Stability and instability of the unbeatable strategy in dynamic processes

A strategy is unbeatable if it is immune to any entrant strategy of any size. This paper investigates static and dynamic properties of unbeatable strategies. We give equivalent conditions for a strategy to be unbeatable and compare it with related equilibrium concepts. An unbeatable strategy is globally stable under replicator dynamics. In contrast, an unbeatable strategy can fail to be globally stable under best response dynamics even if it is also a unique and strict Nash equilibrium.