixBW7K6KzZ\nkMuR34pVwK4H3isit4pIUWc8nyfleQW4qKsys+Kc4tge3gJGiUh+2O1+5p6siCCYadg7gcNAS37N\nAttmQGk2jPoIDJgCZKnqY50/TskAZmMZBm8DL2uUjQY8HgARuQGoUdXnO/E5BJgGXE3sXBy7BBF5\nJ3BGVV8JuW0e0ENVn4vfyGJDtxN3OC/wl2HpWT2wlfxQS4EMrH1XOtRthdmnYN0hrP3eJ4Clqtol\nZd7uSmEelpu7Hlju+mh6PC3iZqX3YHHvM51w/FzgHVjm12PxzoRpKyIyAPgA7H8Eho4F8uA7s6H+\nNHzuCVWOxXuMHaFbinsQETIxr4nrsDZdwTejBkspW67KYRHJAj6KNSY+AnwQ+Imqdlmhg/uiXob1\ncV0JrIzCAMnTzRGRq7CrzadifNzRWCbMFmx9KKmyS9wEbxQ88iBcnwf9XShm83CzHhlUijluPg9s\nVW2+EXei0q3FPRQR0mlos1el2rhYSUT6YH1Z/4Ktsg8Bft/VcUU3jiuA4cAyYK2zNPV4muBm1/cC\nP1fVJoZ37TheV7k4dhqup8MtwLVwoAfsSIMrnM3I89Ngwn4Ydgq7IsnDmqI8rBpNrUzi0K0WVFtC\nlVpVylSpDBd2u19PAo9h8fq3sHzYaP2hY4aqnlTVvwJ/wLJrPikiU3z6pCcSLoT3BnB56O0iiGtB\nGTUhKY55JGaKY6u413w71lv5AAzYAqd7wCmXKFGdCTnV2FV8CeYNNRX4Z2c+mDT4mXsbEZG5wIXA\n48BtwC/j2SFdREZiM6kA5i2yK8GzFDxdjAsr3g/feho+NwGzB86noafwaqyj095IE5tkSnFsDRGu\nxcKqezgfhl05Gjb2hG9Nhf1DoMdZ+Ofn4UvbQh46HHhdlZ91+aDbiRf3NuJmyDdiVgR7sDLmX8Yz\nNOLGNBHLkT+LxUAPxms8nsRChP6w8kvQYypM3gEcx9xRFUseKAQyseKe36nydsNjY9eoOt6IkAV8\nFzgNhPQ9PpILUz4J73wNrk2HEwfg0x+AZ38KV5wIPhxLof6CKsVdPfb24MMybcTNWBZjM588bOZz\nabzHpKpbMGOyjcD7ROT9IlIYz3F54o8II4Evw6ws2FUFR85gwhaaPHAEs+foBXxehNnOxXE6cXRx\n7ASmYuHUsIb2a3vA2Sy4fz9k18A9e2D0AfhxqH2yYhXq87pstB3Ei3s7cJkBf8bCM1sxn4oh8R3V\neR/5NzEf+YPAnSJyo4j0jPPQPHHA9fz9HFAD6Udg9D7YPLKFh5QCJVB1P9z+aSwME28Xx1hyHTZr\nj0Q97BsKmS4DTYFd4U12jgGLXJZdwuPFvZ2oahkm8FdiC1Y3JYqFr6rWqOprmMhXAHeLyFWt2Jx6\nUo/bgQDcNQ6Gfhym3wlfvAgOhDSN+b+R0O9eyPwSjLsdFhfBsiHwuQXwnV8mW+56c7jUxxFEFPeF\nx6FHOTwyDqoD8IPRsHMEVIc7a1Zj4auCTh5uTPAx9w4iIlMwgT8ClKnq4jgPqQkuR/5yLC6/AsuR\nb8Vbx5PMiDAI+DqwH742AQJqPYPP5cNXtsPV62BnLky5Hz7/JNy7Az74btg2GF79NQzrCfxAlXVx\nfilR4dad0jHxzWr6c0QevPwgHC+B2nSoTbOtLs3+frMIHp4BxQEYcQB6VkBmLSx7MuyphgBfVSXh\neyMnXMeWZENVN4pIf2AkMFhE3lbVHfEeVyiu2OofIrICWIj5yL8CrPM58inLpVjNhlrPYIA1g6wh\nfE067O0DPxwJA0vg7v2wcjrcvw1uGgfb02DYWeA6EdZHyqCJBa6PQTNi3K6fisXTq5v+LK6Bqkyo\nD0BmDeSdg/Q6qMiGQwNgdC387nGYtQuy6mDkR+Ad65sZelJMjLy4x4alwK3Yl+lGEXkoES0CXMrm\nX0RkMHa1cbGILAW2JGtqm6dZFmB52hGYsAe2joTtRTC0zNxPJ+6CccXQ91JYWQRXbcVMwHpjsfjg\n7DiWYhzABDiCGDf5eba1/VqbqIgwD6gHrYCDvWH7MCjPhZEHYFcdXHAczgbgE3Ms9/3r4eIeDGPH\n3MqhM/DiHgNUtV5E/oZZFFQC7xSRRxNVMFX1EPAbZ2+6CJgnIkuSsSjF0xRXbZ0D4d4oCmgAcquh\nLB9KR0PPc9CvBEp7wOu9IDsA+0bDc1nQtxDuv1dkxTlMjDOwWWtrQlxFQ7phS/vVdu13pO55OPlx\nWJthxUqj98P4o5Cm8MWr4IMzoD4NxuyDx38LPcNPFv2BVarJ0aXJi3uMUNUqEfkj8DFswWUqsCF0\nH1cdlw7UdNalbltQ1d0i8jNgEnCDiJzGcuQPx3lonjbgiozysPTcfBhUAMsGwJFsC0VUZZmYVQyD\n2gzYMAZ6nobcMqiutjBFep1tVQJFx2DiXuhZDp94Elbsxs2wE3XC0hLu/ZkAYybBHwbByLdgTLGt\nQwR56gXMGLAlMrGr9KTAi3sMUdWTIvJXrHL1XSKyD7QWsym4BhiAmz6JcAB4Btig2qLtcGePWYHN\nIrINS+38gIjsx5wvT7T86Ma4IpERQC5W9HEO2KdKwoWokgEnSrmcF+2IWw+3zzksdHEWis+C1kGf\nMsiphNwqyKuG32RDWU+4bq09w9MBeGoazNprfx/LgBM94YrdzlslH24/rHp7lxnkxRIX058CzAeq\nYOczMPM0BObT9kb3/TArgl2xHWXn4cU9xqjqLhF5Bnq8D775P7aAEwhglsL7sQ+VYAUjdwFVIjwF\nPBNP5zkXr1wjIhuAucBHRGQr5iPf4pdbhH5YTvTVWDw1lDoRc9gEDifCFUu8cbHrUNHuQWThzsPC\nfGfDtiNYYVHw7/LwPHQRhgGTgRPWH7gy0LhncHY9fHIrPHwV/OdEuG8HfHQBDCqGq4675y61xycX\nIpKOTVTmAaeAp4E9qhqcVI0ABgOHojxkX2w97f+S6fPrUyE7AZGSPNj4EOhsKHoDpu5tYfdM7IO2\nAviFamKsxLuc+PnADOBN4DVVPdd4HwQrDHkvdtI6RpPqv1BvfF4A/pyM9qnR4EQ7m5Zn2kExr8KE\nuYym4h3cytqbzSTCBODfgH3wvsvhLwsa73HLK/Doy/CjUfDV66G0F4w4BL95Ai4+BQzDrAiSJgzh\n6kxmARdjJ8DlkVpVitALuA8YCxyFZt0eM7Gr7VLgO6pRnwwSAi/uMUaEDOB+qJsMz/SHE/3gupeg\nX0uLMMECi6XAbxJpduCqWy/HHChfA1apao0T9vcBN2CeJK2dlAKYYKwEfpZMAu9EO4vWBTsfm+E1\nJ9ahot2p/udufee/sJNqW7M7MrDFw39WJeFDMm4icpHb9mKi3mLxlXN4XIBNTnphV0hBW4ZM7Mqq\nEjPjW6JK0lkveHGPMSLMBz4OdxXC4gvhSH+48BiseBjS3aXz8Qx4/9Ww8gKoC8CQYtj5a8x57r9V\n2RLHlxAR51NzJXaV8QpU5UPmnZgnSbRCHTyJ/V2VTm9VGA3OMbG18Eg+5isSUahD/06k4jARpgCf\nxdpJRtvYJYD9j/6oyjOdNLSYICI9sFn6DGA78GpbHVpdZtFEYA6W9hnATobriPN6WEfx4h5D3Gz2\n60AWfG2IrcY/PwHKhsH/LoHLnWjPvdlE/XdPw8hz8PcBcMsRLHyxVZUfxu9VtIzlyPe6BhbfDoPe\nhv8eDIunw5F+MGcTvPaE7fm7IfC1hbB/EEg9TNgLjzwDU88BA4HPqHZevrBrKtFaeCQfO+FEM9MO\nDzclBSJchjWZKYZWF7bTsaurZzFxT0hxEJFeWDx9CmaU93oKmJrFHL+gGlvGYMK1r3FVYOVx2DYV\nhh6D3cD68bDrOzDYCcYtR9zjS4ALRShUJW4e8S2hqodE6jfAiRJYPRAyCuGON+G1AVb9GORYNtz6\nJnzsUciqh5uuh1vfDVt+h82OLgKWtPX53WJZa6GRfOyzHUmoj4b9nZTpfdGiyjIRyrAU3SJsgTHc\nXyUXs/2tB/6ELe4n3HsiIn2xdaAJwFrgx87jyRMBL+6xZQYWcw0jrQJG7YGlC2D7big4BR+9HJZN\ng55n4Z6X4cGtWLwvgF0mLu/CcbeRwHVQdAiuK4Ux/WD7SFiTD5Uhr/0zOxs/5lOr4EN3uD+OA9eL\n8FIw9u7S1loLjeRj8dBIYZGSsNsrU1m024Iqa0X4DNZ74Hpsdh7MrhEsDPFHrECnOdfEuOHsPS4F\nRgGrgB+EL+57muLFPbYU0DRbxLHoLfhTP9g2A472g6wD8Opv4cX+8KWbYdRfYE4p9OgBmyeKLDpK\ng4e0hv0e/rMj92lbRND1nxwD7DVdGHcMRpfAw/2hpj+8Mgmm7oEC9+WrEyjPhKfGwYBS2DQIzmVB\n3iB4/0dFNgUw0c4Cymk6094X9vc5L9ptx/X/XCHCSmwGn4tNJCqB4kRc4HY22pfSkE32j2QNj8UD\nL+6xJUCzxREBhRtfgcdvst9vqYBjA2B2JYwpgacmwqCd0KcPvDUOi4+K2wKt/OzIfSIibTg59M+A\nJ8fDsX52m6gdpraHxdYPD4LtF0BWBWRWQXot7MyAR2fDv71unh3ZVZBfBldugk27acjV9qLdybhw\ny7FWd4wTLjNpBHAZ0AfL0PprIi1UJwte3GPLaWjJyL9HNSxcBY+Pg9G7oXiAFZUEqiGvGBZuBkbA\ntMWq//xSVwzYfZnacFK4OBsmTYdRh0DFbUBmIaTnw4JVUJUOxX3gZC/Y1ge+eSF87BX44grICIYD\n6uB7O1S/l7BC4+k63OdwLCbqOVhYcqN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make 7, 8 \"early adopters\"\n", "graph.node[7]['choice'] = 'A'\n", "graph.node[8]['choice'] = 'A'\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[1, 2, 3, 6, 4, 9, 7, 5, 11, 8, 10, 12, 15, 14, 16, 13, 17]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[n for n in