Infinite Matrix Games Consider the following two-player game. Each player mentions a natural number. The player with the higher number receives one Euro from the player with the lower number. If the...

Infinite Matrix Games

Consider the following two-player game. Each player mentions a natural number. The player with the higher number receives one Euro from the player with the lower number. If the numbers are equal then no player receives anything.

(a) Write this game in the form of an infinite matrix game A.

(b) Compute supp infq pAq and infq supp pAq, where p and q are probability distributions over the rows and the columns of A, respectively. (Conclude that this game has no ‘value’.)