Linear Riley equilibria in quadratic signaling games

We study signaling games with quadratic payoffs. As signaling games admit multiple separating equilibria, many equilibrium selection rules are proposed and a well-known solution is Riley equilibria. They are separating equilibria in which the sender achieves the highest equilibrium payoff for all types among all separating equilibria. We analyze the conditions for Riley equilibria to be linear, a common assumption in many applications. We derive a sufficient and necessary condition for the existence and uniqueness of linear Riley equilibria. We apply the result to confirm the dominance of linear equilibria in some classic examples, and we show that, in some other examples, there exist previously unknown nonlinear Riley equilibria. (c) 2023 Elsevier Inc. All rights reserved.