False Consensus in Games: Embedding Level-k Models into Games of Incomplete Information

Abstract

Level-k models have recently gained popularity as a framework for strategic behavior with bounded rationality. These models make two assumptions: agents of a higher level have richer beliefs, and can also perform more computations. I develop a model that incorporates Level-k models into games of incomplete information, by assuming that players’ beliefs exhibit the false consensus effect, which is the empirical observation that people think others share their beliefs, what allows players to believe others have the same level. A player’s level determines how complex her beliefs and I consider two solution concepts: Interim Correlated Rationalizability (ICR, with which level-0 behavior becomes endogenous), and k-th Best Response, which is the usual concept for Level-k games. My main result is that in this model the product topology and the uniform strategic topology coincide, what implies that players with similar beliefs behave similarly. Therefore, unlike for general type spaces, predictions will be robust to small specification errors. I show that in the Email game of Rubinstein (1989), when players receive few messages they never attack according to ICR; however, when they receive enough messages, they behave as if there was complete information. Other applications show that the model is consistent with experimental evidence of trading in “no-trade” contexts, and recovering multiplicity of equilibria in global games.