Routing games with an unknown set of active players

In many settings there exists a set of potential participants, but the set of participants who are actually active in the system, and in particular their number, is unknown. This topic has been first analyzed by Ashlagi, Monderer, and Tennenholtz [AMT] in the context of simple routing games, where the network consists of a set of parallel links, and the agents can not split their jobs among different paths. AMT used the model of pre-Bayesian games, and the concept of safety-level equilibrium for the analysis of these games. In this paper we extend the work by AMT. We deal with splitable routing games, where each player can split his job among paths in a given network. In this context we generalize the analysis to all two-node networks, in which paths may intersect in unrestricted manner. We characterize the relationships between the number of potential participants and the number of active participants under which ignorance is beneficial to each of the active participants.

[1]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[2]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[3]  Ariel Orda,et al.  Competitive routing in multiuser communication networks , 1993, TNET.

[4]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[5]  L. Shapley,et al.  Potential Games , 1994 .

[6]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[7]  Tim Roughgarden,et al.  How bad is selfish routing? , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[8]  Eitan Altman,et al.  Competitive routing in networks with polynomial cost , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[9]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[10]  Paul G. Spirakis,et al.  The price of selfish routing , 2001, STOC '01.

[11]  Eitan Altman,et al.  Competitive routing in networks with polynomial costs , 2002, IEEE Trans. Autom. Control..

[12]  Moshe Tennenholtz,et al.  Local-Effect Games , 2003, IJCAI.

[13]  Moshe Tennenholtz,et al.  Bundling equilibrium in combinatorial auctions , 2002, Games Econ. Behav..

[14]  Craig Boutilier,et al.  Regret Minimizing Equilibria and Mechanisms for Games with Strict Type Uncertainty , 2004, UAI.

[15]  Csaba D. Tóth,et al.  Uncoordinated Load Balancing and Congestion Games in P2P Systems , 2004, IPTPS.

[16]  Martin Gairing,et al.  Selfish Routing with Incomplete Information , 2005, SPAA '05.

[17]  Yossi Azar,et al.  The Price of Routing Unsplittable Flow , 2005, STOC '05.

[18]  Y. Narahari,et al.  Price of Anarchy of Network Routing Games with Incomplete Information , 2005, WINE.

[19]  Aranyak Mehta,et al.  Fairness and optimality in congestion games , 2005, EC '05.

[20]  Dimitris Bertsimas,et al.  Robust game theory , 2006, Math. Program..

[21]  Itai Ashlagi,et al.  Resource selection games with unknown number of players , 2006, AAMAS '06.

[22]  Dov Monderer,et al.  Multipotential Games , 2007, IJCAI.

[23]  Rune B. Lyngsø,et al.  Lecture Notes I , 2008 .