# Nash equilibrium

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Game:

C1 C2 C3

R1 3,2 2,1 1,a

R2 2,2 b,4 0,2

R3 c,d 3,2 e,4

a) Give a condition on b such that R2 is strictly dominated by R1.

b) Given that a) holds, find a condition on d such that C1 strictly dominates C2.

c) Given that a) and b) hold, find conditions on a and c such that (R1, C1) is a Nash

equilibrium.

d) Given that a) - c) hold, find conditions on d, e such that (R1, C1) is the unique

Nash equilibrium.

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##### Solution Summary

Nash equilibrium is expressed.

##### Solution Preview

The game matrix is the following:

C1 C2 C3

R1 3,2 2,1 1,a

R2 2,2 b,4 0,2

R3 c,d 3,2 e,4

a. For R2 to be strictly dominated by R1 we need a situation where for each strategy C1, C2, and C3, R1 offers a better payoff to player 1 than R2. From the table R1 pays off 3 for C1, 2 for C2, and 1 for C3, while R2 pays off 2 for C1, b for C2, and 0 for C3. R1 is better than R2 for C1 and C3. We only need to ensure that it is better than R2 for C2. R1 offers a pay off of 2 for C2, and as long ...

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