# lecture13 - Lecture XIII: Repeated Games Markus M. M¨obius...

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Unformatted text preview: Lecture XIII: Repeated Games Markus M. M¨obius April 19, 2004 • Gibbons, chapter 2.3.B,2.3.C • Osborne, chapter 14 • Osborne and Rubinstein, sections 8.3-8.5 1 Introduction So far one might get a somewhat misleading impression about SPE. When we first introduced dynamic games we noted that they often have a large number of (unreasonable) Nash equilibria. In the models we’ve looked at so far SPE has ’solved’ this problem and given us a unique NE. In fact, this is not really the norm. We’ll see today that many dynamic games still have a very large number of SPE. 2 Credible Threats We introduced SPE to rule out non-credible threats. In many finite horizon games though credible threats are common and cause a multiplicity of SPE. Consider the following game: 1 B M T L C R 3,1 0,0 5,0 2,1 1,2 3,1 1,2 0,1 4,4 The game has three NE: (T,L), (M,C) and ( 1 2 T + 1 2 M, 1 2 L + 1 2 C ) Suppose that the players play the game twice and observe first period actions before choosing the second period actions. Now one way to get a SPE is to play any of the three profiles above followed by another of them (or same one). We can also, however, use credible threats to get other actions played in period 1, such as: • Play (B,R) in period 1. • If player 1 plays B in period 1 play (T,L) in period 2 - otherwise play (M,C) in period 2. It is easy to see that no single period deviation helps here. In period 2 a NE is played so obviously doesn’t help. • In period 1 player 1 gets 4 + 3 if he follows strategy and at most 5 + 1 if he doesn’t. • Player 2 gets 4 + 1 if he follows and at most 2+1 if he doesn’t. Therefore switching to the (M,C) equilibrium in period 2 is a credible threat . 2 3 Repeated Prisoner’s Dilemma Note, that the PD doesn’t have multiple NE so in a finite horizon we don’t have the same easy threats to use. Therefore, the finitely repeated PD has a unique SPE in which every player defects in each period. 2,-1 0,0 1,1-1,2 C D C D In infinite horizon, however, we do get many SPE because other types of threats are credible....
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## This note was uploaded on 05/19/2010 for the course DFDAS 220 taught by Professor Ding during the Fall '10 term at Academy of Art University.

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lecture13 - Lecture XIII: Repeated Games Markus M. M¨obius...

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