game theory question. Consider the following game played by three players: P1, P

Question

game theory question.

Consider the following game played by three players: P1, P2, and P3. P3 P2 P2 L R L R P1 M2,2,01,2,1 M1,2,01,0,2 D 3,1,21,0,2D 0,2,31,2,2 P1 chooses the row (U, M or D), P2 chooses the column (L or R) and P3 chooses the matrix (A or B) The numbers in the matrices correspond to the payoffs for each player in their respective order. For example, if the players play the strategy profile (U,R,A) then the payoff is (2,1,1), so P1 gets 2, P2 gets 1 and P3 gets 1. Each player has a weakly dominant strategy. Assume all players are rational and care about maximizing their payoff in the game In your responses, write the strategies with capital letters only: P1 weakly dominant strategy is P2 weakly dominant strategy is P3 weakly dominant strategy is Therefore, the strategy profile that will be played is (include the parenthesis for the profile)

Explanation / Answer

Weakly dominant strategy for P1 is M & D because payoff from M & D as response for any of the strategy of P2 is lesser than available other strategy U

SImilalry weakly dominant strategy for P2 is R for the same reason mentioned above

For player 3 we have folwoing reasoning after eliminating weakly dominant strategies we get Pure Nash Equilibrium as (A,U,L), (B,U,L)

From AUL P3 has payoff of 1 and from BUL P3 has payoff of 2

For P3 weakly dominant strategy is A

Ultimate strategy profile that would be played is (B,U,L)

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