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When I use arbitrary numbers for the payoff function for Player 2, I get 2 NEPS, but am not certain about this approach.

QUESTION5 (5) Consider a game with two players, playerl and player 2. Player 1s strategies are up and down, and player 2s strategies are left and rigbt. Suppose that player 1s payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0 Suppose further that player 2s payoff function is such that no two combinations of the players chose n strategies ever give player 2 the same payoff. Choose the right answer among the options below. The game has exactly one NEPS The game has exactly two NEPS The game has exactly four NEPS The game has zero NEPS

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Answer #1

Consider the game with two players “Player 1” and “Player 2”. Now, “P1” have two strategies “UP” and “DOWN” and “P2” have two strategies “LEFT” and “RIGHT”. Now, we have given that “P1’s” payoff function is such that for any combination of the player’s chosen strategies, “P1” always receive payoff equal to “0” and “P2’s” payoff function is such that no two combination of the player’s chosen strategies ever give “P2” the same payoff, => the payoff matrix is given by.

P1P2 LEFT RIGHT UP DOWN 0, c 0,b 0, d 0, a

Now, if “P1” choses “UP” then “P2” will chose either “LEFT” or “RIGHT” depending on “a” or “b” which one is greater. Similarly, if “P1” choses “DOWN” then “P2” will chose either “LEFT” or “RIGHT” depending on “c” or “d” which one is greater and “P1” will always get “0”, => is completely independent of any strategies. SO, there are exactly “2 pure strategy NE”

So, here “2nd” be the correct answer.

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