A coalitional compromised solution for cooperative games

Rong Zou (), Genjiu Xu (), Wenzhong Li () and Xunfeng Hu ()
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Rong Zou: Northwestern Polytechnical University
Genjiu Xu: Northwestern Polytechnical University
Wenzhong Li: Northwestern Polytechnical University
Xunfeng Hu: Guangzhou University

Social Choice and Welfare, 2020, vol. 55, issue 4, No 4, 735-758

Abstract: Abstract The paper aims to study a kind of revenue allocation system with a guarantee of basic interests, which integrates the egalitarianism with the marginalism. This means that a player’s payoff consists of two parts, the basic interests and the performance-based payoff. In cooperative games with coalition structure setting, the Owen value puts emphasis on the individuals’ marginal contribution, in contrast, the equal coalitional division value (ECD-value) gives priority to the egalitarianism. Through introducing the guarantee coefficient $$\alpha$$ α , we propose the compromised solution which is established as the corresponding convex combination of the Owen value and the ECD-value. We call it $$\alpha$$ α -egalitarian Owen value, as the solution degenerates to the corresponding $$\alpha$$ α -egalitarian Shapley value when the coalition structure is trivial. Furthermore, we provide three approaches to characterize an $$\alpha$$ α -egalitarian Owen value, including axiomatization, potential function and implementation.

Date: 2020
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DOI: 10.1007/s00355-020-01262-2

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