The Prekernel of Cooperative Games with $$\alpha $$ α -Excess

Xia Zhang (), René van den Brink () and Arantza Estévez-Fernández ()
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Xia Zhang: NingboTech University
René van den Brink: VU University
Arantza Estévez-Fernández: VU University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 18, 17 pages

Abstract: Abstract In this paper, we introduce a new approach to measure the dissatisfaction for coalitions of players in cooperative transferable utility games. This is done by considering affine (and convex) combinations of the classical excess and the proportional excess. Based on this so-called $$\alpha $$ α -excess, we define new solution concepts for cooperative games, such as the $$\alpha $$ α -prenucleolus and the $$\alpha $$ α -prekernel. The classical prenucleolus and prekernel are special cases. We characterize the $$\alpha $$ α -prekernel by strong stability and the $$\alpha $$ α -balanced surplus property. Also, we show that the payoff vector generated by the $$\alpha $$ α -prenucleolus belongs to the $$\alpha $$ α -prekernel.

Keywords: $$\alpha $$ α -Excess; $$\alpha $$ α -Prenucleolus; $$\alpha $$ α -Prekernel; $$\alpha $$ α -Balanced surplus; 91A12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02745-x

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