4. (10 points) Consider the following 2 x 2 game: Player 2 L R T 1,0 2,9 B 3, 4

Question

4. (10 points) Consider the following 2 x 2 game: Player 2 L R T 1,0 2,9 B 3, 4 2, a (a) (1 point) If player 2 plays L, what is (are) player 1's best response(s)? (b) (2 points) Does player 1 have a strictly dominant strategy? If so, what? (c) (2 points) Does player 1 have a weakly dominant strategy? If so, what? (d) (3 points) For which values of a does player 2 have a weakly dominant strategy? For which values of a does player 2 have a strictly dominant strategy? (e) (2 points) If player 2 plays L with a probability of 2/3. What is the expected payoff from playing T for player 1?

Explanation / Answer

A) If player 2 plays L then player 1 will play B because player 1 gets payoff=3 which is greater than 1. Thus best response of player 1 is B.

B) Dominant startegy is a strategy which a player plays irrespective of what other player. Or strategy which gives always strictly higher payoff as compared to any strategy is known as strictly dominant strategy. Thus player 1 dont have dominant strategy.

C) Weakly dominated startegy is a strategy whiich gives atleast equal to other strategy payoff for some rival strayegy and strictly higher for atleast one action of other player. Thus player 1 has weakly dominant strategy as B.

D) For having player 2, a weakly dominant strategy alpha=a=4

For strictly dominant strategy alpha=a>4.

E) Expected payoff from playing T for player 1=2/3*1+1/3*2=4/3

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