# Traffic routing oligopoly

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## Abstract

The purpose of this paper is to introduce a novel family of transferable utility games related to congested networks. We assume that players are traffic coordinators, who explicitly route their deliveries in the network. The costs of the players are determined by the total latency of the deliveries, which in turn can be calculated by the edge latency functions. Since the edge latency functions assign a latency value to the total flow on the corresponding edge, as cooperating players redesign their routing in order to minimize their overall cost, outsiders will be affected as well. This gives rise to externalities therefore the resulting game is described in partition function form. We show that cooperation may imply both negative and positive externalities in the defined game. We assume that coalitions may determine their routing according to different predictive strategies. We show that the increasing order of predictive strategies may converge to a Nash equilibrium (NE), although convergence is not guaranteed, even if a unique NE exists. Furthermore we analyze the superadditivity and stability properties of the game, and show that subadditivity may arise and the recursive core may be empty if the latency functions are not monotone or not continuous.

## Keywords

Cooperative game theory Partition function form games Routing Externalities## Notes

### Acknowledgments

The authors acknowledge the contribution of the members of the Game Theory Research Group, László Á. Kóczy, Helga Habis and Péter Biró. The work has been supported by the Hungarian Academy of Sciences via grant LP-004/2010, by the Hungarian Scientific Research Fund OTKA NF 104706, and by TÁMOP-4.2.1/B-11/2/KMR-2011-12-0002. The authors dedicate this manuscript to Gábor Holló.

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