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Stackelberg and Nash Equilibria in Games with Linear-Quadratic Payoff Functions as Models of Public Goods

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Optimization and Applications (OPTIMA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13078))

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Abstract

The paper proposes a game model with an additive convolution of two criteria, describing public and personal interests. The first (general) criterion depends on strategies of all players and represents losses from the intensity of their activity. The second (particular) criterion for each player is a function of his strategy and reflects the income from his activities. The negative definite quadratic form is taken as a general criterion. The particular criterion of each player is linear, which is quite natural for the formalization of the income function. It turns out that the resulting game with linear-quadratic payoff functions has good properties, in particular, the independence of the leader’s strategy in the Stackelberg equilibrium from the parameters of the follower’s linear functions (in contrast to the Nash equilibrium). This property means that the leader does not need accurate information about the follower’s objective function, and his strategy has the property of robustness.

The work was carried out within the framework of the project No. AAAA-A20-120122190034-9.

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Author information

Authors and Affiliations

  1. FRC CSC RAS, Vavilova Street 40, 119333, Moscow, Russia

    Victor Gorelik

  2. Moscow Pedagogical State University, M. Pirogovskaya Street 1/1, 119991, Moscow, Russia

    Victor Gorelik

  3. Financial University under the Government of RF, Leningradsky Prospekt 49, 125993, Moscow, Russia

    Tatiana Zolotova

Authors
  1. Victor Gorelik
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  2. Tatiana Zolotova
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Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas N. Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri G. Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Gorelik, V., Zolotova, T. (2021). Stackelberg and Nash Equilibria in Games with Linear-Quadratic Payoff Functions as Models of Public Goods. In: Olenev, N.N., Evtushenko, Y.G., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2021. Lecture Notes in Computer Science(), vol 13078. Springer, Cham. https://doi.org/10.1007/978-3-030-91059-4_20

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  • DOI: https://doi.org/10.1007/978-3-030-91059-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91058-7

  • Online ISBN: 978-3-030-91059-4

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