NDLI: Population monotonic path schemes for simple games

Content Provider	Springer Nature Link
Author	Çiftçi, Barış Borm, Peter Hamers, Herbert
Copyright Year	2008
Abstract	A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.
Starting Page	205
Ending Page	218
Page Count	14
File Format	PDF
ISSN	00405833
Journal	Theory and Decision
Volume Number	69
Issue Number	2
e-ISSN	15737187
Language	English
Publisher	Springer US
Publisher Date	2008-12-04
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cooperative games Simple games Population monotonic path schemes Population monotonic allocation schemes Coalition formation Probabilistic values Operations Research/Decision Theory Methodology of the Social Sciences Game Theory, Economics, Social and Behav. Sciences Game Theory/Mathematical Methods Economic Theory
Content Type	Text
Resource Type	Article
Subject	Arts and Humanities Economics, Econometrics and Finance Developmental and Educational Psychology Social Sciences Decision Sciences Applied Psychology Computer Science Applications

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