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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title Monotone equilibria in signalling games
Organization Unit
  • Shuo Liu
  • Harry Pei
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 252
ISSN 1664-7041
Number of Pages 31
Date 2017
Abstract Text 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.
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Keywords Signalling game, monotone equilibrium, Spence-Mirrlees condition, monotonesupermodular payoff, quasi-concavity preserving, increasing absolute differences over distributions, Signaling, Nash-Gleichgewicht, Auszahlung , Verteilung