6-Game Theory

# 6-Game Theory - Game Theory Econ 382 Brennan Platt Ph.D...

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Game Theory Econ 382 Brennan Platt, Ph.D.

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Crucial Skills Models: •(Applicable to any models of strategic interaction) Set up: •Terminology (Actions, Payoffs, Pure / Mixed Strategies) •Conditions for Nash equilibrium Solve: •Iterated Elimination of Dominated Strategies •Nash Equilibrium •Verify a repeated game Nash Equilibrium Illustrate: •Draw a game tree •Plot a Best Response function to show a Nash Equil. Concepts: •Interpretation of Nash Equilibrium •Interpretation of mixed equilibrium •Credible threats
Game Theory A methodology for modeling strategic interaction Immediately useful to study oligopolies Used increasingly in every field of economics Advantages: Specifically models the reaction to choices of others Helps us identify stable behavior in these strategic interactions

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Components of a Game Theoretic Model Actors : Players. Not necessarily adversaries. Preferences : Payoffs. (utility, profit, or anything else) Choices : Actions. Must have some impact on the payoffs of all players. Players may have different sets of available actions. Once chosen, it is called a strategy A strategy profile indicates the action chosen by each player.
Components of a Game Theoretic Model Constraints : Can have any typical constraint, plus Agency: Cannot control the strategies of others Order of play: Choices may occur in some sequence, or simultaneously. Information: Who knows what and when

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Assumptions All players understand the game Each knows the payoffs to all players for each strategy profile. Once the game ends, everyone will know what strategy was played All possible actions are specified Do they have an option not to play?
Representing a game Normal Form Game Choices of each player are all simultaneous Shown in a payoff matrix or function Extensive Form Game Choice occur in order Shown in a

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## This note was uploaded on 03/17/2010 for the course ECON 388 taught by Professor Mcdonald,j during the Spring '08 term at BYU.

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6-Game Theory - Game Theory Econ 382 Brennan Platt Ph.D...

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