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
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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
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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
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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 A , S B , U A ( a , b ), U B ( a , b )] where S A = strategies available for player A ( a S A ) S B = strategies available for player B ( b S B ) U A = utility obtained by player A when particular strategies are chosen U B = utility obtained by player B when particular strategies are chosen
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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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This note was uploaded on 11/06/2009 for the course ECON ECON111 taught by Professor Smith during the Spring '09 term at Punjab Engineering College.

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

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