  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) and study
the impact of the degree of cooperation on it. We identify another type of
paradox in cooperation scenario. We identify that when we increase the degree
of cooperation of a user while other users keep unchanged their degree of
cooperation, leads to an improvement in performance of that 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.
