1.2 predator prey example

7/31/2019 1.2 Predator Prey Example

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Introduction: Game Theory

Models of strategic interactions: Outcomes depend on more than one players decision

The decisions for one player cannot be separated from tho

of others!

Models miss (important?) aspects of reality That is why they are models


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Wide set of applications

War: Why do some countries arm heavily while others dnot?

Tragedy of the commons: Why do we need internationaagreements on fishing and how should they be structured

Markets: What will happen if two companies are allowedmerge?


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Wide Set of Applications

E-commerce: How should an on-line auction be structuto maximize revenue? How should sellers be policed?

Legal: How should random audits of taxes be conducte Sports: Should a soccer player adjust the fraction of tim

that s/he kicks penalty kicks to a goalies right or left basethe goalie?


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Game Theoretic Models

Provide insights when interactions affect incentives

Applications in many fields

Methodology/tool box tools will vary with the applications!


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Questions About Models

Players: who makes the decisions? Strategies: what are the actions available? Timing: who does what and when? Information: what do players know when choosing? Payoffs: what happens as a function of the actions? and,

what motivates players? ``Solution : how do we predict what will happen?


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Course Outline

Normal Forms

Extensive Forms

Repeated Games

Incomplete Information: Bayesian Games


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Normal Form

An example of a normal form game

The formal model The main ingredients: Players, Strategies, Payoffs

Normal Form games Dominance Equilibrium


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Predator Prey Games

Lets examine an analysis based on a paper by Chen Shi aSheng Bao 2008 ``A Game Theory Based Predation BehaModel (Center for Game Theory in Economics Archive, 2010 Conference)http://www.gtcenter.org/Archive/2010/Conf/Chen956.pdf

Strategies: Active or Passive Predators - active: dragonfly, passive: spider Prey active: fly, passive: mealybugs
http://www.gtcenter.org/Archive/2010/Conf/Chen956.pdfhttp://www.gtcenter.org/Archive/2010/Conf/Chen956.pdf


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``Payoffs

Predator: expected calories captured less expected calorexpended

Active raises calories expended and captured

Prey: penalty for expected death rate less expected caloriesexpended

Active raises calories expended and lowers chances of death

But the expected capture and expended calorie rates are


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Predator/Prey

Large Mammal estimates

Pred\Prey Active PassiveActive 1.7, -.8 3,-1Passive 1.6, -.7 0,0


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Predator/Prey




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Predator/Prey




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Predator/Prey




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Are most large mammals active?

predators: lions, tigers, leopards, wolves, coyotes, dogs,cats.

prey: deer, antelope, zebras, horses, mice, But not all

Simplified game - could enrich strategy set and payoff structure


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Predator/Prey

Small predator prey insects

Pred\Prey Active PassiveActive 2, -7 6, -8Passive 3, -6 -1,0


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Predator/Prey




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Predator/Prey




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Predator/Prey




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Predator/Prey



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Predator/Prey

No stable pair of strategies: prey wants to match, predawants to mismatch



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Predator/Prey

No stable pair of strategies: prey wants to match, predawants to mismatch

Randomization: mixed strategies


1.2 predator prey example

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