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Unformatted text preview: 1. An example of an appropriate payoff matrix is John George Payoffs need to follow the rule ) , ( ) , ( Z Y X X i i < for Y Z and i = George, John. In the above matrix, all offdiagonal cells are Nash equilibria. 2. (a) The set of Nash equilibria is {(U, L), (U, R), (D, R)} The set of asymmetric Nash equilibria is {(U,L)} (b) Yes, since the set of strategies that satisfy ) , ( ) , ( * 2 1 1 * 2 * 1 1 s s s s , for all s 1 also satisfies ) , ( ) , ( * 2 1 1 * 2 * 1 1 s s s s , for all s 1 . 3. (a) Strategy 100 is weakly dominated by strategies 99 and 98. Without loss of generality, consider player one, and first compare strategies 100 and 99: payoffs from these strategies are equal for s 2 98, while ) 99 , 100 ( 97 99 ) 99 , 99 ( 1 1 = = and ) 100 , 100 ( 100 101 ) 100 , 99 ( 1 1 = = . Now compare strategies 100 and 98: payoffs from these strategies are equal for s 2 97 and s 2 =100, while ) 98 , 100 ( 96 98 ) 98 , 98 ( 1 1 = = and ) 99 , 100 ( 97 100 ) 99 , 98 ( 1 1 = = . (b) Strategy 100 is not strongly dominated by any strategy. To see this, note that the set of strategies that strongly dominate 100 is a subset of the set of strategies that weakly dominate 100. Thus, the only possible strategies would be 98 and 99. But we saw in part (a) that the payoff from playing 100 is equal to the payoff from playing 98 in all but two cases. Likewise, the payoff from playing 100 is equal to the payoff from playing 99 in all but two cases. (c) The game is dominance solvable only under weak dominance....
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 Spring '08
 BASU

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