Cost Sharing Mechanisms for Fair Pricing of Resources Usage

We propose a simple and intuitive cost mechanism which assigns costs for the competitive usage of m resources by n selfish agents. Each agent has an individual demand; demands are drawn according to some probability distribution. The cost paid by an agent for a resource she chooses is the total demand put on the resource divided by the number of agents who chose that same resource. So, resources charge costs in an equitable, fair way, while each resource makes no profit out of the agents. We call our model the Fair Pricing model. Its fair cost mechanism induces a non-cooperative game among the agents. To evaluate the Nash equilibria of this game, we introduce the Diffuse Price of Anarchy, as an extension of the Price of Anarchy that takes into account the probability distribution on the demands. We prove: – Pure Nash equilibria may not exist, unless all chosen demands are identical. In contrast, we have been able to prove that pure Nash equilibria do exist for two closely related cost sharing models, namely the Average Cost Pricing and the Serial Cost Sharing models. – A fully mixed Nash equilibrium exists for all possible choices of the demands. Further on, the fully mixed Nash equilibrium is the unique Nash equilibrium in case there are only two agents. – In the worst-case choice of demands, the Price of Anarchy is Θ(n); for the special case of two agents, the Price of Anarchy is less than 2− 1 m . ? Partially supported by the EU within the 6th Framework Programme under contracts 001907 “Dynamically Evolving, Large Scale Information Systems” (DELIS) and 015964 “Algorithmic Principles for Building Efficient Overlay Computers” (AEOLUS), and by the General Secretariat for Research and Technology of the Greek Ministry of Development within the programme PENED 2003. A previous version of this paper appeared at the 1st International Workshop on Internet and Network Economics (WINE 2005). ?? Corresponding Author. Phone: +30 6944 395 691. Fax: +3