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Shortest path games

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  • Rosenthal, Edward C.

Abstract

We study cooperative games that arise from the problem of finding shortest paths from a specified source to all other nodes in a network. Such networks model, among other things, efficient development of a commuter rail system for a growing metropolitan area. We motivate and define these games and provide reasonable conditions for the corresponding rail application. We show that the core of a shortest path game is nonempty and satisfies the given conditions, but that the Shapley value for these games may lie outside the core. However, we show that the shortest path game is convex for the special case of tree networks, and we provide a simple, polynomial time formula for the Shapley value in this case. In addition, we extend our tree results to the case where users of the network travel to nodes other than the source. Finally, we provide a necessary and sufficient condition for shortest paths to remain optimal in dynamic shortest path games, where nodes are added to the network sequentially over time.

Suggested Citation

  • Rosenthal, Edward C., 2013. "Shortest path games," European Journal of Operational Research, Elsevier, vol. 224(1), pages 132-140.
    • Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:132-140
    DOI: 10.1016/j.ejor.2012.06.047
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    Cited by:

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    2. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, Department of Economics.
    3. Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.
    4. repec:has:discpr:1321 is not listed on IDEAS
    5. Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2020. "Stability in shortest path problems," MPRA Paper 98504, University Library of Munich, Germany.
    6. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    7. Balázs Sziklai & Tamás Fleiner & Tamás Solymosi, 2014. "On the Core of Directed Acyclic Graph Games," CERS-IE WORKING PAPERS 1418, Institute of Economics, Centre for Economic and Regional Studies.
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    9. Xiaojin Sun & Kwok Ping Tsang, 2013. "Housing Markets, Regulations and Monetary Policy," Working Papers e07-45, Virginia Polytechnic Institute and State University, Department of Economics.
    10. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    11. Bahel, Eric & Trudeau, Christian, 2019. "A cost sharing example in which subsidies are necessary for stability," Economics Letters, Elsevier, vol. 185(C).
    12. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    13. Borkotokey, Surajit & Kumar, Rajnish & Sarangi, Sudipta, 2015. "A solution concept for network games: The role of multilateral interactions," European Journal of Operational Research, Elsevier, vol. 243(3), pages 912-920.
    14. Uhan, Nelson A., 2015. "Stochastic linear programming games with concave preferences," European Journal of Operational Research, Elsevier, vol. 243(2), pages 637-646.
    15. Eric Bahel, 2014. "On the core and bargaining set of a veto game," Working Papers e07-48, Virginia Polytechnic Institute and State University, Department of Economics.
    16. Rosenthal, Edward C., 2017. "A cooperative game approach to cost allocation in a rapid-transit network," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 64-77.

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