Merge-proofness and cost solidarity in shortest path games

Bahel, Eric and Gómez-Rúa, María and Vidal-Puga, Juan (2024): Merge-proofness and cost solidarity in shortest path games.

Abstract

We study cost-sharing rules in network problems where agents seek to ship quantities of some good to their respective locations, and the cost on each arc is linear in the flow crossing it. In this context, Core Selection requires that each subgroup of agents pay a joint cost share that is not higher than its stand-alone cost. We prove that the demander rule, under which each agent pays the cost of her shortest path for each unit she demands, is the unique cost-sharing rule satisfying both Core Selection and Merge Proofness. The Merge Proofness axiom prevents distinct nodes from reducing their joint cost share by merging into a single node. An alternative characterization of the demander rule is obtained by combining Core Selection and Cost Solidarity. The Cost Solidarity axiom says that each agent's cost share should be weakly increasing in the cost matrix.

• Item Type: MPRA Paper
• Language: English
• Keywords: Shortest path games, cost sharing, core, merge proofness, solidarity
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D85 - Network Formation and Analysis: Theory

References

Bahel, E., Gómez-Rúa, M., and Vidal-Puga, J. (2024). Stable and weakly additive cost sharing in shortest path problems. Journal of Mathematical Economics, 110:102921.

Bahel, E. and Trudeau, C. (2014). Stable lexicographic rules for shortest path games. Economic Letters, 125(2):266-269.

Bergantiños, G. and Vidal-Puga, J. (2007). A fair rule in minimum cost spanning tree problems. Journal of Economic Theory, 137(1):326-352.

de Frutos, M. A. (1999). Coalitional manipulation in a bankruptcy problem. Review of Economic Design, 4(3):255-272.

Gómez-Rúa, M. and Vidal-Puga, J. (2011). Merge-proofness in minimum cost spanning tree problems. International Journal of Game Theory, 40(2):309-329.

Gómez-Rúa, M. and Vidal-Puga, J. (2017). A monotonic and merge-proof rule in minimum cost spanning tree situations. Economic Theory, 63:813-826.

Hezarkhani, B. (2016). Pairwise mergers in bipartite matching games with an application in collaborative logistics. Operations Research Letters, 44(6):818-822.

Horn, H. and Wolinsky, A. (1988). Bilateral monopolies and incentives for merger. Rand Journal of Economics, 19(3):408-419.

Moulin, H. (2008). Proportional scheduling, split-proofness, and merge-proofness. Games and Economic Behavior, 63(2):567-587.

Rosenthal, E. C. (2013). Shortest path games. European Journal of Operational Research, 224(1):132-140.

Sprumont, Y. (2005). On the discrete version of the Aumann-Shapley cost-sharing method. Econometrica, 73(5):1693-1712.

Tijs, S., Borm, P., Lohmann, E., and Quant, M. (2011). An average lexicographic value for cooperative games. European Journal of Operational Research, 213(1):210-220.