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slide4-game-theory

# slide4-game-theory - Game Theory Professor Erkut Ozbay...

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Game Theory Professor Erkut Ozbay Economics 300

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Definition Game theory is the study of mathematical models of conflict and cooperation between intelligent and rational decision makers. Rational: each individual maximizes her expected utility Intelligent: individual understands situation, including fact that others are intelligent rational decision makers
Game Theory Game theory lets us study multi-person decision problems Use game theory to model: Trading process (auctions, bargaining) Competition among firms Sporting events Voting Military decisions Competition or collusion among countries in choosing tariffs, trade policies, environmental standards, etc.

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What is a game? A set of rules specifying: Players Alternatives (actions players choose from) Order of play Outcomes and payoffs
Normal form of a game Players: I = {1, 2, …, N } • Action sets: A 1 , A 2 ,…, A N Players simultaneously choose their actions a 1 , a 2 ,…, a N Payoffs are realized U i ( a 1 , a 2 ,…, a N ) for each player i

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Example: The Prisoner’s Dilemma Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one confesses against the other and the other remains silent, the betrayer goes free and the silent one receives the full 9-year sentence. If both stay silent, both prisoners are sentenced to only 1-year in jail for a minor charge. If each betrays the other, each receives a 6-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?
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slide4-game-theory - Game Theory Professor Erkut Ozbay...

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