Nash equilibria in routing games with edge priorities

In this paper we present a new competitive packet routing model with edge priorities. We consider players that route selfishly through a network over time and try to reach their destinations as fast as possible. If the number of players who want to enter an edge at the same time exceeds the inflow capacity of this edge, edge priorities with respect to the preceding edge solve these conflicts. Our edge priorities are well-motivated by applications in traffic. For this class of games, we show the existence of equilibrium solutions for single-source-single-sink games and we analyze structural properties of these solutions. We present an algorithm that computes Nash equilibria and we prove bounds both on the Price of Stability and on the Price of Anarchy. Moreover, we introduce the new concept of a Price of Mistrust. Finally, we also study the relations to earliest arrival flows.

[1]  José R. Correa,et al.  Existence and Uniqueness of Equilibria for Flows over Time , 2011, ICALP.

[2]  Martin Skutella,et al.  Solving Evacuation Problems Efficiently--Earliest Arrival Flows with Multiple Sources , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

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

[4]  Daniel Schmand,et al.  Competitive Packet Routing with Priority Lists , 2016, MFCS.

[5]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[6]  Martin Hoefer,et al.  Competitive routing over time , 2011, Theor. Comput. Sci..

[7]  David Gale,et al.  Transient flows in networks. , 1959 .

[8]  D. R. Fulkerson,et al.  Constructing Maximal Dynamic Flows from Static Flows , 1958 .

[9]  Martin Skutella,et al.  Packet Routing: Complexity and Algorithms , 2009, WAOA.

[10]  Martin Skutella,et al.  Quickest Flows Over Time , 2007, SIAM J. Comput..

[11]  Maciej M. Syslo,et al.  Characterizations of outerplanar graphs , 1979, Discret. Math..

[12]  Shimon Even,et al.  Graph Algorithms: Flow in Networks , 2011 .

[13]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

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

[15]  Stefan Ruzika,et al.  Earliest arrival flows on series‐parallel graphs , 2011, Networks.

[16]  Michael Florian,et al.  The continuous dynamic network loading problem : A mathematical formulation and solution method , 1998 .

[17]  Zhigang Cao,et al.  A Network Game of Dynamic Traffic , 2017, EC.

[18]  Ali Akbar Shaikh,et al.  Flow in Networks , 2019 .

[19]  Ronald Koch,et al.  Nash Equilibria and the Price of Anarchy for Flows over Time , 2011, Theory of Computing Systems.

[20]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[21]  Peter Kulchyski.  and , 2015 .

[22]  Samuel Yagar.  Dynamic traffic assignment by individual path minimization and queuing , 1971 .

[23]  Dietrich Braess,et al.  Über ein Paradoxon aus der Verkehrsplanung , 1968, Unternehmensforschung.

[24]  W. L. Wilkinson,et al.  An Algorithm for Universal Maximal Dynamic Flows in a Network , 1971, Oper. Res..

[25]  Elias Koutsoupias,et al.  The price of anarchy of finite congestion games , 2005, STOC '05.

[26]  Martin Skutella,et al.  An Introduction to Network Flows over Time , 2008, Bonn Workshop of Combinatorial Optimization.

[27]  Robert W. Rosenthal,et al.  The network equilibrium problem in integers , 1973, Networks.