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Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

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  • Agnieszka Wiszniewska-Matyszkiel

    (University of Warsaw)

Abstract

In this paper, a new concept of equilibrium in dynamic games with incomplete or distorted information is introduced. In the games considered, players have incomplete information about crucial aspects of the game and formulate beliefs about the probabilities of various future scenarios. The concept of belief distorted Nash equilibrium combines optimization based on given beliefs and self-verification of those beliefs. Existence and equivalence theorems are proven, and this concept is compared to existing ones. Theoretical results are illustrated using several examples: extracting a common renewable resource, a large minority game, and a repeated Prisoner’s Dilemma.

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  • 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.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-1034-7
    DOI: 10.1007/s10957-016-1034-7
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    Cited by:

    1. 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.
    2. 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.

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