The 'Price of Anarchy' states that the performance of multi-agent service systems degrades with the agents' selfishness (anarchy). We investigate a service model in which both customers and the firm are strategic. We find that, for a Stackelberg game in which the server invests in capacity before customers decide whether or not to join, there can be a 'Benefit of Anarchy', that is, customers acting selfishly can have a greater overall utility than customers who are coordinated to maximize their overall utility. We also show that customer anarchy can be socially beneficial, resulting in a 'Social Benefit of Anarchy'. We show that such phenomena are rather general and can arise in multiple settings (e.g. in both profit-maximizing and welfare-maximizing firms, in both capacity-setting and price-setting firms, and in both observable and unobservable queues). However, the underlying mechanism leading to the Benefit of Anarchy can differ significantly from one setting to another.