Observable implications of nash and subgame-perfect behavior in extensive games

In this paper we develop tests for whether play in a game is consistent with equilibrium behavior when preferences are unobserved. We provide necessary and sufficient conditions for observed outcomes in extensive game forms to be rationalized first, partially, as a Nash equilibrium and then, fully, as the unique subgame-perfect equilibrium. Thus one could use these conditions to find that play is (a) consistent with subgame-perfect equilibrium, or (b) not consistent with subgame-perfect behavior but is consistent with Nash equilibrium, or (c) consistent with neither. Further, we discuss the relevance of the test outcomes for rationalization of data by multiple preference profiles.