Online Appendix to “Endogenous Beliefs in Models of Politics”

Let G be a finite extensive form game with perfect information and chance moves, referred to here as a game. Fix a set of players N = {1, 2, ..., n} and a set of histories H, such that the root history ∅ ∈ H and, for any a = (a1, ..., at−1, at) ∈ H, (a1, ..., at−1) ∈ H. The set of terminal histories is Z ⊂ H, and the player assignment function identifies a subset of players (or Nature) at each nonterminal history, P : H \ Z → 2 ∪ {Nature}. The set of i’s moves is Hi = h ∈ H : i ∈ P (h). For any nonterminal history h ∈ H \ Z, the action set for i at h is Ai(h) = {a : (h, a) ∈ H}. Each player i ∈ N has preferences over Z represented by a utility function ui : Z → R. At Nature’s moves, each player i ∈ N has the beliefs given by conditional probability distribution F (a|h) ∈ F , where F is the family