# ch08 - Chapter 8 Strategy and Game Theory Game Theory Game...

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Chapter 8 Strategy and Game Theory

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Game Theory Game theory studies strategic interactions Game theory models portray complex strategic situations in a highly simplified and stylized setting abstract from personal and institutional details to get a mathematically tractable representation Games can be Static: all players move simultaneously Dynamic: at least some players move after others Players’ information about other players can be Complete: example – Cournot pricing game Incomplete: example – Auctions
Basic Concepts In a strategic setting, a person may not always have an obvious choice of what is best may depend on the actions of another person Two basic tasks when using game theory to analyze an economic situation distill the situation into a simple game solve the game results in a prediction about what will happen

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Game Theory A game is an abstract model of a strategic situation All games have three elements players strategies payoffs Games may be cooperative or non-cooperative We will analyze non-cooperative games
Players Each decision-maker in a game is called a player can be an individual, a firm, an entire nation Each player has the ability to choose among a set of possible actions The specific identity of the players is irrelevant no “good guys” or “bad guys”

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Strategies Each player i has a set of possible actions A i Suppose player i ’s possible actions are right ( r ) and left ( l ); then A i = { l , r } A strategy is a probability distribution over A i E.g., play l and r with probability p and 1 – p Pure strategy: play l (or r ) with probability 1 Mixed strategy: play l and r with probability 0.65 & 0.35 Strategies are assumed to be well-defined In noncooperative games, players are uncertain about the strategies used by other players
Payoffs The final returns to the players at the end of the game are called payoffs Payoffs are usually measured in terms of utility monetary payoffs are also used It is assumed that players can rank the payoffs associated with a game

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Notation We will denote a game G between two players ( A and B ) by G [ S , S , U ( a , b ), U ( a , b )] where S A = strategies available for player A ( a S A ) S = strategies available for player B
Prisoners’ Dilemma The Prisoners’ Dilemma is one of the most famous games studied in game theory Two suspects are arrested for a crime The DA wants to extract a confession so he offers each a deal The Deal “if you fink on your companion, but your companion doesn’t fink on you, you get a one-year sentence and your companion gets a four-year sentence” “if you both fink on each other, you will each get a three- year sentence” “if neither finks, we will get tried for a lesser crime and each get a two-year sentence”

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Prisoners’ Dilemma There are 4 combinations of strategies and two payoffs for each combination useful to use a game tree or a matrix to show the payoffs a game tree is called the extensive form a matrix is called the normal form
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