Balanced Externalities and the Proportional Allocation of Nonseparable Contributions

Tinbergen Institute Discussion Paper 2021-024/II

33 Pages Posted: 19 Mar 2021

See all articles by Rene van den Brink

Rene van den Brink

Vrije Universiteit Amsterdam, School of Business and Economics

Youngsub Chun

Seoul National University - School of Economics

Yukihiko Funaki

Waseda University, School of Political Science and Economics

Zhengxing Zou

Beijing Institute of Technology

Date Written: March 12, 2021

Abstract

In this paper, we study the implications of extending the balanced cost reduction property from queueing problems to general games. As a direct translation of the balanced cost reduction property, the axiom of balanced externalities for solutions of games, requires that the payoff of any player is equal to the total externality she inflicts on the other players with her presence. We show that this axiom and efficiency together characterize the Shapley value for 2-additive games. However, extending this axiom in a straightfoward way to general games is incompatible with efficiency. Keeping as close as possible to the idea behind balanced externalities, we weaken this axiom by requiring that every player's payoff is the same fraction of its total externality inflicted on the other players. This weakening, which we call weak balanced externalities, turns out to be compatible with efficiency. More speci fically, the unique efficient solution that satisfi es this weaker property is the proportional allocation of nonseparable contribution (PANSC) value, which allocates the total worth proportional to the separable costs of the players. We also provide characterizations of the PANSC value using a reduced game consistency axiom.

Keywords: Cooperative game, balanced externalities, proportional allocation of nonseparable contributions, consistency

JEL Classification: C71

Suggested Citation

van den Brink, Rene and Chun, Youngsub and Funaki, Yukihiko and Zou, Zhengxing, Balanced Externalities and the Proportional Allocation of Nonseparable Contributions (March 12, 2021). Tinbergen Institute Discussion Paper 2021-024/II, Available at SSRN: https://ssrn.com/abstract=3807467 or http://dx.doi.org/10.2139/ssrn.3807467

Rene Van den Brink (Contact Author)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
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

Zhengxing Zou

Beijing Institute of Technology ( email )

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

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