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Statics and Dynamics of Selfish Interactions in Distributed Service Systems

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  • Fabrizio Altarelli
  • Alfredo Braunstein
  • Luca Dall’Asta

Abstract

We study a class of games which models the competition among agents to access some service provided by distributed service units and which exhibits congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.

Suggested Citation

  • Fabrizio Altarelli & Alfredo Braunstein & Luca Dall’Asta, 2015. "Statics and Dynamics of Selfish Interactions in Distributed Service Systems," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-29, July.
    • Handle: RePEc:plo:pone00:0119286
    DOI: 10.1371/journal.pone.0119286
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    References listed on IDEAS

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    2. Gilat Levy, 2005. "The Politics of Public Provision of Education," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(4), pages 1507-1534.
    3. Mark Lijesen & Victoria Shestalova, 2007. "Public and private roles in road infrastructure: an exploration of market failure, public instruments and government failure," CPB Document 146, CPB Netherlands Bureau for Economic Policy Analysis.
    4. A. Ramezanpour & J. Realpe-Gomez & R. Zecchina, 2011. "Statistical physics approach to graphical games: local and global interactions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 81(3), pages 327-339, June.
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