Conjectural Equilibrium in Multiagent Learning

Learning in a multiagent environment is complicated by the fact that as other agents learn, the environment effectively changes. Moreover, other agents' actions are often not directly observable, and the actions taken by the learning agent can strongly bias which range of behaviors are encountered. We define the concept of a conjectural equilibrium, where all agents' expectations are realized, and each agent responds optimally to its expectations. We present a generic multiagent exchange situation, in which competitive behavior constitutes a conjectural equilibrium. We then introduce an agent that executes a more sophisticated strategic learning strategy, building a model of the response of other agents. We find that the system reliably converges to a conjectural equilibrium, but that the final result achieved is highly sensitive to initial belief. In essence, the strategic learner's actions tend to fulfill its expectations. Depending on the starting point, the agent may be better or worse off than had it not attempted to learn a model of the other agents at all.