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 ai,j= -aj,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