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Evolutionary Dynamics for Designing Multi-Period Auctions 1

Mechanism design (MD) has recently become a very popular approach in the design of distributed systems of autonomous agents. Also called ‘inverse game theory’ [4], MD is concerned with designing the games or systems in which agents interact, and to do this in such a way that rational agent behavior in those games leads to certain desirable properties for the system as a whole. A key assumption in MD is that agents behave rationally, since this provides the predictability of agent behavior required for optimizing the mechanism’s design. In many practical circumstances, however, agents don’t behave rationally since, in general, finding Nash equilibrium strategies to play is intractable [2]. Because of such negative results, many have resorted to heuristic approaches to these problems. Here, we propose studying the interaction between the mechanism designer and the game participants as a higher level, ‘meta-game,’ in which the designer chooses among alternative mechanism designs, while the agents choose among alternative strategies to play. We solve this game ‘heuristically’ using evolutionary game theory techniques, specifically, the (coupled) replicator dynamics (RD) [3]. To illustrate, we adopt the multi-period auction scenario developed by Pardoe and Stone (PS) [5].