“Greedy” demand adjustment in cooperative games

Montero, Maria; Possajennikov, Alex

Abstract

This paper studies a simple process of demand adjustment in cooperative games. In the process, a randomly chosen player makes the highest possible demand subject to the demands of other coalition members being satisfied. This process converges to the aspiration set; in convex games, this implies convergence to the core. We further introduce perturbations into the process, where players sometimes make a higher demand than feasible. These perturbations make the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, the one most resistant to mutations. We fully analyze this process for 3-player games. We further look at weighted majority games with two types of players. In these games, if the coalition of all small players is winning, the process converges to the unique separating aspiration; otherwise, there are many separating aspirations and the process reaches a neighbourhood of a separating aspiration.

Citation

Montero, M., & Possajennikov, A. (2023). “Greedy” demand adjustment in cooperative games. Annals of Operations Research, https://doi.org/10.1007/s10479-023-05179-8

• Journal Article Type: Article
• Acceptance Date: Jan 6, 2023
• Online Publication Date: Jan 25, 2023
• Publication Date: Jan 25, 2023
• Deposit Date: Jan 26, 2023
• Publicly Available Date: Jan 27, 2023
• Journal: Annals of Operations Research
• Print ISSN: 0254-5330
• Electronic ISSN: 1572-9338
• Publisher: Springer Science and Business Media LLC
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s10479-023-05179-8
• Keywords: Management Science and Operations Research, General Decision Sciences
• Public URL: https://nottingham-repository.worktribe.com/output/16503178
• Publisher URL: https://link.springer.com/article/10.1007/s10479-023-05179-8#citeas
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