Consider the following game between player 1, who chooses among strategies U, M, and D, and...

Consider the following game between player 1, who chooses among strategies U, M, and D, and player 2, who chooses among strategies A, B, and C. The most reasonable prediction in this game is what? (Show your steps)

	A	B	C
U	10, 5	5, 5	8, 6
M	8, 7	5, 8	6, 5
D	5, 10	9, 6	7, 7

Solutions

Expert Solution

If player 1 plays strategy U, it is best for player 2 to play strategy C because it earns player 2 the highest payoff. So the strategy becomes (U,C).

If player 1 plays strategy M, player 2 will be better off by playing B (because payoff 8 is greater than payoff 7 and 5 from choosing A and C respectively). So, the strategy becomes (M,B).

If player 1 plays D, player 2 will be better off by choosing A (because payoff 10 is greater than 6 and 7 from choosing B and C respectively). So the strategy becomes (D,A).

Now, if player 2 plays strategy A, it is best for player 1 to play U (because payoff 10 is greater than 8 and 5 from choosing M and D respectively). So the strategy becomes (U,A).

If player 2 plays strategy B, it is best for player 1 to play D. So the strategy becomes (D,B).

If player 2 plays strategy C, player 1 will be better off by choosing U. So, the strategy becomes (U,C).

Therefore, the Nash equilibrium or, most reasonable prediction in this game is (U,C) with payoff (8,6).

Rahul Sunny answered 1 year ago

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