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576
Worstcase equilibria
 IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1999
"... In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a ver ..."
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Cited by 845 (17 self)
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In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.
The price of stability for network design with fair cost allocation
 In Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS
, 2004
"... Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite differ ..."
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Cited by 281 (30 self)
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Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite different from the centrally enforced optimum. We study the quality of the best Nash equilibrium, and refer to the ratio of its cost to the optimum network cost as the price of stability. The best Nash equilibrium solution has a natural meaning of stability in this context — it is the optimal solution that can be proposed from which no user will defect. We consider the price of stability for network design with respect to one of the most widelystudied protocols for network cost allocation, in which the cost of each edge is divided equally between users whose connections make use of it; this fairdivision scheme can be derived from the Shapley value, and has a number of basic economic motivations. We show that the price of stability for network design with respect to this fair cost allocation is O(log k), where k is the number of users, and that a good Nash equilibrium can be achieved via bestresponse dynamics in which users iteratively defect from a starting solution. This establishes that the fair cost allocation protocol is in fact a useful mechanism for inducing strategic behavior to form nearoptimal equilibria. We discuss connections to the class of potential games defined by Monderer and Shapley, and extend our results to cases in which users are seeking to balance network design costs with latencies in the constructed network, with stronger results when the network has only delays and no construction costs. We also present bounds on the convergence time of bestresponse dynamics, and discuss extensions to a weighted game.
Selfish Routing and the Price of Anarchy
 MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
, 2007
"... Selfish routing is a classical mathematical model of how selfinterested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this in ..."
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Cited by 256 (11 self)
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Selfish routing is a classical mathematical model of how selfinterested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this inefficiency. We survey recent work that analyzes the price of anarchy of selfish routing. We also describe related results on bounding the worstpossible severity of a phenomenon called Braess’s Paradox, and on three techniques for reducing the price of anarchy of selfish routing. This survey concentrates on the contributions of the author’s PhD thesis, but also discusses several more recent results in the area.
Intrinsic Robustness of the Price of Anarchy
 STOC'09
, 2009
"... The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium ..."
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Cited by 101 (12 self)
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The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regretminimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a “canonical sufficient condition ” for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regretminimizing players (or “price of total anarchy”). Smoothness arguments also have automatic implications for the inefficiency of approximate and BayesianNash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomiallength bestresponse sequences. We also identify classes of games — most notably, congestion games with cost functions restricted to an arbitrary fixed set — that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worstcase upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with nonpolynomial cost functions, and the first
Revenue generation for truthful spectrum auction in dynamic spectrum access
 In Proc. ACM International Symposium on Mobile Ad Hoc Networking and Computing
, 2009
"... Spectrum is a critical yet scarce resource and it has been shown that dynamic spectrum access can significantly improve spectrum utilization. To achieve this, it is important to incentivize the primary license holders to open up their underutilized spectrum for sharing. In this paper we present a s ..."
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Cited by 87 (4 self)
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Spectrum is a critical yet scarce resource and it has been shown that dynamic spectrum access can significantly improve spectrum utilization. To achieve this, it is important to incentivize the primary license holders to open up their underutilized spectrum for sharing. In this paper we present a secondary spectrum market where a primary license holder can sell access to its unused or underused spectrum resources in the form of certain finegrained spectrumspacetime unit. Secondary wireless service providers can purchase such contracts to deploy new service, enhance their existing service, or deploy ad hoc service to meet flash crowds demand. Within the context of this market, we investigate how to use auction mechanisms to allocate and price spectrum resources so that the primary license holder’s revenue is maximized. We begin by classifying a number of alternative auction formats in terms of spectrum demand. We then study a specific auction format where secondary wireless service providers have demands for fixed locations (cells). We propose an optimal auction based on the concept of virtual valuation. Assuming the knowledge of valuation distributions, the optimal auction uses the VickreyClarkeGroves (VCG) mechanism to maximize the expected revenue while enforcing truthfulness. To reduce the computational complexity, we further design a truthful suboptimal auction with polynomial time complexity. It uses a monotone allocation and critical value payment to enforce truthfulness. Simulation results show that this suboptimal auction can generate stable expected revenue.
On approximately fair allocations of indivisible goods
 In ACM Conference on Electronic Commerce (EC
, 2004
"... We study the problem of fairly allocating a set of indivisible goods to a set of people from an algorithmic perspective. Fair division has been a central topic in the economic literature and several concepts of fairness have been suggested. The criterion that we focus on is the maximum envy between ..."
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Cited by 71 (3 self)
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We study the problem of fairly allocating a set of indivisible goods to a set of people from an algorithmic perspective. Fair division has been a central topic in the economic literature and several concepts of fairness have been suggested. The criterion that we focus on is the maximum envy between any pair of players. An allocation is called envyfree if every player prefers her own share than the share of any other player. When the goods are divisible or when there is sufficient amount of one divisible good, envyfree allocations always exist. In the presence of indivisibilities however this is not the case. We first show that when all goods are indivisible, there always exist allocations in which the envy is bounded by the maximum marginal utility and we present a simple polynomial time algorithm for computing such allocations. We further show that our algorithm can be applied to the continuous cakecutting model as well and obtain a procedure that produces ɛenvyfree allocations with a linear number of cuts. We then look at the optimization problem of finding an allocation with minimum possible envy. In the general case, there is no polynomial time algorithm (or even approximation algorithm) for the problem, unless P = NP. We consider natural special cases (e.g. additive utilities) which are closely related to a class of job scheduling problems. Polynomial time approximation algorithms as well as inapproximability results are obtained. Finally we investigate the problem of designing truthful mechanisms for producing allocations with bounded envy. 1
Coordination mechanisms
 PROCEEDINGS OF THE 31ST INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING, IN: LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and noncolluding agents. The quality of a coordination mechanism is measured by its price of anarchy—the worstcase performance of a Nash equilibrium over the (centrally controlled) soc ..."
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Cited by 57 (5 self)
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We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and noncolluding agents. The quality of a coordination mechanism is measured by its price of anarchy—the worstcase performance of a Nash equilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games.
Methodologies for analyzing equilibria in wireless games
 IEEE Signal Processing Magazine, Special issue on Game Theory for Signal Processing
, 2009
"... Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure s ..."
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Cited by 48 (25 self)
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Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide nonexhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection and efficiency.
Bridging Game Theory and Cryptography: Recent Results and Future Directions
"... Abstract. Motivated by the desire to develop more realistic models of, and protocols for, interactions between mutually distrusting parties, there has recently been significant interest in combining the approaches and techniques of game theory with those of cryptographic protocol design. Broadly spe ..."
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Cited by 40 (3 self)
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Abstract. Motivated by the desire to develop more realistic models of, and protocols for, interactions between mutually distrusting parties, there has recently been significant interest in combining the approaches and techniques of game theory with those of cryptographic protocol design. Broadly speaking, two directions are currently being pursued: Applying cryptography to game theory: Certain gametheoretic equilibria are achievable if a trusted mediator is available. The question here is: to what extent can this mediator be replaced by a distributed cryptographic protocol run by the parties themselves? Applying gametheory to cryptography: Traditional cryptographic models assume some honest parties who faithfully follow the protocol, and some arbitrarily malicious players against whom the honest players must be protected. Gametheoretic models propose instead that all players are simply selfinterested (i.e., rational), and the question then is: how can we model and design meaningful protocols for such a setting? In addition to surveying known results in each of the above areas, I suggest some new definitions along with avenues for future research. 1