90 research outputs found
Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability
The price of anarchy and price of stability are three well-studied
performance metrics that seek to characterize the inefficiency of equilibria in
distributed systems. The distinction between these two performance metrics
centers on the equilibria that they focus on: the price of anarchy
characterizes the quality of the worst-performing equilibria, while the price
of stability characterizes the quality of the best-performing equilibria. While
much of the literature focuses on these metrics from an analysis perspective,
in this work we consider these performance metrics from a design perspective.
Specifically, we focus on the setting where a system operator is tasked with
designing local utility functions to optimize these performance metrics in a
class of games termed covering games. Our main result characterizes a
fundamental trade-off between the price of anarchy and price of stability in
the form of a fully explicit Pareto frontier. Within this setup, optimizing the
price of anarchy comes directly at the expense of the price of stability (and
vice versa). Our second results demonstrates how a system-operator could
incorporate an additional piece of system-level information into the design of
the agents' utility functions to breach these limitations and improve the
system's performance. This valuable piece of system-level information pertains
to the performance of worst performing agent in the system.Comment: 14 pages, 4 figure
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 scenario approach meets uncertain game theory and variational inequalities
Variational inequalities are modeling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle stochastic optimization problems, take decisions based on historical data, and quantify their risk. The overarching goal of this manuscript is to bridge these two areas of research, and thus broaden the class of problems amenable to be studied under the lens of the scenario approach. First and foremost, we provide out-of-samples feasibility guarantees for the solution of variational and quasi variational inequality problems. Second, we apply these results to two classes of uncertain games. In the first class, the uncertainty enters in the constraint sets, while in the second class the uncertainty enters in the cost functions. Finally, we exemplify the quality and relevance of our bounds through numerical simulations on a demand-response model
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
An asynchronous, forward-backward, distributed generalized Nash equilibrium seeking algorithm
In this paper, we propose an asynchronous distributed algorithm for the
computation of generalized Nash equilibria in noncooperative games, where the
players interact via an undirected communication graph. Specifically, we extend
the paper "Asynchronous distributed algorithm for seeking generalized Nash
equilibria" by Yi and Pavel: we redesign the asynchronous update rule using
auxiliary variables over the nodes rather than over the edges. This key
modification renders the algorithm scalable for highly interconnected games.
The derived asynchronous algorithm is robust against delays in the
communication and it eliminates the idle times between computations, hence
modeling a more realistic interaction between players with different update
frequencies. We address the problem from an operator-theoretic perspective and
design the algorithm via a preconditioned forward-backward splitting. Finally,
we numerically simulate the algorithm for the Cournot competition in networked
markets.Comment: Submitted to European Control Conference 2019 (under review
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