Abstract
We propose a simple and intuitive cost mechanism which assigns costs for the competitive usage of mresources 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:
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Pure Nash equilibria may not exist, unless all chosen demands are identical; in contrast, 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.
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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 \(2 - \frac{1}{m}\).
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Assume now that demands are drawn from a bounded, independent probability distribution, where all demands are identically distributed and each is at most a (universal for the class) constant times its expectation. Then, the Diffuse Price of Anarchy is at most that same constant, which is just 2 when each demand is distributed symmetrically around its expectation.
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.
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Mavronicolas, M., Panagopoulou, P.N., Spirakis, P.G. (2005). A Cost Mechanism for Fair Pricing of Resource Usage. In: Deng, X., Ye, Y. (eds) Internet and Network Economics. WINE 2005. Lecture Notes in Computer Science, vol 3828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11600930_21
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DOI: https://doi.org/10.1007/11600930_21
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