TY - GEN

T1 - Polynomial time equilibria in bottleneck congestion games

AU - Busch, Costas

AU - Kannan, Rajgopal

PY - 2018/6/11

Y1 - 2018/6/11

N2 - We consider bottleneck congestion games in an arbitrary graph G where player strategies are flows in G. The player's objective is to select a flow that minimizes the maximum load on any edge, that is, minimize the bottleneck congestion. We consider splittable and unsplittable games with pure strategies. It has been an open problem for many years to determine whether it is possible to compute in polynomial time Nash equilibriums for bottleneck congestion games in arbitrary graphs. For splittable games we provide a polynomial time algorithm to compute a Nash equilibrium which is also a global optimum. The unsplittable game problem is known to be PLS-complete, and so we focus on approximate Nash equilibria where players are approximately stable. For uniform player demands we give an algorithm to compute a O(logm)-approximate unsplittable equilibrium in polynomial time, where m is the number of edges. For non-uniform player demands we give an algorithm to compute a O(log(m))-approximate unsplittable equilibrium in polynomial time, where = O(1 + log(dmax/dmin)) and dmax, dmin are the respective maximum and minimum player demands. To our knowledge, these are the first general results for efficiently computing equilibria of pure bottleneck congestion games in arbitrary graphs, both for the splittable and unsplittable cases.

AB - We consider bottleneck congestion games in an arbitrary graph G where player strategies are flows in G. The player's objective is to select a flow that minimizes the maximum load on any edge, that is, minimize the bottleneck congestion. We consider splittable and unsplittable games with pure strategies. It has been an open problem for many years to determine whether it is possible to compute in polynomial time Nash equilibriums for bottleneck congestion games in arbitrary graphs. For splittable games we provide a polynomial time algorithm to compute a Nash equilibrium which is also a global optimum. The unsplittable game problem is known to be PLS-complete, and so we focus on approximate Nash equilibria where players are approximately stable. For uniform player demands we give an algorithm to compute a O(logm)-approximate unsplittable equilibrium in polynomial time, where m is the number of edges. For non-uniform player demands we give an algorithm to compute a O(log(m))-approximate unsplittable equilibrium in polynomial time, where = O(1 + log(dmax/dmin)) and dmax, dmin are the respective maximum and minimum player demands. To our knowledge, these are the first general results for efficiently computing equilibria of pure bottleneck congestion games in arbitrary graphs, both for the splittable and unsplittable cases.

KW - Arbitrary graphs

KW - Bottleneck congestion

KW - Equilibrium computation

KW - Nash equilibrium

KW - Polynomial time

UR - http://www.scopus.com/inward/record.url?scp=85050166010&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050166010&partnerID=8YFLogxK

U2 - 10.1145/3219166.3219221

DO - 10.1145/3219166.3219221

M3 - Conference contribution

AN - SCOPUS:85050166010

T3 - ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

SP - 393

EP - 409

BT - ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

PB - Association for Computing Machinery, Inc

T2 - 19th ACM Conference on Economics and Computation, EC 2018

Y2 - 18 June 2018 through 22 June 2018

ER -