Monotone equilibria in signalling games

Shuo Liu and Harry Pei

No 252, ECON - Working Papers from Department of Economics - University of Zurich

Abstract: 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 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, etc.

Keywords: Signalling game; monotone equilibrium; Spence-Mirrlees condition; monotonesupermodular payoff; quasi-concavity preserving; increasing absolute differences over distributions (search for similar items in EconPapers)
JEL-codes: C72 D82 (search for similar items in EconPapers)
Date: 2017-05
New Economics Papers: this item is included in nep-dcm, nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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