Population Monotonic Paths Schemes for Simple Games

CentER Discussion Paper Series No. 2006-113

18 Pages Posted: 30 Nov 2006

See all articles by Baris Ciftci

Baris Ciftci

Tilburg University - Center for Economic Research (CentER)

Peter Borm

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Date Written: November 2006

Abstract

A path scheme for a simple 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. We show 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. Extensions of these results to other probabilistic values are discussed.

Keywords: cooperative games, simple games, population monotonic path schemes, coalition formation, probabilistic values

JEL Classification: C71, D72

Suggested Citation

Ciftci, Baris and Borm, Peter E. M. and Hamers, Herbert, Population Monotonic Paths Schemes for Simple Games (November 2006). Available at SSRN: https://ssrn.com/abstract=948410 or http://dx.doi.org/10.2139/ssrn.948410

Baris Ciftci (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Peter E. M. Borm

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Herbert Hamers

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

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