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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.pdf7/31/2019 1.2 Predator Prey Example
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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
Large Mammal estimates
Pred\Prey Active PassiveActive 1.7, -.8 3,-1Passive 1.6, -.7 0,0
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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
Large Mammal estimates
Pred\Prey Active PassiveActive 1.7, -.8 3,-1Passive 1.6, -.7 0,0
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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
Small predator prey insects
Pred\Prey Active PassiveActive 2, -7 6, -8Passive 3, -6 -1,0
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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
Small predator prey insects
Pred\Prey Active PassiveActive 2, -7 6, -8Passive 3, -6 -1,0
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Predator/Prey
Pred\Prey Active PassiveActive 2, -7 6, -8Passive 3, -6 -1,0
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Predator/Prey
No stable pair of strategies: prey wants to match, predawants to mismatch
Pred\Prey Active PassiveActive 2, -7 6, -8Passive 3, -6 -1,0
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Predator/Prey
No stable pair of strategies: prey wants to match, predawants to mismatch
Randomization: mixed strategies
Pred\Prey Active PassiveActive 2, -7 6, -8Passive 3, -6 -1,0
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