23,721 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
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
Sharing Non-Anonymous Costs of Multiple Resources Optimally
In cost sharing games, the existence and efficiency of pure Nash equilibria
fundamentally depends on the method that is used to share the resources' costs.
We consider a general class of resource allocation problems in which a set of
resources is used by a heterogeneous set of selfish users. The cost of a
resource is a (non-decreasing) function of the set of its users. Under the
assumption that the costs of the resources are shared by uniform cost sharing
protocols, i.e., protocols that use only local information of the resource's
cost structure and its users to determine the cost shares, we exactly quantify
the inefficiency of the resulting pure Nash equilibria. Specifically, we show
tight bounds on prices of stability and anarchy for games with only submodular
and only supermodular cost functions, respectively, and an asymptotically tight
bound for games with arbitrary set-functions. While all our upper bounds are
attained for the well-known Shapley cost sharing protocol, our lower bounds
hold for arbitrary uniform cost sharing protocols and are even valid for games
with anonymous costs, i.e., games in which the cost of each resource only
depends on the cardinality of the set of its users
Allocation in Practice
How do we allocate scarcere sources? How do we fairly allocate costs? These
are two pressing challenges facing society today. I discuss two recent projects
at NICTA concerning resource and cost allocation. In the first, we have been
working with FoodBank Local, a social startup working in collaboration with
food bank charities around the world to optimise the logistics of collecting
and distributing donated food. Before we can distribute this food, we must
decide how to allocate it to different charities and food kitchens. This gives
rise to a fair division problem with several new dimensions, rarely considered
in the literature. In the second, we have been looking at cost allocation
within the distribution network of a large multinational company. This also has
several new dimensions rarely considered in the literature.Comment: To appear in Proc. of 37th edition of the German Conference on
Artificial Intelligence (KI 2014), Springer LNC
Designing Network Protocols for Good Equilibria
Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
Cooperative game theory and its application to natural, environmental, and water resource issues : 3. application to water resources
This paper reviews various applications of cooperative game theory (CGT) to issues of water resources. With an increase in the competition over various water resources, the incidents of disputes have been in the center of allocation agreements. The paper reviews the cases of various water uses, such as multi-objective water projects, irrigation, groundwater, hydropower, urban water supply, wastewater, and transboundary water disputes. In addition to providing examples of cooperative solutions to allocation problems, the conclusion from this review suggests that cooperation over scarce water resources is possible under a variety of physical conditions and institutional arrangements. In particular, the various approaches for cost sharing and for allocation of physical water infrastructure and flow can serve as a basis for stable and efficient agreement, such that long-term investments in water projects are profitable and sustainable. The latter point is especially important, given recent developments in water policy in various countries and regional institutions such as the European Union (Water Framework Directive), calling for full cost recovery of investments and operation and maintenance in water projects. The CGT approaches discussed and demonstrated in this paper can provide a solid basis for finding possible and stable cost-sharing arrangements.Town Water Supply and Sanitation,Environmental Economics&Policies,Water Supply and Sanitation Governance and Institutions,Water Supply and Systems,Water and Industry
Cooperative game theory and its application to natural, environmental, and water resource issues : 1. basic theory
Game theory provides useful insights into the way parties that share a scarce resource may plan their use of the resource under different situations. This review provides a brief and self-contained introduction to the theory of cooperative games. It can be used to get acquainted with the basics of cooperative games. Its goal is also to provide a basic introduction to this theory, in connection with a couple of surveys that analyze its use in the context of environmental problems and models. The main models (bargaining games, transfer utility, and non-transfer utility games) and issues and solutions are considered: bargaining solutions, single-value solutions like the Shapley value and the nucleolus, and multi-value solutions such as the core. The cooperative game theory (CGT) models that are reviewed in this paper favor solutions that include all possible players and ignore the strategic stages leading to coalition building. They focus on the possible results of the cooperation by answering questions such as: Which coalitions can be formed? And how can the coalitional gains be divided to secure a sustainable agreement? An important aspect associated with the solution concepts of CGT is the equitable and fair sharing of the cooperation gains.Environmental Economics&Policies,Economic Theory&Research,Livestock&Animal Husbandry,Education for the Knowledge Economy,Education for Development (superceded)
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