On the stability of evolutionary dynamics in games with incomplete information

In an interaction it is possible that one agent has features it is aware of but the opponent is not. These features (e.g. cost, valuation or fighting ability) are referred to as the agent’s type. The paper compares two models of evolution in symmetric situations of this kind. In one model the type of an agent is fixed and evolution works on strategies of types. In the other model every agent adopts with fixed probabilities both types, and type-contingent strategies are exposed to evolution. It is shown that the dynamic stability properties of equilibria may differ even when there are only two types and two strategies. However, in this case the dynamic stability properties are generically the same when the payoff of a player does not depend directly on the type of the opponent. Examples illustrating these results are provided.