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<h2 class="hd hd-2 unit-title">Introduction</h2>
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<h2 class="hd hd-2 unit-title">Motivation</h2>
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<h2 class="hd hd-2 unit-title">The Binary Choice Model</h2>
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<h2 class="hd hd-2 unit-title">Population Arithmetic</h2>
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<h3 class="hd hd-2">Population Arithmetic</h3>
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<h2 class="hd hd-2 unit-title">Probability Matching Explained</h2>
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<h2 class="hd hd-2 unit-title">Interactive: Probability Matching</h2>
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<p style="text-align: left;">The interactive graph below simulates the binary choice model described in the lecture. You start with a population of 10 individuals that can live on top of a plateau or in a valley. Depending on the weather and on the location of an individual, each creature will have a number [mathjaxinline] X_a [/mathjaxinline] or [mathjaxinline] X_b [/mathjaxinline] of offsprings ([mathjaxinline] X_a [/mathjaxinline] if the creature lives in the valley, and [mathjaxinline] X_b [/mathjaxinline] if the creature lives on top of the plateau)<span style="font-size: 1em;">. Given the type </span>[mathjaxinline] f [/mathjaxinline]<span style="font-size: 1em;"> (a number between 0 and 1) of the creature, it will send a fraction </span>[mathjaxinline] f [/mathjaxinline] of its offsprings to the valley and a fraction [mathjaxinline] (1-f) [/mathjaxinline] of its offsprings to the plateau.</p>
<p style="text-align: left;">To use the interactive widget below, start by selecting the probability of having a sunny weather, the initial number of creatures that will start in the valley (out of 10 creatures in total), as well as the number of offsprings [mathjaxinline] X_a [/mathjaxinline] that <span style="font-size: 1em;">a creature living in the valley could have when it is sunny or rainy, and </span>the number of offsprings [mathjaxinline] X_b [/mathjaxinline] that <span style="font-size: 1em;">a creature living on top of the plateau could have when it is sunny or rainy.</span></p>
<p style="text-align: left;">The simulation below will show you the possible growth of populations with various types [mathjaxinline] f [/mathjaxinline]. We denote by [mathjaxinline] f^* [/mathjaxinline] the type of the creature that will give rise to the largest population growth.</p>
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<h2 class="hd hd-2 unit-title">Other Applications</h2>
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<h3 class="hd hd-2">Other Applications</h3>
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