Dominated Strategies and Equilibrium Selection

A rational player will never play a strictly dominated strategy. It might be tempting therefore to eliminate such strategies from any subsequent analysis. However, if equilibrium selection is an issue it may be wrong to do so. In models of adaptive learning with state-independence mutations, (after KMR, 1993) global risk-dominance is a sufficient condition for selection in larger games. This paper presents an alternative perspective. State-dependent mutations are endogenously generated by a reasonable underlying economic framework where players are different (following Myatt and Wallace, 1997). Agents play best responses to frequency observations in m strategy, 2 player games. As the idiosyncrasy in the population vanishes, dominated strategies do not lose their significance. It is always possible to add a strategy to a coordination game which (a) is strictly dominated, (b) retains the global risk-dominance of the originally selected equilibrium but (c) results in the selection of an alternative equilibrium. Dominated strategies are important features of coordination games not to be discarded at once. They can provide a novel and intuitive solution to the equilibrium selection problem.