Chinese postman games with repeated players

Tinbergen Institute Discussion Paper 2018-081/II

29 Pages Posted: 28 Nov 2018

See all articles by Arantza Estevez-Fernandez

Arantza Estevez-Fernandez

VU University Amsterdam - Department of Econometrics and Operations Research; Tinbergen Institute

Herbert Hamers

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

Date Written: October 26, 2018

Abstract

This paper analyses Chinese postman games with repeated players, which generalize Chinese postman games by dropping the one-to-one relation between edges and players. In our model, we allow players to own more than one edge, but each edge belongs to at most one player. The one-to-one relation between edges and players is essential for the equivalence between Chinese postman-totally balanced and Chinese postman-submodular graphs shown in Granot et al. (1999). We illustrate the invalidity of this result in our model. Besides, the location of the post office has a relevant role in the submodularity and totally balancedness of Chinese postman games with repeated players. Therefore, we focus on sufficient conditions on the assignment of players to edges to ensure submodularity of Chinese postman games with repeated players, independently of the associated travel costs. Moreover, we provide some insights on the difficulty of finding necessary conditions on assignment functions to this end.

Keywords: Chinese Postman Games With Repeated Players, Balanced Game, Totally Balanced Game, Submodular Game, Assignment Function

JEL Classification: C71

Suggested Citation

Estevez-Fernandez, Arantza and Hamers, Herbert, Chinese postman games with repeated players (October 26, 2018). Tinbergen Institute Discussion Paper 2018-081/II. Available at SSRN: https://ssrn.com/abstract=3278565 or http://dx.doi.org/10.2139/ssrn.3278565

Arantza Estevez-Fernandez (Contact Author)

VU University Amsterdam - Department of Econometrics and Operations Research ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
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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