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Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information

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  • Agnieszka Wiszniewska-Matyszkiel

    (Mechanics Warsaw University)

Abstract

In this paper the concept of belief distorted Nash equilibrium (BDNE) is introduced. It is a new concept of equilibrium for games in which players have incomplete, ambiguous or distorted information about the game they play, especially in a dynamic context. The distortion of information of a player concerns the fact how the other players and/or an external system changing in response to players’ decisions, are going to react to his/her current decision. The concept of BDNE encompasses a broader concept of pre-BDNE, which reflects the fact that players best respond to their beliefs, and self-verification of those beliefs. The relations between BDNE and Nash or subjective equilibria are examined, as well as the existence and properties of BDNE. Examples are presented, including models of a common ecosystem, repeated Cournot oligopoly, a repeated Minority Game or local public good with congestion effect and a repeated Prisoner’s Dilemma.

Suggested Citation

  • Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-015-1920-7
    DOI: 10.1007/s10479-015-1920-7
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    Cited by:

    1. Agnieszka Wiszniewska-Matyszkiel & Rajani Singh, 2020. "When Inaccuracies in Value Functions Do Not Propagate on Optima and Equilibria," Mathematics, MDPI, vol. 8(7), pages 1-25, July.
    2. Mathew P. Abraham & Ankur A. Kulkarni, 2019. "New results on the existence of open loop Nash equilibria in discrete time dynamic games via generalized Nash games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 157-172, April.
    3. Katarzyna Kańska & Agnieszka Wiszniewska-Matyszkiel, 2022. "Dynamic Stackelberg duopoly with sticky prices and a myopic follower," Operational Research, Springer, vol. 22(4), pages 4221-4252, September.
    4. Agnieszka Wiszniewska-Matyszkiel, 2017. "Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 984-1007, March.

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    More about this item

    Keywords

    Distorted information; Noncooperative games; Games with a continuum of players; n-player dynamic games; Nash equilibrium; Belief-distorted Nash equilibrium (BDNE); Pre-BDNE; Subjective equilibrium; Self-verification of beliefs; Common ecosystem; Cournot oligopoly; Competitive equilibrium; Minority Game; Prisoner’s Dilemma;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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