Question

5. Consider the following game matrix of payoffs: M t 1,1 5,4 4,6 0,2 4,7 3,1 3,0 b 2,0 2,12 Find the pure strategy Nash Equi libria for the above game, ass uming that it is a simultaneo us a) move game. b) Suppose Column moves first, and Row moves sequentially after that. Draw a game tree and solve for the equilibrium path. Would Column want to move first? Would Row want to let them? c) Answer the same questions in (b) a bove, only assum ing that Row would move first! Would Row want to do so? Would Column want to allow them to move first? Explain. E A

Answer 1

Date a)- Da Page no. If player a moves t, the best response of player 2 is to choose R. If player 2 choose R, the best response og player I is to choose t.. So, It is a nash equilibrium t RJ. If player 1 chooses M, Player 2 choose t If player 2 chooses L, Player I chooses M. so, This is also a nash equilibrium [M, L] If player I chooses b, Player 2 choose M. If player 2 chooset M Player I chooses t. So If is not a nash equilibrium. Ans - [ t, R] and [m, L] - Nash equilibria.. (11)

Ans - [+, RJ and [m, L ] = Nash equilibria. (1,1) (4,7) player 1 m Player a TM Player 22,0) Ers, u) m 10, 2) Ces column moves) > Player 2, 12) + 114,60 6 (31) As player 1 get maximum when he chooses Ml given that player 2 chooses L) - G. Similarly, (, 4) & (4,6) DELTA My NoteBook

Page no Game reduce to Player 1 (M) (4,7) Player M Player 1 (T) (5, 4) -Player 1 (T) (46) The best strategy for Player 2 is to choose Las he will get maxi pay off. so equilibrium = 1 m2 Row let = {1, M} = {4,7}. Also, Yes -5492 N them allow. 27 c) If Row move first means Player 1 choose first. I t Player & (R) (4,6) Player 1 m Player 2 (2) (4,7) - Player 3 → (M) (2,12) Player 1 is indifferent between Choosing t or choosing m so, equilibrium are again tea (M, L) and (A, R. Ty, Colermon let Row allow to move first of