4. Consider the following 3 X 5 game between players R (Row) and C Column). The

Question

4. Consider the following 3 X 5 game between players R (Row) and C Column). The first element in any square represents the payoff of R and the second element, the payoff to C L1 | L2 | M | R1 | R2 1,3 | 0,5 | 3,4 | 3,2 | 2,4 C2,41,20,34,52,3 D3,52,31,23,40,2 See if you can find any strategies for player C that is strictly dominated by another; do the same for player R. Eliminate these dominated strategies and consider the reduced game. Repeat this same step of deletion of strictly dominated strategies in the reduced game. Continue this process until you can reduce the game no further i.e. no player has a dominated strategy At this point, you should have arrived at a 2 X 2 game. Find all the Nash equilibria for this game, including mixed-strategy ones.

Explanation / Answer

So we have R2 dominates M for the column player. Then C dominates U for the row player. Then we have L1 dominates R2 for the column player. Then L1 dominates L2 for the column player. So we have the reduced game (C,D) for row player and (L1,R1) for the column player. There are thus 2 Nash equilibria in pure strategies in this game and these are given by (D,L1) and (C,R1) with pay offs of (3,5) and (4,5) for the row and column players respectively.

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