We consider a splittable atomic game with lossy links on a ring in which the cost that each player i minimizes is their own loss rate of packets. The costs are therefore non-additive (unlike costs based on delays or tolls) and moreover, there is no flow conservation (total flow entering a link is greater than the flow leaving it). We derive a closed-form for the equilibrium, which allows us to obtain insight on the structure of the equilibrium. We also derive the globally optimal solution and obtain conditions for the equilibrium to coincide with the globally optimal solution.