“The Relevance of Dominated Strategies in Evolutionary Equilibrium Selection” by Chongmin KIM
Chinese University of Hong Kong
We re-examine the robustness of the KMR process  for selecting Nash equilibria with respect to the manipulation of adding or eliminating dominated (or even totally dominated) strategies. We show that any strict Nash equilibrium for a given normal form game can be selected as a unique long rum equilibrium under the KMR process for the new game that is obtained from the given game by adding a (totally) dominated strategy. In this sense, dominated strategies do matter in selecting long run equilibria even though they can never be a part of them. In response to this negative result, we introduce a state dependent mutational process called the hierarchic process and show that the stochastic long run equilibria of such a process are generically robust with respect to adding or eliminating totally dominated strategies.