NashTrigger - Play { b } in all periods as long as player 2...

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Notes on Nash Trigger Strategies Daniel Egel November 10, 2008 1 Nash Trigger Strategy Lets take a look at one of our familiar examples: Player 1 Player 2 i j k l a 1,2 2,4 3,1 5,3 b 2,1 3,3 4,2 4,4 c 1,2 3,2 1,1 4,2 Now if only Nash threat points are available that means that player 1 would punish by playing { c } and player 2 would punish by playing { j } . Thus an individually rational play in this setup would have to beat this point. Note the following: The stage game Nash is { c;j } . Thus there are only two individually rational plays: { b;l } , { a;l } Question: Can the individually rational stage-game outcome ( b,j ) be supported by Nash trigger strategies? The answer is no since it is not individually rational. 1 Lets consider another point, say { b;l } . From class we learned that any individually rational play can “support” a SPE. Lets show that this is true for this point. Assume a discount rate of δ = 0 . 9 and a game with infinite periods. A Nash trigger strategy for these two players would be Player 1:
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Unformatted text preview: Play { b } in all periods as long as player 2 has always played { l } Play { c } if player 2 has ever played something other than { l } Player 2: Play { l } in all periods as long as player 2 has always played { b } Play { j } if player 2 has ever played something other than { b } So the rst question is who might have an incentive to deviate from the cooperation point. Clearly it is player 1. Now let see if our strategy can convince player 1 not to deviate: 1 Hence the confusion in class. 1 If he cooperates he gets 4 1- = 40 If he defects he gets 5 + 3 1- = 32 So clearly he will not want to defect Is it ex-post rational? In other words, will player 1 have any incentive to deviate from this strategy? Given that they are playing at the threat point, { c;j } neither player will have an incentive to deviate Thus it is a SPE 2...
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This note was uploaded on 12/25/2010 for the course PO 137 taught by Professor Power during the Fall '10 term at University of California, Berkeley.

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NashTrigger - Play { b } in all periods as long as player 2...

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