Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

This paper studies convergence and stability properties of Sjöström’s (1994) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics and bestreply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibria, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibria contain limit points of the learning dynamics. Furthermore, even if the dynamics converge to the “right” set of equilibria (i.e. the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires