Lect04_Slides

# Lect04_Slides - Simultaneous Decision making without...

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Simultaneous Move Games Decision making without knowledge of the strategy choice of opponents

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Simultaneous Moves Arise when players have to make their strategy choices simultaneously without knowing the strategies that have been simultaneously, without knowing the strategies that chosen by the other player(s). – Student studies for a test; the teacher writes questions. f d d l d d h h d l d k – 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. 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.
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 fi t d th l l ff i li t d d first and the column player’s payoff is listed second. Column Player R S C1 S C2 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 the payoffs sum to zero (or some other constant) allows us to write a simultaneous move game in normal form more simply: Warden P i Cli b W ll Guard Wall 1 Inspect Cells 1 Payoffs are shown only for the Prisoner; the Prisoner Climb Wall Dig Tunnel 1 1 Warden’s payoffs are the negative of the prisoner’s payoff prisoner s payoff
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. After 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 opponent(s) The same is true of the opponent(s) opponent(s). The same is true of the opponent(s).

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Coordination Game Example How would you play this game?
Example of the Role of Beliefs Consider the pure coordination game.

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