GTCS Assignment 3

From Theory

Notes for CS 8803 - Game Theory and Computer Science. Spring 2008

1 Problem 1
2 Problem 2
3 Problem 3
4 Problem 4
5 Problem 5

Problem 1

A game $G = (N, A, u)$ is symmetric if $A_1=A_2=\ldots=A_n$ and for every permutation on players, if you permute the players actions their payoffs are permuted accordingly. Prove that every finite normal-form symmetric game has a symmetric Nash equilibrium $σ$ , i.e., such that $\sigma_1=\sigma_2=\ldots=\sigma_N$ .

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Problem 2

	A	B
A	5, 5	-1, 7
B	7, -1	-5, -5
Problem 2-3 game

Does the following game have an Evolutionarily Stable Strategy (ESS)? If so, give one.

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Problem 3

Characterize the set of payoff pairs achievable at correlated equilibrium in the game on the right.

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Problem 4

Give an example of a two-person game that has a correlated equilibrium where each payoff is strictly worse than that of every Nash equilibrium. You will get partial credit if the sum of the payoffs in the correlated equilibrium is less than the sum of the payoffs in every Nash equilibrium.

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