Monotone Equilibria in Signalling Games

37 Pages Posted: 15 Apr 2017 Last revised: 4 Jun 2020

See all articles by Shuo Liu

Shuo Liu

Peking University - Guanghua School of Management

Harry Di Pei

Northwestern University - Department of Economics

Date Written: April 9, 2018


We study the monotonicity of sender’s equilibrium strategy with respect to her type in signalling games. We use counterexamples to show that when the sender’s payoff is non-separable, the Spence-Mirrlees condition cannot rule out equilibria in which the sender uses non-monotone strategies. These equilibria can survive standard refinements as incentives are strict and the sender plays every action with positive probability. We provide sufficient conditions under which the sender’s strategy is monotone in every Nash equilibrium. Our conditions require the sender’s payoff to have strictly increasing differences between the state and the action profile and to be monotone with respect to each player’s action. We also identify and fully characterize a novel property on the sender’s payoff that we call increasing absolute differences over distributions, under which every pair of distributions over the receiver’s actions can be ranked endogenously. Our sufficient conditions fit into a number of applications, including advertising, warranty provision, education and job assignment.

Keywords: signalling game, monotone equilibrium, Spence-Mirrlees condition, monotone-supermodular payoff, quasi-concavity preserving, increasing absolute differences over distributions

JEL Classification: C72, D82

Suggested Citation

Liu, Shuo and Pei, Harry Di, Monotone Equilibria in Signalling Games (April 9, 2018). European Economic Review, Vol. 124, Available at SSRN: or

Shuo Liu (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871

Harry Di Pei

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States

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