graph]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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TcLCFZ03Uq24v7s3gztwzMevP51R1Q4SPq5vl/6tDc6Y9icbLwD2ESdH8Nfzt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\nwXfPhU8shq8ug7S6cEAN/Hib6o/jVmg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulation, step 1\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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MPYHfqAk42MKzJupVtxf3JnBn7pmY9eezqrqhhY8LzvL/1aE5055E4yXgHiKk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\npCec6A5besJ3psLHF8NXlkFaMBxQAz/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulation, step 2\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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YSchW2s29e6LOlpGGLKbewM/VBBxs4VmT9arbi3sLuDP3LMz68xlV3Rjl44Kz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\n+zEf+OER7kuJkAx0A+OwUEQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulation, step 3\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)\n", "# No changes after 3 steps." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Cascade:** a sequence of adoptions of a behavior\n", "\n", "Two possible outcomes of a cascade:\n", "\n", "1. **incomplete cascade:** converges to partial adoption\n", "2. **complete cascade:** converges to total adoption\n", "\n", "The choice of initial adopters can *cause* a complete cascade or an incomplete cascade." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# How can we increase likelihood of a cascade?\n", "\n", "



\n", "\n", "1. Increase payoff $a$ (e.g., make a better product)\n", "2. Better selection of initial adopters (e.g., market to certain people more)\n", "\n", "


" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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1KOaZ2DJMUl51e3FvAXfmno1Zfz6tqpuifFxwlv+PTs2Z9iQbLwD3ESFF8+fw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\n6uB7O1S/l7BC4+k63OdwLCbqOVhYcqN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's increase payoff a from 3->4\n", "\n", "graph = create_large_graph()\n", "# Make 7, 8 \"early adopters\"\n", "graph.node[7]['choice'] = 'A'\n", "graph.node[8]['choice'] = 'A'\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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tI3VZTD2BX6kJONjCsybqVbcX9yZwZ+6ZmPXns6q6oYWPC87yn+7QnGlPovES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\nC0WkAPhfLG+9yXZ6hyFvGUy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulation, step 1\n", "simulate(graph, 4, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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j1p8vOec2hvk4/yz/hXbNmTbijdeBewmRovk4/P0/4fIZMMsHSaNg7+/gbD1E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\ngZzlMGEWrMuGynVwSVd45hz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulation, step 