Monotone Signalling Games and the Existence of Perfect Sequential Equilibrium

I propose a class of games generalizing Athey & Levin (2018) monotone decision problem approach to two-person noncooperative games of incomplete information, called Monotone Signalling Games, where a player’s payoff is monotone in their opponent’s belief about their unknown type, and only a higher type can credibly signal that they are of that type if operating under common knowledge. I show that if the type space is a totally ordered finite lattice, the existence of perfect sequential equilibrium is guaranteed in such games. A variety of problems including bargaining and principal-agent models with adverse selection are given as examples