Abstract

The cognitive hierarchy model is an approach to decision making in multi-agent interactions motivated by laboratory studies of people. It bases decisions on empirical assumptions about agents’ likely play and agents’ limited abilities to second-guess their opponents. It is attractive as a model of human reasoning in economic settings, and has proved successful in designing agents that perform effectively in interactions not only with similar strategies but also with sophisticated agents, with simpler computer programs, and with people. In this paper, we explore the qualitative structure of iterating best response solutions in two repeated games, one without messages and the other including communication in the form of non-binding promises and threats. Once the model anticipates interacting with sufficiently sophisticated agents with a sufficiently high probability, reasoning leads to policies that disclose intentions truthfully, and expect credibility from the agents they interact with, even as those policies act aggressively to discover and exploit other agents’ weaknesses and idiosyncrasies. Non-binding communication improves overall agent performance in our experiments.