class: center, middle, inverse, title-slide .title[ # Game Theory ] .author[ ###
Dylan Padilla
Spring, 2023
dpadil10@asu.edu
https://dylanpadilla.netlify.app/
] --- # Outline <br/><br/> - What game theory is and how/why it is applied to biology -- - Evolutionarily stable strategies (ESS) and frequency dependent selection -- - Examples --- # Netlogo Model of Hawk-Dove Games <br/><br/> - Download NetLogo from [here](https://ccl.northwestern.edu/netlogo/6.2.0/). NetLogo does have an HTML format but this model is too outdated to be used on it - Download the Hawk - Dove model [here](https://drive.google.com/file/d/1_OowptjexVBiWE0FBsq8pH82uI0dBjEd/view?usp=sharing) --- # Game Theory <br/><br/> - Game Theory is the study of mathematical models of conflict and cooperation -- - Forms the basis of many economic theories, war strategies, sociological theories, and even board games -- - John Maynard Smith emphasized the potential for its use in behavioral ecology --- # Evolutionary Game Theory Evolutionary game theory focuses more on dynamics of strategy change. Influenced by the frequency of the competing strategies in the population <center> .pull-left[ <img src = "img/book.png" height = 300px, width = 200px> ] .pull-right[ ![](img/maynard.jpeg) ] </center> --- # Behavioral polymorphism - Two or more morphs in a population or species - Constant competition/cooperation between them <center> .pull-left[ ![](https://cdn.kqed.org/wp-content/uploads/sites/35/2016/05/DL309-Lizards-three-colors-in-hand.jpg) ] .pull-right[ ![](https://cdn.kqed.org/wp-content/uploads/sites/35/2016/05/DL312_Lizards_RockPaperScissors_500.gif) ] </center> --- # Game theory features - Individual players make decisions -- - The players will behave rationally, and according to some criterion of self-interest -- - The strategy of each individual will depend in part by the strategies of the other players <center> ![](img/monopoly.jpeg) --- # Evolutionary game theory models .pull-left[ <img src = "img/prisonersdilemma.png" width = 500px, height = 500px> ] .pull-right[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years ] --- # Evolutionary game theory models .pull-left[ <img src = "img/prisonersdilemma.png" width = 500px, height = 500px> ] .pull-right[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Payoff Matrix</span> ] --- # The prisoner's dilemma .pull-left[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Payoff Matrix</span> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-1-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # The prisoner's dilemma .pull-left[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Payoff Matrix</span> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-2-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # The prisoner's dilemma .pull-left[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Payoff Matrix</span> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-3-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # The prisoner's dilemma .pull-left[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Payoff Matrix</span> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-4-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # The prisoner's dilemma .pull-left[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Payoff Matrix</span> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-5-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # The prisoner's dilemma .pull-left[ <span style='color: orange;'>Dylan</span> and <span style='color: skyblue;'>Katy</span> were arrested the same day! - 2 years for drugs - If confess, 1 year and the other 10 years - If deny, 10 years and the other 1 year - If both confess, both get 3 years <br> # <span style='color: skyblue;'>Nash Equilibrium</span> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-6-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # Hawk-Dove game <center> .pull-left[ <img src = "img/hawk.gif" width = 200px, height = 200px> <img src = "img/dove.gif" width = 300px, height = 200px> ] </center> .pull-right[ 1. Two competing organisms exploit the same resource 2. Competition is by displays (dove strategy) or fights (hawk strategy) 3. <span style='color: orange;'>Hawks always beat doves in competition</span> 4. <span style='color: orange;'>When hawks meet hawks or doves meet doves, they get half of the resource</span> Payoffs: - get resources: 50 - lose resources: 0 - lose fight (injury): 100 - cost of dove display: 10 ] --- # What is the best strategy? <span style='color: orange;'>Hawk</span> or <span style='color: skyblue;'>Dove</span>? <center> .pull-left[ `\(V=50\)` `\(C=100\)` `\(c=10\)` <br> ![](img/surprised.gif) ] </center> .pull-right[ <img src="index_files/figure-html/unnamed-chunk-7-1.png" width="100%" style="display: block; margin: auto;" /> ] --- # What is the best strategy? <span style='color: orange;'>Hawk</span> or <span style='color: skyblue;'>Dove</span>? <img src="index_files/figure-html/unnamed-chunk-8-1.png" width="55%" style="display: block; margin: auto;" /> --- # What is the best strategy? <span style='color: orange;'>Hawk</span> or <span style='color: skyblue;'>Dove</span>? .pull-left[ <img src="index_files/figure-html/unnamed-chunk-9-1.png" width="90%" style="display: block; margin: auto;" /> ] .pull-right[ <br><br> The best strategy dependes on the frequency of other strategies <span style='color: orange;'>Hawks</span>: - Better than doves when many doves - Worse than doves when many hawks <span style='color: skyblue;'>Doves</span>: - Better than hawks when many hawks - Worse than hawks when many doves ] --- # Modeling the dynamics of the population .pull-left[ <img src="index_files/figure-html/unnamed-chunk-10-1.png" width="90%" style="display: block; margin: auto;" /> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-11-1.png" width="40%" style="display: block; margin: auto;" /> - There is an equilibrium hawk frequency, adding individuals of each strategy lowers fitness relative to the alternative strategy - No best "pure" strategy, no <span style='color: orange;'>Evolutionary Stable Strategy</span> - Fitness for strategies are **frequency dependant** ] --- # Modeling the dynamics of the population .pull-left[ <img src="index_files/figure-html/unnamed-chunk-12-1.png" width="90%" style="display: block; margin: auto;" /> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-13-1.png" width="40%" style="display: block; margin: auto;" /> - There is an equilibrium hawk frequency, adding individuals of each strategy lowers fitness relative to the alternative strategy - No best "pure" strategy, no <span style='color: orange;'>Evolutionary Stable Strategy</span> - Fitness for strategies are **frequency dependant** ] --- # Modeling the dynamics of the population .pull-left[ <img src="index_files/figure-html/unnamed-chunk-14-1.png" width="90%" style="display: block; margin: auto;" /> ] .pull-right[ <img src="index_files/figure-html/unnamed-chunk-15-1.png" width="50%" style="display: block; margin: auto;" /> - The fitness of individuals is lower at equilibrium than in all dove population - <span style='color: orange;'>Selection acts to lower the population mean fitness</span> ] --- # Time for Netlogo <img src = "img/netlogo.png" width = 800px, height = 500px>