Computational Game Theory

Homework number 2

1. Symmetric zero sum game

A symmetric two player game has u₁(i,j)= u₂(j,i).

For a zero sum game matrix A it implies that a_i,j= -a_j,i.

Show that a symmetric zero sum game has value zero.

2. e-Nash: Show, for every e > 0, an example of a two player game where there is an e-Nash which in which both players have a much higher payoff then in any Nash equilibrium.

3. Symmetric game: Show that every symmetric game has a symmetric Nash equilibrium.

4. Action elimination:

a. Show that in a two-player zero sum game, elimination of actions of the MAX player can only reduce the value of the game.

b. Show an example of a general two player game in which eliminating a given action of player 1 can increase player 1 payoff in every Nash equilibrium.

The homework is due April 20