On the Approximation Performance of Fictitious Play in Finite Games

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essentially matching upper bound of 1/2 - O(1/n)

Subgame perfect implementation with almost perfect information and the hold-up problem

The foundations of incomplete contracts have been questioned using or extending the subgame perfect implementation approach of Moore and Repullo (1988). We consider the robustness of subgame perfect implementation to the introduction of small amounts of asymmetric information. We show that Moore- Repullo mechanisms may not yield (even approximately) truthful revelation in pure or totally mixed strategies as the amount of asymmetric information goes to zero. Moreover, we argue that a wide class of extensive-form mechanisms are subject to this fragility

Diversity and Adaptation in Large Population Games

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be plagued by the maladaptive behavior of the players, we find that diversity among the players improves the system efficiency, though it slows the convergence to the steady state. Diversity causes a mild spread of resources at the transient state, but reduces the uneven distribution of resources in the steady state.Comment: 8 pages, 3 figure