Lecture 4 - Game Theory - Econ 102B Game Theory Basic...

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Econ 102B Game Theory
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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
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Basic Concepts 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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Basic Concepts A game is an abstract model of a strategic situation Three elements to a game players strategies payoffs
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Players Each decision maker is a player may be individuals, firms, countries, etc. have the ability to choose from among a set of possible actions
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Strategies Each course of action open to a player is a strategy it may be a simple action or a complex plan of action S i is the set of strategies open to player i s i is the strategy chosen by player i , s i S i
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Payoffs Payoffs are measured in levels of utility obtained by the players players are assumed to prefer higher payoffs to lower ones u 1 ( s 1 , s 2 ) denotes player 1’s payoff assuming she follows s 1 and player 2 follows s 2 u 2 ( s 2 , s 1 ) would be player 2’s payoff under the same circumstances
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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
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Prisoners’ Dilemma 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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Extensive Form for the Prisoners’ Dilemma Each node represents a decision point The dotted oval means that the nodes for player 2 are in the same information set player 2 doesn’t know player 1’s move
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Normal Form for the Prisoners’ Dilemma Sometimes it is more convenient to represent games in a matrix
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Nash Equilibrium Nash equilibrium involves strategic choices that, once made, provide no incentives for players to alter their behavior best choice for each player given the other players’ equilibrium strategies
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Nash Equilibrium s i is the best response for player i to rivals’ strategies s -i , denoted s i BR i ( s -i ) if i i -i
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Nash Equilibrium In a 2-player game, ( s * 1 , s * 2 ) is a Nash equilibrium if
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Nash Equilibrium Drawbacks to Nash equilibrium there may be multiple Nash equilibria it is unclear how a player can choose a best- response strategy before knowing how rivals will play
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This note was uploaded on 10/15/2010 for the course ECONOMICS Econ 105A taught by Professor Someone... during the Spring '09 term at UC Riverside.

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Lecture 4 - Game Theory - Econ 102B Game Theory Basic...

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