A Note on the Balancedness and the Concavity of Highway Games

CentER Discussion Paper Series No. 2008-29

14 Pages Posted: 23 May 2008

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: March 2008

Abstract

A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera and Zarzuelo (2006) introduce highway problems and the corresponding cooperative cost games called high-way games to address the problem of fair allocation of the construction costs in case the underlying graph is a chain. In this note, we study the concavity and the balancedness of highway games on more general graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. The main result of our study is that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we provide sufficient conditions on highway problems defined on cyclic graphs such that the corresponding highway games are balanced.

Keywords: cooperative games, highway games, costs sharing

JEL Classification: C71

Suggested Citation

Ciftci, Baris and Borm, Peter E. M. and Hamers, Herbert, A Note on the Balancedness and the Concavity of Highway Games (March 2008). Available at SSRN: https://ssrn.com/abstract=1107106 or http://dx.doi.org/10.2139/ssrn.1107106

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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