Axiomatizations of the Proportional Division Value

Tinbergen Institute Discussion Paper 2019-072/II

39 Pages Posted: 12 Nov 2019

See all articles by Zhengxing Zou

Zhengxing Zou

Beijing Institute of Technology

René van den Brink

VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute

Youngsub Chun

Seoul National University - School of Economics

Yukihiko Funaki

Waseda University, School of Political Science and Economics

Date Written: October 31, 2019

Abstract

We present axiomatic characterizations of the proportional division value for TU-games, a value that distributes the worth of the grand coalition in proportion to the stand-alone worths of its members. First, a new proportionality principle, called balanced treatment, is introduced by strengthening Shapley's symmetry axiom, which states that if two players make the same contribution to any nonempty coalition, then they receive the amounts in proportion to their stand-alone worths.We characterize the family of values satisfying efficiency, weak linearty, and balanced treatment. We also show that this family is incompatible with the dummy player property. However, we show that the proportional division value is the unique value in this family that satisfies the dummifying player property. Second, we propose three appropriate monotonicity axioms by considering two games in which the stand-alone worths of all players are equal or in the same proportion to each other, and obtain three axiomatizations of the proportional division value without both weak linearity and the dummifying player property. Third, from the perspective of a variable player set, we show that the proportional division value is the only one that satisfies proportional standardness and projection consistency. Finally, we provide characterizations of proportional standardness.

Keywords: cooperative game, proportional division value, monotonicity, consistency

JEL Classification: C71

Suggested Citation

Zou, Zhengxing and van den Brink, J.R. (René) and Chun, Youngsub and Funaki, Yukihiko, Axiomatizations of the Proportional Division Value (October 31, 2019). Tinbergen Institute Discussion Paper 2019-072/II, Available at SSRN: https://ssrn.com/abstract=3479365 or http://dx.doi.org/10.2139/ssrn.3479365

Zhengxing Zou (Contact Author)

Beijing Institute of Technology ( email )

5 South Zhongguancun street
Center for Energy and Environmental Policy Researc
Beijing, Haidian District 100081
China

J.R. (René) Van den Brink

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Youngsub Chun

Seoul National University - School of Economics ( email )

San 56-1, Silim-dong, Kwanak-ku
Seoul 151-742
Korea

Yukihiko Funaki

Waseda University, School of Political Science and Economics ( email )

1-6-1 Nishi-Waseda
Shinjuku-ku, Tokyo 169-8050, Tokyo 169-8050
Japan

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
18
Abstract Views
259
PlumX Metrics