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2350pqset0005gametheoryAnswers - Game 3 There is no N.E in...

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Y ORK U NIVERSITY - AS/ECON2350 – V.B ARDIS A NSWERS TO P RACTICE S ET 5 1. 3. Game 1: The unique N.E. is (U,R)~(0,0) since this is the only strategy combination such that neither player has an incentive to deviate (act differently) given what the other did. Game 2: This game has two N.E. in pure strategies, (U,L)~(2,1) and (D,R)~(1,2) and one N.E. in mixed strategies such that player 1 chooses between U and D with probabilities 2/3 and 1/3 respectively, player 2 chooses between L and R with probabilities 1/3 and 2/3 respectively, and each player's expected payoff is 4/3.
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Unformatted text preview: Game 3: There is no N.E. in pure strategies in this game. This is a zero-sum game, that is, the payoffs in each box add up to zero. an so in every outcome 'one player's gain is the other player's loss' . Here the losing player always `regrets her action' (i.e., wishes to deviate) which means there is no N.E. in pure strategies. The mixed-strategy equilibrium entails each person assigning probability 1/2 to each of her actions, thereby receiving an expected payoff of 0. 5. 6. See notes. 7. See notes ....
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