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Nash Equilibria in Competitive Societies, with Applications to Facility Location, Traffic Routing and Auction (2002)
| Citations: | 124 - 6 self |
BibTeX
@INPROCEEDINGS{Vetta02nashequilibria,
author = {Adrian Vetta},
title = {Nash Equilibria in Competitive Societies, with Applications to Facility Location, Traffic Routing and Auction},
booktitle = {},
year = {2002},
pages = {416--425},
publisher = {}
}
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Abstract
We consider the following class of problems. The value of an outcome to a society is measured via a submodular utility function (submodularity has a natural economic interpretation: decreasing marginal utility). Decisions, however are controlled by noncooperative agents who seek to maximise their own private utility. We present, under some basic assumptions, guarantees on the social performance of Nash equilibria. For submodular utility functions, any Nash equilibrium gives an expected social utility within a factor 2 of optimal, subject to a function-dependent additive term. For non-decreasing, submodular utility functions, any Nash equilibrium gives an expected social utility within a factor 1 + of optimal, where 0 1 is a number based upon the discrete curvature of the function. A condition under which all sets of social and private utility functions induce pure strategy Nash equilibria is presented. The case in which agents, themselves, make use of approximation algorithms in decision making is discussed and performance guarantees given. Finally we present some specific problems that fall into our framework. These include the competitive versions of the facility location problem and k-median problem, a maximisation version of the traffic routing problem of Roughgarden and Tardos [16], and multiple-item auctions.
Keyphrases
nash equilibrium submodular utility function traffic routing competitive society facility location social utility k-median problem noncooperative agent pure strategy nash equilibrium social performance function-dependent additive term decision making facility location problem competitive version following class maximisation version performance guarantee private utility function discrete curvature approximation algorithm multiple-item auction basic assumption natural economic interpretation specific problem decreasing marginal utility private utility
