Distributed resource allocation through utility design - Part I: optimizing the performance certificates via the price of anarchy

07/03/2018
by   Dario Paccagnan, et al.
0

Game theory has emerged as a novel approach for the coordination of multiagent systems. A fundamental component of this approach is the design of a local utility function for each agent so that their selfish maximization achieves the global objective. In this paper we propose a novel framework to characterize and optimize the worst case performance (price of anarchy) of any resulting equilibrium as a function of the chosen utilities, thus providing a performance certificate for a large class of algorithms. More specifically, we consider a class of resource allocation problems, where each agent selects a subset of the resources with the goal of maximizing a welfare function. First, we show that any smoothness argument is inconclusive for the design problems considered. Motivated by this, we introduce a new approach providing a tight expression for the price of anarchy (PoA) as a function of the chosen utility functions. Leveraging this result, we show how to design the utilities so as to maximize the PoA through a tractable linear program. In Part II we specialize the results to submodular and supermodular welfare functions, discuss complexity issues and provide two applications.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset