Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when the empirical distribution on action profiles generated by every behavior strategy in one can also be generated by an appropriately chosen behavior strategy in the other. This paper provides a characterization of empirical equivalence. The central idea is to relate a game's information structure to the conditional independencies in the empirical distributions it generates. We present a new analytical device, the influence opportunity diagram of a game, describe how such a diagram is constructed for a given extensive-form game, and demonstrate that it provides a complete summary of the information needed to test empirical equivalence between two games.