A Network Game of Dynamic Traffic

Selfish routing is one of the fundamental models in the study of network traffic systems. While most literature assumes essentially static flows, game theoretical models of dynamic flows began to draw attention recently [1, 5]. We study a new dynamic flow game with atomic agents. The game is played over an acyclic directed network, with two special vertices called the origin o and the destination d, respectively, such that each edge is on at least one o-d path. Each edge of this network is associated with an integer capacity and a positive integer free-flow transit cost. Time horizon is infinite and discretized as 1,2,…. At each time point, a set of selfish agents enter the network from the origin, trying to reach the destination as quickly as possible. When an agent uses an edge, two costs are incurred to him: the fixed transit cost of the edge and a variable waiting cost dependent on the volume of the traffic flow on that edge and the edge capacity as well as the agent's position in the queue of agents waiting at that edge. The total cost to each agent, the latency he experiences in the network, is the sum of the two costs on all edges he uses (which form an o-d path in the network).