2\n", "simulate(graph, 4, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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nF69n3SbuTeAduaej1p8vO+c2hnk/f5T/YrvWTBvxxhvAfYQo0XwC/v6fcMUM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\nQM1PYftPnYtZoTE6Du9zOAIV9Qw0Lbn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulation, step 3\n", "simulate(graph, 4, 2)\n", "draw_graph(graph)\n", "# All adopt A after 4 steps." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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1KOaZ2DJMUl51e3FvAXfmno1Zfz6tqpuifFxwlv+PTs2Z9iQbLwD3ESFF8+fw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\n6uB7O1S/l7BC4+k63OdwLCbqOVhYcqN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TcLCFZ03Uq24v7s3gztwzMevP51R1Q4SPq5vl/6tDc6Y9icbLwD2ESdH8Nfzt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\nRU5ErkJggg==\n", 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MPYHfqAk42MKzJupVtxf3JnBn7pmY9eezqrqhhY8LzvL/1aE5055E4yXgHiKk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\npCec6A5besJ3psLHF8NXlkFaMBxQAz/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YSchW2s29e6LOlpGGLKbewM/VBBxs4VmT9arbi3sLuDP3LMz68xlV3Rjl44Kz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\n+zEf+OER7kuJkAx0A+OwUEQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Next, let's go back to 3/2 payoffs,\n", "# but convince 12 to adopt.\n", "graph = create_large_graph()\n", "# Make 7, 8 \"early adopters\"\n", "graph.node[7]['choice'] = 'A'\n", "graph.node[8]['choice'] = 'A'\n", "draw_graph(graph)\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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28XrVbeLeBN6Zezpq/fmSc25jmI/zz/JfaNecaSPeeB24lxApmo/D3/8DLp8B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\nMxiHBSKSB/wvmrfeZDu9I5C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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Convince 12 to adopt 'A'\n", "graph.node[12]['choice'] = 'A'\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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j1p8vOec2hvk4/yz/hXbNmTbijdeBewmRovk4/P0/4fIZMMsHSaNg7+/gbD1E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\ngZzlMGEWrMuGynVwSVd45hz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Cascade continues...\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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j1p8vOec2hvk4/yz/hXbNmTbijdeBewmRovk4/P0/4fIZMMsHSaNg7+/gbD1E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\ngZzlMGEWrMuGynVwSVd45hz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Cascade stops.\n", "simulate(graph, 3, 2)\n", "draw_graph(graph)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "** What prevents cascade from affecting nodes 1,2,3?**\n", "\n", "



" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Cascades and Clusters\n", "\n", " A cluster of density $p$ is a set of nodes such that each node has at least a $p$ fraction of its neighbors in the set.\n", " \n", "![density](density.png)\n", "\n", "What cluster has density 1?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Conjectures:** \n", "(i) A cascade halts at dense clusters; \n", "(ii) This is the only thing that halts a cascade." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "More formally:\n", "\n", "Consider a set of initial adopters of behavior $A$, with a threshold of $q$ for nodes in the remaining network to adopt behavior $A$.\n", "\n", "(i) If the remaining network contains a cluster of density greater than $(1 − q)$, then the set of initial adopters will not cause a complete cascade.\n", "\n", "(ii) Moreover, whenever a set of initial adopters does not cause a complete cascade with threshold $q$, the remaining network must contain a cluster of density greater than $(1 − q)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Proof of Claim 1:** *A cascade halts at dense clusters*\n", "\n", "![cluster](cluster.png)\n", "\n", "By contradiction:\n", "- Assume node $v$ is in a cluster with density greater than $1-q$\n", "- Assume that $v$ is the first to adopt $A$ in that cluster (contradiction)\n", "- For this to happen, fraction $q$ of $v$'s neighbors must have adopted $A$\n", "- Since $v$ is first to adopt in this cluster, all neighbors that adopted $A$ must be *outside* of cluster.\n", "- But, by definition, more than $1-q$ neighbors are in cluster, thus less than $q$ neighbors are outside of cluster. \n", "**contradition** $\\Box$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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j1p8vOec2hvk4/yz/hXbNmTbijdeBewmRovk4/P0/4fIZMMsHSaNg7+/gbD1E\nJlRlqi3BW28795T/di8TK8/b8tHsrXwgR0ROUF/wjwHHO0kYJ6ywjIhkATegmTW/D5q41Z+1xxkm\n7o3gfWmuQhfDHnct83iZD+x2zu1ol8EZ8coGdGGzQROJa+DINfB7gB2Q9yEMGtuwNWMm6kd0Fm/y\ncIAg8zavkKgHKvT5qIdRPmrdUEx9wS8EjiWAX0860Pc4ZF0KPf8FvRA52FjRl+fW+mlgI7A4REaQ\niXvMItINOBeNpXVDV7lLgfeBZcDBUD0ORaQf8AlgO/BMS2Y6XjhmBBaOMYJxrgqRhcCNaIVqyFS1\nYXBsOwzaAfkjVHhBhfkwEFb2hzcDPeJtZ/Gqd7tTJ/ojgPOAHp5Fc6Dg+0U/tk3LNGw6G60BSMmE\n5P+C0enw30ChZ762OtAyW0SGoN/xRc65tY0c2cQ95hDJRWPkM71bTlBnqZuKZrtcCmxH5G94Pi9e\nGGYGcAGw0Dm3uWVPezYc86KFY4xGeA01tToXTaVtOLkAxsKuDTBiGBzzqRjXAj9vazaGV73rF+66\n59T8/W7Uif5ANDMsX0QqqR/e8Z8AotuGUWPlN6Lf51o0r72yFDJP6GvYh9Yk3AJ8CpFHce59EZmM\nunH+0zm3u4lnMHGPKfQs/mU0o+AgDbMJzlBXnNIXeACRX4hWlF3tPe5x1zqDpnloOGZ7q8ZuJD7O\n1SDyOJpCN5u6Yqd6DISiXeAOw8R+sBP4Mc4dCd4vcsNytdRZNpytgPUmPF1QscxDPW7Ge38jIsGC\nX4hW6bav6Kuw34muie0lwM6hAlKSPSteNJZ+GshwcN+PRNZ6+z7hmnfZjGtxT6wiJp2xP4jGNJuq\nGA0kswgG3QQ7F8JS9DKtxQtO3mXeNWixks3ajabRmfIU1PZ3KDoJqaTOzz21EORhqLwKvjotxnz9\nAzpx5QdteWjFbHB4pxD15YlMBo/Ip9Gr7wYz713QYzf0vUTXOACoAt8KGJ8DPTPg3lHOhWpsHfQU\ncjWw34WxbyySaOL+eWDindB/IUw6DD1nwMZ34DmAVyD/s3DNMV0kZSAc/k9YOxDyxsK+fnB7ayrL\nPGOlu9DCpg8j+pqMxEZFcgAq9N1RYT+NXkluEK2U3O6cW9n4QWILz4vfn72TH/B7FnplEBziOdEi\n/33tl/B9YD8BM/Y0+Lp/D4AqSLoEVj0LbyyDcVlw5nw4kqydrr4Rar0t6HV8GlgVr9/pxAnLaKuy\nqcCB/tCtzjkcAAAgAElEQVT1Lli6CIZV1HW1YSycfgqemgEnT0HqXbDgQZi3FR7pqp4Q49HF1pYy\nD9gbrx8CI4qowOzztoaILAY+JSJr48U2wFuA3e9tZ/EmQX6hz0OrPPOBriJyktAZPKFe82xU1Otd\nBVTAdwE+gP6HIPtquPZq2LUYpvSDw1Ngr+frMwhd92iup0IOcRyWSRxx1xV/B9Q+6GUUrIa+BQHi\nPhDKB0L5IeiyHM5JgYrjkNlV09JOAVcgsqa5M3ogIjIYGI1lxxjtgHPusIjsRxdg34n2eNqCl2p5\nyNvO4hUR9aBO+EehAt5dRE4TIPjToPhduCylCVOwSkj+F/TLgjP9oMco2DGq/v4V6CJsc+Ie1zH3\nRBL3uTTSss2PA9bBwPPhpgr1nJYb4E3v7iI09tmjueP48WYiV6PZMbGdLmbEM28Ct4rI+4m4nuOt\ncRV421m8DJ5c6sI7Q7Jg5Hsw9Tgcz4SybCjNgbJuUJoLZVlQVQkpr8PomXDsXNjUTxuzBHICvWpo\nlIC+q8G1BnFDYoi7xi27EVTIEUg1+N6AiQ44Av9XAbXfhElD1ZLVTy0aFwy3V+U8YJ+FY4z2xDlX\nKCLb0avTN5vbP1HwFl/9JmxbARAZ6WD4KTh2Qj15sk5CzgHoVabfXTbDgF2Q9wg8HULYQTNpMhGR\nJq7SM4EzMd2Ltxl80R5AhBD0tTQaTimH5B0aiqmuBV9PqPo5rP4GXLPF+1B4JIX1hBqOGUPDpriG\n0R4sAc71yuU7MzUCdIXyIXBiEuyfDdsuh7WzYF0S1CyHtMFwbH5QAVcAPqCmmfBrXIdkIFHEXc/w\n5TRxJZINlZNgZRHkvgVT3oURJyG1ClK26MIJ6Emi2cteC8cYHY1Xd7EBjUV3ZkoJ0q1akLUw8F2Y\nOBp2rYSc2VB4WgsWQ5FO/Sv2UJi4xxAfoPFyysF3EpJrQGpBTkJyOfhWQ812SB0Ee4sh+Vr4dAZU\nzdJ4ezrqjx1OfvwlaP5rh/ayNDo9y4BJItIl2gOJIgVo+LUbQDGkvw4TC6H7xfD+CkgthpwbYeN2\n7WMaih407HIVTNyLe2LE3JU30IwCboY5/1A/GQByYcJ1sGQsHP0VjP0mzEyGyiFw6NuwZDlMnQQV\nveCxjGbSzURkEDAW+FV7vhjDCMY5d1pE1qDdgF5sbv+ExDmHyEIHd26DtC0wfAjsmwAHfOB+DxOn\nwpapsG8FjJsE+3z1w7X+sOt7IY4eiIl7DLEDPat3eaoJM/1vwuY1MOg4dJsH6wUohJzDMOVyGL9N\n087Wh6qk85z2rkZ9ZywcY0SDd4B7ROTdFjqVJgwPwLZPQJ8iSJ4F6wIbn7wZcNJLg8o90H1o/a5Y\nfYAVOBdOWCbUYmzckDhhGRXjJ9FLrsZibQBMgn01kLRBGydIPuRNgEe2wZ/QRsd3ichor8Q6kEuA\ng865re3xEgyjOZxzZeis86IoDyUqiMiw78Jtv4NnLoSDPZvoRDUIDu3S77iffDQN8u9hPFVcFzBB\nIok7gHPrUU/s/mgMPSQ+cDNgy24YUqIFE8uBp51z+4An0KYKFwO3eWEYf9Pcc9AGuIYRTVYAw0TL\n8DsFIpIiIlegV87PPezco0nwMNATb60tmOFw9DTknNRsuP7oYuyPcC6cGXnch2USy1vGj8gM4HY0\n7HSChv+kVKDXAch/GgpOwt3/FRRr94oYxqPFUSfQD8czNms3YgGvcfMA51w4s9C4xmtzeS1aZVo/\nQ01kOGr7Owx12jzu/RQg/UM4R6B2BPwTeDpMYUdE7gWeDMM5MmZJTHEHEMlGu5QvQMuaA2PolcCi\nUng7G+alQUE5rEFn+9VAKXr56y+Nvhv1rfkX8GYr7YANI2J46z/3An93zh1sbv94xJtgne9trwAb\nQloJa/i0H3UNrrPR7/HJTbDmcjjnAPxvC5vufA34STxXBCeuuPvRD0g/9NLMh/q5H8K5CkRy9sEF\nW+E/p8ORXJ3h++Psq4E3cqHipDb+eBz94MxA0y6XuoDOLobR0YjINGCMc+5P0R5LpBHtonYNmuny\nnGt+AbSpY90MrHXObWh2Z86eOL8CfCeqzUjaSCJly4RGF1rrudMh4kPkKuCjAyHJwc63oe9lsD1V\nF2h8wIRqmPEk9HkZvvcz/XC9JSKr0FS0e0RkJfBuvHZHN+KetcAsERnsnNsT7cFEAi+JYQJwGZoZ\ntDwCHvCr0UlZWOKOF2+PZ2GHRFtQDQftIXkb2j+xANg3CPZ3g5OrNG4HGsIpeB+SekLtz+CTXmwP\n51ypc+5l4FG0kOJeEZnphW8Mo8PwfE/eAi4OkdkVd4hIJnqVPAv4o3PunQg199iGOkyGuwAd94up\n0BnFXRdmLkA7uJyNwZ0LO45D993eyvsh6HIYeo3SWHwZcD8ivf37O+eKnHPPoumTQ9GZ/EQvTmgY\nHcUGIAMYHu2BtAURGYa2zTsFPOoi2FLQOwmuQdfgwiEhxL1zzTZ11X3B3dDzBZgf2KkpDWqWgLtO\nOyrVAj4HrgrmPwWPXqexv2sJqkx1zhUAf/VSJuehl8mL0O45cX1ZZ8Q+zrla0YYeF4vIjnj7zHnx\n7XmoCd9zzmtW3w6sAe4UkUWu+W5rJu5xyCygpi+cCtWp6Ufw3g1QuAsG94YjL0LqEzDn43AYvcqZ\nhkh3QlQGOuf2isjvgJHoh3W290EK3WHHMCLHVvRqdCywKcpjCZugFMdH2rPq2zlXLCJ7Ca/bWkKI\ne+cJIYiko6J79EHY8nXY2k0zZ+rRF44XQ14unHoeJl4C6703yR/7O6+xp3DKNuDX6Ezh4yLyyc5U\nbGJ0PN5sfTEwNx7CgiLiE5HZwE2oGdo/O8jOYzUwLYz1ibivToXOJO4wEJ2lN3pJVg2+dTBqOry3\nFEbtgEFfgPUBu5xAV92bxDlX65xbh1bQ7QFuEZFrvPQuw2gPdqIVmE12GIo23nfgFnSN4FHn3Acd\nGEraiday9GtmP5u5xxkZze2wCfqmQcUU2LsYMofAifPqmwdVof/4sHDOVTvnlgM/R/2jPycil1vD\nBSPSeAL5BnBRLGZuiTIRuAP4EM2GaXXuemvw3qPVNL+wmg2cbv8RtS+dSdybnR2kQVU5pFVC0jIY\nfBHsWw8DWnqcBk/sXIVz7k3gl+h7/nkRudBr+mEYEcFb3ykEpkR7LIG0Y4pja1gHjBaRpiZ7NnOP\nM5qN6Y2Cgm5Q/AOYdQpyvgpv7YEBR+tm62m04YzunCtxzr0EPIZaItwnIueK5t4bRiRYDFzgZaFE\nnfZMcWwNXlX5h2i1eQO8eHwWcdwY209nEve9qMCnN9apSYDzYPtLMHQy7BsBp8bAjlUwplrfq27A\n220diJcj/zTwZzS75h4RmZAIhShGdHHOHUYrss+N5jiCXRydc6+0xNulnWlqYTUDqIyhsbaaziPu\nmtv6KpB/M8zJhQeeh9krYEIuPHCzWgpQAr610PtCOLED8kZBQSaUrdHq1VpgZeSG5I445/6MGpKd\ni+bhjjCRN9rIm8D5ohliHY6X4ngHesX7SDvmrreW/ajNyOAQ9yVESAY6g3FYICJ5wA/QvPUm2+kd\ngZzlMGEWrMuGynVwSVd45hz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GXDRWFXgr7P0GFP8UBv4O3n4cxn4I/W6Gg8th+DhIytHZ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\nxQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_graph(graph)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- density$(\\{1,2,3\\}) = \\frac{2}{3}$ (For node 2, edges (2,1) and (2,3) are in the cluster, edge to 6 is out of the cluster.)\n", "- For payoff, $a=3$ and $b=2$, so node adopts if\n", "$$\n", "p \\ge \\frac{b}{a+b} \\ge \\frac{2}{5}\n", "$$\n", "so\n", "$$\n", "q = \\frac{2}{5}\n", "$$\n", "\n", "- Node 2 does not adopt because $p_2 = \\frac{1}{3} < \\frac{2}{5} $ (only 6 has adopted; 1 and 3 have not)\n", "- Is density$(\\{1,2,3\\}) \\ge 1-q$ ?\n", " - $\\frac{2}{3} \\ge \\frac{3}{5}$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Proof of Claim 2:** *Dense clusters are the only things that halt cascades.*\n", "\n", "![obstacles](obstacles.png)\n", "\n", "- Show that whenever a cascade halts, there exists a cluster with density greater than $(1-q)$.