Cycles with undistinguished actions and extended Rock-Paper-Scissors games

This paper examines zero-sum games that are based on a cyclic preference relation defined over undistinguished actions. For each of these games, the set of Nash equilibria is characterized. When the number of actions is odd, a unique Nash equilibrium is always obtained. On the other hand, in the case of an even number of actions, every such game exhibits an infinite number of Nash equilibria. Our results give some insights as to the robustness of Nash equilibria with respect to perturbations of the action set.