The Price of Anarchy (PoA) is a concept in game theory and mechanism design that measures how the social welfare of a system degrades due to selfish behavior of its agents. It has been studied extensively in various contexts, particularly in auctions. In an auction, there are one or more items and one or more agents with different valuations for the items. The items have to be divided among the agents. It is desired that the social welfare - the sum of values of all agents - be as high as possible. Obviously .