Regularity of dynamic opinion games

• 成果类型: Article
• 署名作者: Venel, Xavier
• 署名单位: Luiss Guido Carli University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2020.12.007
• 发表日期: 2021
• 页码: 305-334
• 关键词: Game theory; social network; dynamic games; targeting; stochastic games

摘要

We analyze a class of stochastic games where two lobbies compete by influencing the opinions in a society. We assume that the opinions evolve according to De Groot opinion formation and that the decisions of the lobbies change the structure of the network representing the society. We show that the regularity of discounted Nash equilibrium payoffs when players become patient is highly model-dependent. We provide two extreme cases. First, we present an example where the sequence of discounted Nash equilibrium payoffs does not converge. Hence, the solution is highly sensitive to the discount factor and a modeler needs to know the discount factor precisely in order to compute equilibria. Second, we focus on a subclass of problems where lobbies are restricted and show the existence of a uniform equilibrium. Hence, in this restricted framework, a modeler can predict some approximate equilibria with an imprecise knowledge of the discount factor. (C) 2021 Elsevier Inc. All rights reserved.