Paradoxes in a Multi-criteria Routing Game

In this paper, we consider a routing game in a network that contains lossy links. We consider a multi-objective problem where the players have each a weighted sum of a delay cost and a cost for losses. We compute the equilibrium and optimal solution (which are unique). We discover here in addition to the classical Kameda type paradox another paradoxical behavior in which higher loss rates have a positive impact on delay and therefore higher quality links may cause a worse performance even in the case of a single player.