\n", "- Let $S$ be the set of nodes that have not yet adopted $A$\n", "- Show that $S$ has density greater than $1-q$.\n", "- Consider any $w \\in S$\n", " - Since $w$ has not adopted $A$, the fraction of its neighbors adopting $A$ is less than $q$ (by definition)\n", " - Hence, fraction of its neighbors adopting $B$ is greater than $1-q$.\n", " - Since $S$ contains all nodes adopting $B$, the fraction of $w$'s neighbors in $S$ is greater than $1-q$.\n", " - Since this is true for all $w \\in S$, $S$ is a cluster with density greater than $(1-q)$. $\\Box$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ ">**A set of initial adopters can cause a complete cascade at threshold $q$ if and only if the remaining network contains no cluster of density greater than $(1 − q)$.**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Weak ties and diffusion\n", "\n", "![weak](weak.png)\n", "\n", "Will $u$ or $v$ adopt from $w,x$?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ ">**\"Although a world-spanning system of weak ties in the global friendship network is able to spread awareness of a joke or an on-line video with remarkable speed, political mobilization moves more sluggishly, needing to gain momentum within neighborhoods and small communities.\"**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Extension 1: Each node has a different payoff\n", "\n", "\n", "\n", "\n", "\n", "\n", "
      $w$
$v$$A$$B$
$A$$a_v$,$a_w$ 0,0
$B$0,0 $b_v$,$b_w$
\n", "\n", "- If $v$ chooses $A$, payoff=$pda_v$\n", "- If $v$ chooses $B$, payoff=$(1-p)db_v$\n", "- $A$ should be chosen iff\n", "\n", "$$\n", "pda_v \\ge (1-p)db_v\n", "$$\n", "\n", "equivalently\n", "\n", "$$\n", "p \\ge \\frac{b_v}{a_v+b_v}\n", "$$\n", "\n", "Let $$q_v = \\frac{b_v}{a_v+b_v}$$\n", "\n", "$q_v$ is a **personal threshold**. $v$ chooses $A$ iff a $q_v$ fraction of neighbors do." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**How does diversity of $q_v$ affect cascade?**\n", "\n", "![personal](personal.png)\n", "\n", "**Influenceable people?** (**susceptibility**)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Extension 2: Add edge weights\n", "\n", "- Edge $e_{u,v} \\in [0,1]$ specify the **influence** $u$ has on $v$\n", " - e.g., $e_{\\hbox{teacher, student}} > e_{\\hbox{student, teacher}}$ (maybe?)\n", "\n", "- Let $A_v$ be the neighbors of $v$ that adopt $A$\n", "\n", "- $v$ adopts $A$ if:\n", "\n", "$$\\sum_{u \\in A_v} e_{u,v} \\ge q_v$$\n", "\n", "**Linear Threshold Model** (See [Watts 2002](http://research.microsoft.com/apps/pubs/default.aspx?id=164520))\n" ] } ], "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": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 0 }