Pruning Algorithms for A Replicator Dynamics Method in Multiple OD Selfish Routing Games

Abstract

A traffic flow allocation has been studied by many researches. This problem is treated by both urban planning research and game theoretical approaches. We stand on game theory to consider the traffic flow allocation problem by treating a class of congestion games on the network. The traffic flow allocation is called, in context the congestion game, a selfish routing game. In this game, our proposal is to find an equilibria of decision making of the players. The player's decision is amounts of flows for each origin-destination path. It is known that the equilibrium searching problem as edge based modeling is able to compute easily by using Frank-Wolfe method, however, the edge based model has weak expressiveness. Thus we employ a path based modeling that can treat some complex phenomena. In this model, since we need to handle many paths in a network, it is known that the equilibrium searching problem is difficult. In this paper, we study a solving method for a multi OD selfish routing game, and a method for solving standard routing games and its high speeding method. Our algorithm employs a replicator dynamics which is one of iterative optimization techniques. In the solution based on the replicator dynamics, the calculation time is very large, since the calculation is also performed for all paths. Therefore, as a preprocessing of solving by replicator dynamics, the policy of the proposed method is to make computation time faster by deleting unused paths. This paper evaluates the algorithm by numerical experiment.