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International Conference on Mathematical Optimization Theory and Operations Research

MOTOR 2020: Mathematical Optimization Theory and Operations Research pp 184–199Cite as

On the Cooperative Behavior in Multistage Multicriteria Game with Chance Moves

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12095))

Abstract

We consider a class of multistage multicriteria games in extensive form with chance moves where the players cooperate to maximize their expected joint vector payoff. Assuming that the players have agreed to accept the minimal sum of relative deviations rule in order to choose a unique Pareto optimal payoffs vector, we prove the time consistency of the optimal cooperative strategy profile and corresponding optimal bundle of the cooperative trajectories. Then, if the players adopt a vector analogue of the Shapley value as the solution concept, they need to design an appropriate imputation distribution procedure to ensure the sustainability of the achieved cooperative agreement. We provide a generalization of the incremental payment schedule that is applicable for the games with chance moves and satisfies such advantageous properties as the efficiency, strict balance condition and the time consistency property in the whole game. We illustrate our approach with an example of the extensive-form game tree with chance moves.

The reported study was funded by RFBR under the research project 18-00-00727 (18-00-00725).

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Author information

Authors and Affiliations

  1. Saint Petersburg State University, Universitetskaya nab. 7/9, 199034, St. Petersburg, Russia

    Denis Kuzyutin, Ekaterina Gromova & Nadezhda Smirnova

  2. National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, 190008, St. Petersburg, Russia

    Denis Kuzyutin, Ekaterina Gromova & Nadezhda Smirnova

Authors
  1. Denis Kuzyutin
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  2. Ekaterina Gromova
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  3. Nadezhda Smirnova
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Corresponding author

Correspondence to Ekaterina Gromova .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov

  2. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A Kalyagin

  4. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Kuzyutin, D., Gromova, E., Smirnova, N. (2020). On the Cooperative Behavior in Multistage Multicriteria Game with Chance Moves. In: Kononov, A., Khachay, M., Kalyagin, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Lecture Notes in Computer Science(), vol 12095. Springer, Cham. https://doi.org/10.1007/978-3-030-49988-4_13

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