Conjectural Equilibrium in Multiagent Learning

  • Authors:
  • Michael P. Wellman;Junling Hu

  • Affiliations:
  • University of Michigan, Ann Arbor, MI 48109-2110. wellman@umich.edu;University of Michigan, Ann Arbor, MI 48109-2110. junling@umich.edu

  • Venue:
  • Machine Learning
  • Year:
  • 1998

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Abstract

Learning in a multiagent environment is complicated by the fact thatas other agents learn, the environment effectively changes. Moreover,other agents‘ actions are often not directly observable, and theactions taken by the learning agent can strongly bias which range ofbehaviors 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 bebetter or worse off than had it not attempted to learn a model of theother agents at all.