Chess-Like Games May Have No Uniform Nash Equilibria Even in Mixed Strategies
Figure 2
The normal form of the positional game structures from Figure 1. Each player has only two strategies: to terminate () or proceed (). Hence, is represented by a table, each entry of which contains terminals corresponding to the potential initial positions of . The rows and columns are the strategies of the players and , while two strategies of the player are the left and right subtables. The corresponding game has no uniform NE whenever a utility function satisfies the constraints specified in the figure.
