 When quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-5646
URL: https://drops.dagstuhl.de/opus/volltexte/2006/564/
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### A Cost Mechanism for Fair Pricing of Resource Usage

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### Abstract

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: (1) 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. (2) In the worst-case choice of demands, the Price of Anarchy is \$Theta (n)\$; for the special case of two agents, the Price of Anarchy is less than \$2 - frac{1}{m}\$. (3) 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.

### BibTeX - Entry

```@InProceedings{mavronicolas_et_al:DSP:2006:564,
author =	{Marios Mavronicolas and Panagiota Panagopoulou and Paul G. Spirakis},
title =	{A Cost Mechanism for Fair Pricing of Resource Usage},
booktitle =	{Algorithmic Aspects of Large and Complex Networks},
year =	{2006},
editor =	{Stefano Leonardi and Friedhelm Meyer auf der Heide and Dorothea Wagner},
number =	{05361},
series =	{Dagstuhl Seminar Proceedings},
ISSN =	{1862-4405},
publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
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