The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games

Resource allocation problems play a key role in many applications, including traffic networks, telecommunication networks and economics. In most applications, the allocation of resources is determined by a finite number of independent players, each optimizing an individual objective function. An important question in all these applications is the degree of suboptimality caused by selfish resource allocation. We consider the worst-case efficiency of cost sharing methods in resource allocation games in terms of the ratio of the minimum guaranteed surplus of a Nash equilibrium and the maximal surplus. Resource allocation games are closely related to congestion games and model the strategic interaction of players competing over a finite set of congestible resources. Our main technical result is an upper bound on the efficiency loss that depends on the class of allowable cost functions and the class of allowable cost sharing methods. We demonstrate the power of this bound by evaluating the worst-case efficiency loss for three well known cost sharing methods: incremental cost sharing, marginal cost pricing, and average cost sharing.