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Chinese postman games with multi-located players

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  • Estévez-Fernández, Arantza
  • Hamers, Herbert

Abstract

This paper analyses Chinese postman games with multi-located players, which generalize Chinese postman games by dropping the one-to-one relation between edges and players. In our model, we allow players to be located on more than one edge, but at most one player is located on each edge. 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 the literature. 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 multi-located players. Therefore, we focus on sufficient conditions on the assignment of players to edges to ensure submodularity of Chinese postman games with multi-located 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.

Suggested Citation

  • Estévez-Fernández, Arantza & Hamers, Herbert, 2020. "Chinese postman games with multi-located players," European Journal of Operational Research, Elsevier, vol. 285(2), pages 458-469.
    • Handle: RePEc:eee:ejores:v:285:y:2020:i:2:p:458-469
    DOI: 10.1016/j.ejor.2020.01.062
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    References listed on IDEAS

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    1. Hamers, Herbert, 1997. "On the concavity of delivery games," European Journal of Operational Research, Elsevier, vol. 99(2), pages 445-458, June.
    2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    3. Hamers, Herbert & Borm, Peter & van de Leensel, Robert & Tijs, Stef, 1999. "Cost allocation in the Chinese postman problem," European Journal of Operational Research, Elsevier, vol. 118(1), pages 153-163, October.
    4. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    5. Arantza Estévez-Fernández & Peter Borm & Pedro Calleja & Herbert Hamers, 2008. "Sequencing games with repeated players," Annals of Operations Research, Springer, vol. 158(1), pages 189-203, February.
    6. Silvia Miquel & Bas Van Velzen & Herbert Hamers & Henk Norde, 2009. "Assignment Situations With Multiple Ownership And Their Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-13.
    7. Granot, D. & Hamers, H.J.M. & Tijs, S.H., 1999. "On some balanced, totally balanced and submodular delivery games," Other publications TiSEM e0496604-0162-4a27-992c-a, Tilburg University, School of Economics and Management.
    8. Granot, Daniel & Hamers, Herbert & Kuipers, Jeroen & Maschler, Michael, 2011. "On Chinese postman games where residents of each road pay the cost of their road," Games and Economic Behavior, Elsevier, vol. 72(2), pages 427-438, June.
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