Modeling bounded rationality of agents during interactions

In this paper, we propose that bounded rationality of another agent be modeled as errors the agent is making while deciding on its action. We are motivated by the work on quantal response equilibria in behavioral game theory which uses Nash equilibria as the solution concept. In contrast, we use decision-theoretic maximization of expected utility. Quantal response assumes that a decision maker is approximately rational, i.e., is maximizing its expected utility but with an error rate characterized by a single error parameter. Another agent’s error rate may be unknown and needs to be estimated during an interaction. We show that this error rate can be estimated using Bayesian update of a suitable conjugate prior, and that it has a sufficient statistic of fixed dimension under strong simplifying assumptions. However, if the simplifying assumptions are relaxed, the quantal response does not admit a finite dimensional sufficient statistic, and a more complex update is needed.