Converging Better Response Dynamics in Sender-Receiver Games

• 成果类型: Article; Early Access
• 署名作者: Semirat, Stephan; Forges, Francoise
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); INRAE; Centre National de la Recherche Scientifique (CNRS); Institut National Polytechnique de Grenoble; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Institut de Recherche pour le Developpement (IRD); Laboratoire dEconomie de Dauphine LEDa
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2024.0535
• 发表日期: 2025
• 关键词: CHEAP; refinements; equilibria

摘要

We consider information transmission between a sender, who has finitely many types, and a receiver, who must choose a decision in a real interval. The payoffs depend on the sender's type and the receiver's decision. We assume that the payoff functions are wellbehaved. We characterize the pure strategy perfect Bayesian equilibrium outcomes as incentive-compatible partitions of the sender's types. We propose an algorithm, which starts from the finest partition. Then, at every step, if the current partition is not incentive compatible, a random type of the sender improves its payoff, and the receiver best responds. We show that every possible run of the algorithm converges to a unique incentive-compatible partition Pi & lowast;. This partition Pi & lowast; is such that any partition with more cells than Pi & lowast; is not incentive compatible, so the algorithm determines to which extent information transmission can be effective. The partition Pi & lowast; also satisfies some refinement criteria for perfect Bayesian equilibria in sender-receiver games. Furthermore, in a discrete version of a popular class of examples (namely, if the sender's type is uniformly distributed and payoff functions are quadratic, with a constant upward bias for the sender), Pi & lowast; ex ante Pareto dominates every other incentive-compatible partition.