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Class activity: more on sequential move games, backward induction and reputation– ultimatum and centipede games

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Suggested reading Kreps, D. M Microeconomics for Managers. Norton. Chapter 21 Allen et al Managerial Economics. Norton. Chapter 11 Carmichael, F A Guide to Game Theory, Pearson. Chapter 4 Rasmusen, E Games and Information, Blackwell. Chapter 12

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An ultimatum game AB offer accept reject 0, , 0.05 A offers B a share of a pie If B rejects the offer the pie is lost What will be the outcome of this game?

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Centipede games Example 1: a small centipede ABA 2, 1 10, 01, -103, 3 D d D R r R What is the likely outcome if both players are rational and understand game theory?

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Small centipede Outcome is A chooses D at the start ABA 2, 1 10, 01, -10 3, 3 D d D R r R A anticipates that B would choose r given the chance as B should anticipate that A will choose R

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Centipede games Example 2: a longer centipede ABA 2, 1 10, 2 3, 3 4, 4 D d D d D R r R r R What is the likely outcome? 10, 0 BA 1, -10

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Centipede games Example 2: a longer centipede ABA 2, 1 10, 2 3, 34, 4 D d D d D R r R r R Likely outcome is still that A chooses D at start 10, 0 BA 1, -10

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The full-size centipede game A B A 0, 24, 1 1, 0 D d D d D d R r R r R r What is the outcome predicted by game theory? Whats wrong with this outcome? 3, 100 BA 102, 99 B 101, , 101 each player chooses between right (continues game) or down

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The full-size centipede game A B A 0, 24, 1 1, 0 D d D d D d R r R r R r 3, 100 BA 102, 99 B 101, , 101 each player chooses between right (continues game) or down Likely outcome is still that A chooses D at start – but this seems unlikely

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Implications The analysis of ultimatum and centipede games suggests limitations of the game theoretic idea of backward induction –Outcomes seem unlikely – players are actually better off if they make mistakes In experiments players rarely choose the equivalent of down in their first move But as the game progresses they are more likely to choose the equivalent of down And if the game is repeated players tend to choose down earlier

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