When is Anarchy Beneficial

In many service systems, customers acting to maximize their individual utility (selfish customers) will result in a policy that does not maximize their overall utility; this effect is known as the Price of Anarchy (PoA). More specifically, the PoA, defined to be the ratio of selfish utility (the overall average utility for selfish customers) to collective utility (the overall average utility if customers act to maximize their overall average utility) is generally less than one. Of course, when the environment is fixed, the best case PoA is one, by definition of the maximization problem. However, we show that in systems with feedback, where the environment may change depending on customer behavior, there can be a Benefit of Anarchy, i.e., we can have a PoA that is strictly larger than one. We give an example based on a Stackelberg game between a service provider and customers in a singleserver queue.