Applications of approximation algorithms to cooperative games

The Internet, which is intrinsically a common playground for a large number of players with varying degrees of collaborative and sel sh motives, naturally gives rise to numerous new game theoretic issues. Computational problems underlying solutions to these issues, achieving desirable economic criteria, often turn out to be NP-hard. It is therefore natural to apply notions from the area of approximation algorithms to these problems. The connection is made more meaningful by the fact that the two areas of game theory and approximation algorithms share common methodology { both heavily use machinery from the theory of linear programming. Various aspects of this connection have been explored recently by researchers [8, 10, 15, 20, 21, 26, 27, 29]. In this paper we will consider the problem of sharing the cost of a jointly utilized facility in a \fair" manner. Consider a service providing company whose set of possible customers, also called users, is U . For each set S U C(S) denotes the cost incurred by the company to serve the users in S. The function C is known as the cost function. For concreteness, assume that the company broadcasts news of common interest, such as nancial news, on the net. Each user, i, has a utility, u 0 i , for receiving the news. This utility u 0 i is known only to user i. User i enjoys a bene t of u 0 i x i if she gets the news at the price x i . If she does not get the news then her bene t is 0. Each user is assumed to be sel sh, and hence in order to maximize bene t, may misreport her utility as some other number, say u i . For the rest of the discussion, the utility of user i will mean the number u i . A cost sharing mechanism determines which users receive the broadcast and at what price. The mechanism is strategyproof if the dominant strategy of each user is to reveal the