Midterm Exam Worksheets With Answers - Prof. James Peck - The Ohio State University, Department Of Economics - 2010 Page 4

4. (20 points) For the normal-form game depicted below, ﬁnd the mixed-

strategy Nash equilibrium.

player 2

player 1 T

1, 0

−1, 3

−1, 2

1, 1

Answer:

In the MSNE, player 1’s strategy is of the form (p, 1 − p) and player 2’s

strategy is of the form (q, 1 − q). For player 1 to be willing to mix, he must

be indiﬀerent between choosing T and B, so we set his expected payoﬀ from T

equal to his expected payoﬀ from B:

q(1) + (1 − q)(−1) = q(−1) + (1 − q)(1).

Solving this equation gives q =

, so player 2’s strategy must be σ

= (

For player 2 to be willing to mix, she must be indiﬀerent between choosing L

and R, so we set her expected payoﬀ from L equal to her expected payoﬀ from

R (looking at the second number along each column):

p(0) + (1 − p)(2) = p(3) + (1 − p)(1) or

2 − 2p = 3p + 1 − p

Solving this equation gives p =

, so player 1’s strategy must be σ

= (

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