Week 9 B

Week 9 B - COMM 295 November 4, 2010 Game Theory (Part 2)...

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COMM 295 November 4, 2010 Game Theory (Part 2)
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Topics Examined Maximin Strategies Repeated Prisoners’ Dilemma with Punishment Infinite versus finite repeated games Introduction to sequential games Solution through backward induction in extensive form representation of game
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Maximin A maximin strategy is played in order to maximize the minimum possible payoff you might receive This is done if the consequences of your opponent choosing a strategy different than the one predicted by Nash (i.e., a mistake is made), is severe A maximin strategy is appropriate if the player is highly risk averse The game can be solved with just one firm playing Maximin or both firms playing maximin
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A Uses Maximin Strategy Firm B Don’t Invest Invest Firm A Don’t Invest 0, 0 -10 , 10 Invest -100 , 0 20, 10 For A, identify the worst outcome for each of B’s strategies Nash Maximin for A is to not invest because –10 > -100 Maximin Equilbrium
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Mixed Strategy • All of the games we will examine in this course used “pure” strategies • A mixed strategy is one where players randomly choose what action to choose • Players must use a mixed strategy when playing “Rocks, Paper, Scissors if they wish to be successful • Some games do not have a pure strategy equilibrium, but if this is the case, a mixed strategy equilibrium always exists
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Consider This Prisoners’ Dilemma Firm B Price Low Price High Firm A Price Low 10, 10 100, -50 Price High -50 , 100 50, 50 Nash Equilibrium Firms desire this collusive outcome
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Temptation to Cheat The reason for the prisoners’ dilemma is that firm A has an incentive to cheat by pricing low if firm B prices high Why? Earning 100 by cheating with low price is better than earning 50 by non-cheating Firm B faces same incentive to cheat; in Nash equilibrium, both firms cheat and both firms are worse off compared to not cheating Firms are not able to threaten each other with future punishment since game happens just once
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Repeated Play Suppose the two firms played the previous game over and over again, indefinitely Can this repetition help the firms avoid the prisoners’ dilemma (i.e., support the collusive outcome at the bottom right of the payoff matrix)? Consider the following strategy:
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This note was uploaded on 01/03/2011 for the course COMM 290 taught by Professor Brian during the Winter '09 term at UBC.

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Week 9 B - COMM 295 November 4, 2010 Game Theory (Part 2)...

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