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Regularity of dynamic opinion games

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  • Venel, Xavier

Abstract

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.

Suggested Citation

  • Venel, Xavier, 2021. "Regularity of dynamic opinion games," Games and Economic Behavior, Elsevier, vol. 126(C), pages 305-334.
    • Handle: RePEc:eee:gamebe:v:126:y:2021:i:c:p:305-334
    DOI: 10.1016/j.geb.2020.12.007
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    References listed on IDEAS

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    1. Xavier Venel & Bruno Ziliotto, 2016. "Pathwise uniform value in gambling houses and Partially Observable Markov Decision Processes," Working Papers hal-01302567, HAL.
    2. Xavier Venel & Bruno Ziliotto, 2016. "Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01395429, HAL.
    3. Renault, Jérôme & Ziliotto, Bruno, 2020. "Hidden stochastic games and limit equilibrium payoffs," Games and Economic Behavior, Elsevier, vol. 124(C), pages 122-139.
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    7. Xavier Venel & Bruno Ziliotto, 2016. "Pathwise uniform value in gambling houses and Partially Observable Markov Decision Processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01302567, HAL.
    8. Kostas Bimpikis & Asuman Ozdaglar & Ercan Yildiz, 2016. "Competitive Targeted Advertising Over Networks," Operations Research, INFORMS, vol. 64(3), pages 705-720, June.
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    10. Xavier Venel & Bruno Ziliotto, 2016. "Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes," Post-Print hal-01395429, HAL.
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