  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 than 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 lower number of parameters. We discuss extensions to
games with more than two players and heterogeneous beliefs.
