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Generalized Efficiency Bounds In Distributed Resource Allocation (2012)
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BibTeX
@MISC{Marden12generalizedefficiency,
author = {Jason R. Marden and Tim Roughgarden},
title = { Generalized Efficiency Bounds In Distributed Resource Allocation},
year = {2012}
}
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Abstract
Game theory is emerging as a popular tool for distributed control of multiagent systems. In order to take advantage of these game theoretic tools the interactions of the autonomous agents must be designed within a game theoretic environment. A central component of this game theoretic design is the assignment of a local objective function to each decision-maker. One promising approach to utility design is assigning each agent an objective function in accordance with the agent’s Shapley value. This method frequently results in games that possess many desirable features including the existence and efficiency of pure Nash equilibria. In this paper we explore the relationship between the Shapley value utility design and the resulting efficiency of both pure Nash equilibria and coarse correlated equilibria. To study this relationship we introduce a simple class of resource allocation problems. Within this class of resource allocation problems, we derive an explicit relationship between the structure of the resource allocation problem and the efficiency of the resulting equilibria. Lastly, we derive a bicriteria bound for this class of resource allocation problems. By bicriteria bound, we mean a bound on the value of the optimal allocation relative to the value of an equilibrium allocation with additional agents.
Keyphrases
resource allocation problem efficiency bound distributed resource allocation bicriteria bound pure nash equilibrium shapley value utility design utility design simple class objective function many desirable feature optimal allocation relative agent shapley value multiagent system additional agent resulting efficiency equilibrium allocation game theoretic design popular tool explicit relationship distributed control game theoretic environment autonomous agent central component local objective function game theory
