Abstract We introduce NLK, a model that connects the Nash equilibrium (NE) and level-k. It allows a player in a game to believe that her opponent may be either less or as sophisticated as she is, a view supported in psychology. We apply NLK to data from five published papers on static, dynamic, and auction games. NLK provides different predictions from those of the NE and level-k; moreover, a simple version of NLK explains the experimental data better in many cases, with the same or fewer parameters. We discuss extensions to games with more than two players and heterogeneous beliefs.

We propose an axiomatic approach to study the superior performance of mechanisms with obviously dominant strategies to those with only dominant strategies. Guided by the psychological inability to reason state-by-state, we develop Obvious Preference as a weakening of Subjective Expected Utility Theory. We show that a strategy is an obviously dominant if and only if any Obvious Preference prefer it to any deviating strategy at any reachable information set. Applying the concept of Nash Equilibrium to Obvious Preference, we propose Obvious Nash Equilibrium to identify a set of mechanisms that are more robust than mechanisms with only Nash Equilibria.