Question

(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between a strategy that is a best response versus a strategy that is strictly dominant. (b) (6) Consider the following game: player 2 D E F C A 3,7 7,3 1,2 4,3 player 1 B 8,9 8,5 2,8 5,2 C 0,10 7,01,9 2,2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following game: player 2 R. TI 10.4 | 1,2 | 1,0 player 1 M 6,4 2,0 3,0 В|9,0 | 3,3 | 4,8 Find all the Nash equilibria (including mixed strategy ones).

Answer 1

a) in game theory the best response is the strategy which produce the most favourable outcome for a player , taking other players strategies , the concept of a best respore is central to John Nash's best known contribution the Nash equilibrium , the point at which each player in a game had selected the best response to the other players strategies. A strategy is strictly dominant if , regardless of what any other players do the strategy earn a player a strictly higher pay off than any other . Strictly dominant strategy exists for one player in the game , that player will play that strategy in each of the games Nash equilibrium .if both players have a strictly dominant strategy , the game has only one unique Nash equilibrium .

In the first round of 1 ESDS, we eliminate player 2, L strategy since C strictly diameter L. the games become the second round of 1 ESDS is harder none of the remaining pure strategies for either player of strictly dominates any of the other we can use mixed strategies to eliminate player B strategy suppose player plays both T and M with strictly but not B so mixed where p elementof (0, 1) payoffs from this strategy are v_B (sigma B, C) = 1 p + 2 (1 - p) = 1 p + z- 2p - 2 - p - U_B U_B(sigma_B, R) = 1p + 3(1 - p) = 3 - 2p = u_B (B, R) the mixed strategy sigma_b strictly derivate B and we can eliminate B