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Optimization implementation of solution concepts for cooperative games with stochastic payoffs

Panfei Sun (), Dongshuang Hou () and Hao Sun ()
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Panfei Sun: Northwestern Polytechnical University
Dongshuang Hou: Northwestern Polytechnical University
Hao Sun: Northwestern Polytechnical University

Theory and Decision, 2022, vol. 93, issue 4, No 5, 724 pages

Abstract: Abstract In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) stable solutions. Inspired by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models.

Keywords: Game theory; Solution concept; Stochastic payoffs; Optimization; Nucleolus; Axiomatization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11238-022-09865-0

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