Observable Implications of Nash and Subgame - Perfect Behavior in Extensive Games

Revealed preference theory is a powerful tool for testing models of individual choice. It is now being extended to collective choice models as well. 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 suffcient conditions for observed outcomes in extensive game forms to be rationalised 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) is not consistent with subgame perfect behavior but is consistent with Nash equilibrium, or (c) is consistent with neither. Further, we discuss the relevance of the test outcomes for rationalization of data by multiple preference profiles