Hierarchic Process and Relevance of Dominated Strategies in the Long Run

Kim and Wong (2010) re-examine the robustness of the KMR process (Kandori, Mailath, and Rob 1993) showing that any strict Nash equilibrium for the base game can be selected as a unique long run equilibrium under the KMR process by adding a totally dominated strategy. 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. However the proposed mutational process is not enough to justify eliminating strictly but not necessarily totally dominated strategies.