Complete Information Outcomes without Common Knowledge

In this paper we examine the robustness of existing models of agent decision making which rely on the assumption of common knowledge. The research we report on involves testing equilibria predicted by traditional, common-knowledge intensive models in laboratory settings wherein the underlying common knowledge assumptions are violated in a specified manner. This approach provides insight into when we may employ narrow but tractable models in an "as if" mode: when common knowledge is lacking, are models that assume common knowledge still likely to perform well? In general we find that with an opportunity to coordinate plans, either through communication or via histories, cooperative outcomes emerge. Furthermore, these collusive outcomes often extensively and efficiently exploit the multi-period nature of the interaction, achieving the complete information collusive allocation of profits. This strongly suggests that predictions of collusive behavior in repeated play settings are quite robust with respect to relaxing common knowledge assumptions: a small degree of information exchange or coordination yields outcomes that are generally indistinguishable from the complete information outcomes.