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2020 | OriginalPaper | Chapter

On the Cooperative Behavior in Multistage Multicriteria Game with Chance Moves

Authors : Denis Kuzyutin, Ekaterina Gromova, Nadezhda Smirnova

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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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.

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Title: On the Cooperative Behavior in Multistage Multicriteria Game with Chance Moves
Authors: Denis Kuzyutin
Ekaterina Gromova
Nadezhda Smirnova
Publisher: Springer International Publishing
Book: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-49987-7

Electronic ISBN: 978-3-030-49988-4

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-49988-4_13

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