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“Greedy” demand adjustment in cooperative games

Montero, Maria; Possajennikov, Alex

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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.


Montero, M., & Possajennikov, A. (2023). “Greedy” demand adjustment in cooperative games. Annals of Operations Research,

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
Keywords Management Science and Operations Research, General Decision Sciences
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Additional Information This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit


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