An Adaptive Model of Demand Adjustment in Weighted Majority Games

Montero, Maria; Possajennikov, Alex

Abstract

This paper presents a simple adaptive model of demand adjustment in cooperative games and analyzes this model in weighted majority games. In the model, a randomly chosen player sets her demand to the highest possible value subject to the demands of other coalition members being satisfied. This basic process converges to the aspiration set. By introducing some perturbations into the process, we show that the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, is the one most resistant to mutations. We then apply the process to weighted majority games. We show that in symmetric majority games and in apex games, the unique separating aspiration is the unique stochastically stable one.

Citation

Montero, M., & Possajennikov, A. (2021). An Adaptive Model of Demand Adjustment in Weighted Majority Games. Games, 13(1), Article 5. https://doi.org/10.3390/g13010005

• Journal Article Type: Article
• Acceptance Date: Dec 21, 2021
• Online Publication Date: Dec 26, 2021
• Publication Date: Dec 26, 2021
• Deposit Date: Jan 31, 2022
• Publicly Available Date: Jan 31, 2022
• Journal: Games
• Electronic ISSN: 2073-4336
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 1
• Article Number: 5
• DOI: https://doi.org/10.3390/g13010005
• Keywords: Applied Mathematics; Statistics, Probability and Uncertainty; Statistics and Probability
• Public URL: https://nottingham-repository.worktribe.com/output/7171421
• Publisher URL: https://www.mdpi.com/2073-4336/13/1/5