Weak Sequential Equilibria and Ex Post Masquerade

In this appendix, we develop a way to construct fully revealing equilibria by working directly with ex post masquerading payoffs, without having to aggregate them.By doing so, we can show existence of a fully revealing equilibrium when the ex post masquerading payoffs have increasing differences, regardless of the information structure. The idea is that to enforce full revelation, players can be skeptical by attributing messages that deviate from full revelation to a worst case type of the ex post masquerade relation. Indeed, if all players but i have revealed their type, the other players can condition their beliefs on t−i. The existence of ex post worst case types is sufficient to get a fully revealing equilibrium independently of the specifics of the information structure. However, the caveat of this construction is that, in general, such beliefs violate one of the implications of strong sequential equilibria that we derived in Lemma 1. So the approach presented in this appendix sacrifices strong belief consistency and weakens the equilibrium concept used in the paper. The Equilibrium Notion. We use the notion of weak sequential equilibria in the sense of Myerson (1991). They are defined as equilibria that satisfy sequential rationality and weak belief consistency. Weak consistency here means Bayesian consistency on the equilibrium path and off-path beliefs that are consistent with evidence.