30 research outputs found
Utility Design for Distributed Resource Allocation -- Part I: Characterizing and Optimizing the Exact Price of Anarchy
Game theory has emerged as a fruitful paradigm for the design of networked
multiagent systems. A fundamental component of this approach is the design of
agents' utility functions so that their self-interested maximization results in
a desirable collective behavior. In this work we focus on a well-studied class
of distributed resource allocation problems where each agent is requested to
select a subset of resources with the goal of optimizing a given system-level
objective. Our core contribution is the development of a novel framework to
tightly characterize the worst case performance of any resulting Nash
equilibrium (price of anarchy) as a function of the chosen agents' utility
functions. Leveraging this result, we identify how to design such utilities so
as to optimize the price of anarchy through a tractable linear program. This
provides us with a priori performance certificates applicable to any existing
learning algorithm capable of driving the system to an equilibrium. Part II of
this work specializes these results to submodular and supermodular objectives,
discusses the complexity of computing Nash equilibria, and provides multiple
illustrations of the theoretical findings.Comment: 15 pages, 5 figure
Nash and Wardrop equilibria in aggregative games with coupling constraints
We consider the framework of aggregative games, in which the cost function of
each agent depends on his own strategy and on the average population strategy.
As first contribution, we investigate the relations between the concepts of
Nash and Wardrop equilibrium. By exploiting a characterization of the two
equilibria as solutions of variational inequalities, we bound their distance
with a decreasing function of the population size. As second contribution, we
propose two decentralized algorithms that converge to such equilibria and are
capable of coping with constraints coupling the strategies of different agents.
Finally, we study the applications of charging of electric vehicles and of
route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The
first three authors contributed equall
The Anarchy-Stability Tradeoff in Congestion Games
This work focuses on the design of incentive mechanisms in congestion games,
a commonly studied model for competitive resource sharing. While the majority
of the existing literature on this topic focuses on unilaterally optimizing the
worst case performance (i.e., price of anarchy), in this manuscript we
investigate whether optimizing for the worst case has consequences on the best
case performance (i.e., price of stability). Perhaps surprisingly, our results
show that there is a fundamental tradeoff between these two measures of
performance. Our main result provides a characterization of this tradeoff in
terms of upper and lower bounds on the Pareto frontier between the price of
anarchy and the price of stability. Interestingly, we demonstrate that the
mechanism that optimizes the price of anarchy inherits a matching price of
stability, thereby implying that the best equilibrium is not necessarily any
better than the worst equilibrium for such a design choice. Our results also
establish that, in several well-studied cases, the unincentivized setting does
not even lie on the Pareto frontier, and that any incentive with price of
stability equal to 1 incurs a much higher price of anarchy.Comment: 27 pages, 1 figure, 1 tabl
In Congestion Games, Taxes Achieve Optimal Approximation
In this work, we consider the problem of minimising the social cost in atomic congestion games. For this problem, we provide tight computational lower bounds along with taxation mechanisms yielding polynomial time algorithms with optimal approximation. Perhaps surprisingly, our results show that indirect interventions, in the form of efficiently computed taxation mechanisms, yield the same performance achievable by the best polynomial time algorithm, even when the latter has full control over the agents' actions. It follows that no other tractable approach geared at incentivizing desirable system behavior can improve upon this result, regardless of whether it is based on taxations, coordination mechanisms, information provision, or any other principle. In short: Judiciously chosen taxes achieve optimal approximation. Three technical contributions underpin this conclusion. First, we show that computing the minimum social cost is NP-hard to approximate within a given factor depending solely on the admissible resource costs. Second, we design a tractable taxation mechanism whose efficiency (price of anarchy) matches this hardness factor, and thus is worst-case optimal. As these results extend to coarse correlated equilibria, any no-regret algorithm inherits the same performances, allowing us to devise polynomial time algorithms with optimal approximation