Central European Journal of Operations Research

, Volume 23, Issue 4, pp 743–762 | Cite as

Traffic routing oligopoly

  • Dávid Csercsik
  • Balázs Sziklai
Original Paper


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.


Cooperative game theory Partition function form games Routing Externalities 



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.


  1. Altman E, Boulognea T, El-Azouzi R, Jimenez T, Wynter L (2006) A survey on networking games in telecommunications. Comput Oper Res 33:286–311zbMATHMathSciNetCrossRefGoogle Scholar
  2. Devroye N, Vu M, Tarokh V (2008) Cognitive radio networks: highlights of information theoretic limits, models and design. IEEE Signal Process Mag 25:12–23CrossRefADSGoogle Scholar
  3. Feldmann R, Gairing M, Lucking T, Monien B, Rode M (2003) Selfish routing in non-cooperative networks: a survey. In: Rovan B, Vojtás P (eds) Mathematical foundations of computer science 2003, lecture notes in computer science, vol 2747. Springer, Berlin, Heidelberg, pp 21–45CrossRefGoogle Scholar
  4. Grabisch M, Funaki Y (2012) A coalition formation value for games in partition function form. Eur J Oper Res 221(1):175–185zbMATHMathSciNetCrossRefGoogle Scholar
  5. Karakostas G, Kolliopoulos S (2009) Stackelberg strategies for selfish routing in general multicommodity networks. Algorithmica 53:132–153Google Scholar
  6. Khandani A, Modiano E, Abounadi J, Zheng L (2005) Cooperative routing in wireless networks. In: Szymanski B, Bulent Y (eds) Advances in pervasive computing and networking. Springer, US, pp 97–117CrossRefGoogle Scholar
  7. Khandani A, Abounadi J, Modiano E, Zheng L (2007) Cooperative routing in static wireless networks. IEEE Trans Commun 55:2185–2192CrossRefGoogle Scholar
  8. Kóczy LÁ (2007) A recursive core for partition function form games. Theory Decis 63(1):41–51Google Scholar
  9. Kóczy LÁ (2009) Sequential coalition formation and the core in the presence of externalities. Games Econ Behav 66(1):559–565zbMATHCrossRefGoogle Scholar
  10. Korilis Y, Lazar A, Orda A (1997) Achieving network optima using stackelberg routing strategies. IEEE/ACM Trans Netw 5:161–173CrossRefGoogle Scholar
  11. Koutsoupias E, Papadimitriou C (2009) Worst-case equilibria. Comput Sci Rev 3(2):65–69Google Scholar
  12. Nisan N, Roughgarden T, Tardos E, Vazirani V (2007) Algorithmic game theory. Cambridge University Press, 32 Avenue of the Americas, New York, NY 10013–2473, USAGoogle Scholar
  13. Pigou A (1920) The economics of welfare. Macmillan, LondonGoogle Scholar
  14. Roughgarden T (2005) Selfish routing and the price of anarchy. MIT Press, 55 Hayward Street Cambridge, MA 02142–1493 USAGoogle Scholar
  15. Roughgarden T (2006) Selfish routing and the price of anarchy. Tech. report, Department of Computer Science, Stanford University.
  16. Thrall RM, Lucas WF (1963) \(n\)-person games in partition function form. Naval Res Logist Q 10(4):281–298zbMATHMathSciNetCrossRefGoogle Scholar
  17. Wardrop J (1952) Some theoretical aspects of road traffic research communication networks. Proc Inst Civil Eng 1:325–378Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Information TechnologyPázmány Péter Catholic UniversityBudapestHungary
  2. 2.Game Theory Research Group, Centre for Economic and Regional StudiesHungarian Academy of SciencesBudapestHungary

Personalised recommendations