Repeated Selfish Routing with Incomplete Information

Abstract

<p>Selfish routing is frequently discussed. The general framework of a system of non-cooperative users can be used to model many different optimization problems such as network routing, traffic or transportation problems.</p> <p>It is well known that the Wardrop user equilibria (i.e. the user optima) generally do not optimize the overall system cost in a traffic routing problem.</p> <p>In order to induce the equilibrium flow to be as close to the optimal flow as possible, the term “toll” is introduced. With the addition of tolls, a traffic system does not show the actual cost to the users but the displayed cost of users, which is the summation of the actual cost and the toll. A common behavioral assumption in traffic network modeling is that every user chooses a path which is perceived as the shortest path, then the whole system achieves the equilibrium of the displayed cost. It is proved that there exists an optimal toll which can induce the equilibrium flow under displayed cost to be the optimal flow in reality.</p> <p>However, this conclusion holds only if the selfish routing executes only once. If the game is played repeatedly, the users will detect the difference between the actual and displayed costs. Then, they will not completely trust the information given by the system and calculate the cost. The purpose of this thesis is to find out the optimal strategy given by the system–how to set tolls in order to maintain the flow as close to the optimal flow as possible.</p>