Lect04_Slides

Lect04_Slides - Simultaneous SimultaneousMoveGames Decision...

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multaneous Move Games Simultaneous Move Games Decision making without knowledge of the strategy choice of opponents
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multaneous Moves Simultaneous Moves Arise when players have to make their strategy choices multaneously without knowing the strategies at ave een simultaneously, without knowing the strategies that have been chosen by the other player(s). – Student studies for a test; the teacher writes questions. – Two firms independently decide whether or not to develop and market a new product. While there is no information about what other players will actually choose, we assume that the strategic choices available to each player are known by all players. layers ust think not only about their own est strategic Players must think not only about their own best strategic choice but also the best strategic choice of the other player(s). We will consider both discrete and continuous strategy spaces.
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Normal or Strategic Form A simultaneous move game is depicted in “Normal” or “Strategic” form using a game table that relates the strategic choices of the players to their payoffs. The convention is that the row player’s payoff is listed t d l l’ ff i li t d d first and the column player’s payoff is listed second. Column Player Row Player Strategy R1 Strategy C1 a , b Strategy C2 c , d Strategy R2 e , f g , h For example, if Row player chooses R2 and Column player chooses C1, the Row player’s payoff is e and the Column player’s payoff is f.
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Special Zero Sum Form For zero (or constant sum games), knowing e payoffs sum to zero (or some other the payoffs sum to zero (or some other constant) allows us to write a simultaneous move game in normal form more simply: Warden i li bWl l Guard Wall Inspect Cells ayoffs are shown only for the Prisoner; the Prisoner Climb Wall 1 1 Dig Tunnel 1 1 Payoffs are shown only for the Prisoner; the Warden’s payoffs are the negative of the risoner’s payoff prisoner s payoff
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The Role of Beliefs When players move simultaneously, what does it mean to say that in equilibrium strategies are a mutual best response? One cannot see what the other is doing and condition your behavior on their move. In simultaneous move games, rational players consider all of the strategies their opponents may take and they form beliefs (subjective probabilities) about the likelihood of each strategy their opponent(s) could take. fter forming these beliefs rational players maximize After forming these beliefs, rational players maximize their expected payoff by choosing the strategy that is a best response to their beliefs about the play of their pponent(s) The same is true of the opponent(s) opponent(s). The same is true of the opponent(s).
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oordination Game Example Coordination Game Example How would you play this game? y py g
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Example of the Role of Beliefs Consider the pure coordination game.
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This note was uploaded on 12/26/2011 for the course ECON 171 taught by Professor Charness,g during the Fall '08 term at UCSB.

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Lect04_Slides - Simultaneous SimultaneousMoveGames Decision...

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