Mechanism design (MD) has recently become a very popular approach in the design of distributed systems of autonomous agents. A key assumption required for the application of MD is that agents behave rationally in the mechanism or game, since this provides the predictability of agent behavior required for optimal design of the mechanism. In many cases, however, we are confronted with the intractability both of establishing rational equilibrium behavior, as well as of designing optimal mechanisms even if rational agent behavior can be assumed. In this paper, we study both sides of the problem simultaneously by designing and analyzing a `meta-game' involving both the designer of the mechanism (game, multi-agent system) and the agents interacting in the system. We use coupled replicator dynamics to investigate equilibrium outcomes in this game. In addition, we present an algorithm for determining the expected payoffs required for our analysis, thus sidestepping the need for extensive...