Routing games : From egoism to altruism

The paper studies the routing in the network shared by several users. Each user seeks to optimize either its own performance or some combination between its own performance and that of other users, by controlling the routing of its given flow demand. We parameterize the degree of cooperation which allows to cover the fully non-cooperative behavior, the fully cooperative behavior, and even more, the fully altruistic behavior, all these as special cases of the parameter´s choice. A large part of the work consists in exploring the impact of the degree of cooperation on the equilibrium. Our first finding is to identify multiple Nash equilibria with cooperative behavior that do not occur in the non-cooperative case under the same conditions (cost, demand and topology). We then identify Braess like paradox (in which adding capacity or adding a link to a network results in worse performance to all users) in presence of user´s cooperation. We identify another type of paradox in cooperation scenario: when a given user increases its degree of cooperation while other users keep unchanged their degree of cooperation, this may lead to an improvement in performance of that given user. We then pursue the exploration and carry it on to the setting of Mixed equilibrium (i.e. some users are non atomic-they have infinitesimally small demand, and other have finite fixed demand). We finally obtain some theoretical results that show that for low degree of cooperation the equilibrium is unique, confirming the results of our numerical study.