The Experts below are selected from a list of 21408 Experts worldwide ranked by ideXlab platform
Aaron Roth - One of the best experts on this subject based on the ideXlab platform.
-
regret minimization and the price of total Anarchy
Symposium on the Theory of Computing, 2008Co-Authors: Avrim Blum, Mohammadtaghi Hajiaghayi, Katrina Ligett, Aaron RothAbstract:We propose weakening the assumption made when studying the price of Anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total Anarchy" matches the Nash price of Anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of Anarchy and the recently introduced price of sinking, which require all players to behave in a prescribed manner, we show that the price of total Anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total Anarchy is an upper bound on the price of Anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of Anarchy in mixed strategies.
-
STOC - Regret minimization and the price of total Anarchy
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08, 2008Co-Authors: Avrim Blum, Mohammadtaghi Hajiaghayi, Katrina Ligett, Aaron RothAbstract:We propose weakening the assumption made when studying the price of Anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total Anarchy" matches the Nash price of Anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of Anarchy and the recently introduced price of sinking, which require all players to behave in a prescribed manner, we show that the price of total Anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total Anarchy is an upper bound on the price of Anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of Anarchy in mixed strategies.
-
SAGT - The Price of Stochastic Anarchy
Algorithmic Game Theory, 2008Co-Authors: Christine Chung, Katrina Ligett, Kirk Pruhs, Aaron RothAbstract:We consider the solution concept of stochastic stability, and propose the price of stochastic Anarchyas an alternative to the price of (Nash) Anarchyfor quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages that the set of stochastically stable states of a game avoid: unlike Nash equilibria, stochastically stable states are the result of natural dynamics of computationally bounded and decentralized agents, and are resilient to small perturbations from ideal play. The price of stochastic Anarchy can be viewed as a smoothed analysis of the price of Anarchy, distinguishing equilibria that are resilient to noise from those that are not. To illustrate the utility of stochastic stability, we study the load balancing game on unrelated machines. This game has an unboundedly large price of Nash Anarchy even when restricted to two players and two machines. We show that in the two player case, the price of stochastic Anarchy is 2, and that even in the general case, the price of stochastic Anarchy is bounded. We conjecture that the price of stochastic Anarchy is O(m), matching the price of strong Nash Anarchy without requiring player coordination. We expect that stochastic stability will be useful in understanding the relative stability of Nash equilibria in other games where the worst equilibria seem to be inherently brittle.
Éva Tardos - One of the best experts on this subject based on the ideXlab platform.
-
Strong Price of Anarchy and Coalitional Dynamics.
Algorithmic Game Theory, 2014Co-Authors: Yoram Bachrach, Éva Tardos, Vasilis Syrgkanis, Milan VojnovicAbstract:We introduce a framework for studying the effect of cooperation on the quality of outcomes in utility games. Our framework is a coalitional analog of the smoothness framework of non-cooperative games. Coalitional smoothness implies bounds on the strong price of Anarchy, the loss of quality of coalitionally stable outcomes, as well as bounds on coalitional versions of coarse correlated equilibria and sink equilibria, which we define as out-of-equilibrium myopic behavior as determined by a natural coalitional version of best-response dynamics. Our coalitional smoothness framework captures existing results bounding the strong price of Anarchy of network design games. We show that in any monotone utility-maximization game, if each player's utility is at least his marginal contribution to the welfare, then the strong price of Anarchy is at most 2. This captures a broad class of games, including games with a very high price of Anarchy. Additionally, we show that in potential games the strong price of Anarchy is close to the price of stability, the quality of the best Nash equilibrium.
-
pure and bayes nash price of Anarchy for generalized second price auction
Foundations of Computer Science, 2010Co-Authors: Renato Paes Leme, Éva TardosAbstract:The Generalized Second Price Auction has been the main mechanism used by search companies to auction positions for advertisements on search pages. In this paper we study the social welfare of the Nash equilibria of this game in various models. In the full information setting, socially optimal Nash equilibria are known to exist (i.e., the Price of Stability is 1). This paper is the first to prove bounds on the price of Anarchy, and to give any bounds in the Bayesian setting. Our main result is to show that the price of Anarchy is small assuming that all bidders play un-dominated strategies. In the full information setting we prove a bound of 1.618 for the price of Anarchy for pure Nash equilibria, and a bound of 4 for mixed Nash equilibria. We also prove a bound of 8 for the price of Anarchy in the Bayesian setting, when valuations are drawn independently, and the valuation is known only to the bidder and only the distributions used are common knowledge. Our proof exhibits a combinatorial structure of Nash equilibria and uses this structure to bound the price of Anarchy. While establishing the structure is simple in the case of pure and mixed Nash equilibria, the extension to the Bayesian setting requires the use of novel combinatorial techniques that can be of independent interest.
-
FOCS - Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction
2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 2010Co-Authors: Renato Paes Leme, Éva TardosAbstract:The Generalized Second Price Auction has been the main mechanism used by search companies to auction positions for advertisements on search pages. In this paper we study the social welfare of the Nash equilibria of this game in various models. In the full information setting, socially optimal Nash equilibria are known to exist (i.e., the Price of Stability is 1). This paper is the first to prove bounds on the price of Anarchy, and to give any bounds in the Bayesian setting. Our main result is to show that the price of Anarchy is small assuming that all bidders play un-dominated strategies. In the full information setting we prove a bound of 1.618 for the price of Anarchy for pure Nash equilibria, and a bound of 4 for mixed Nash equilibria. We also prove a bound of 8 for the price of Anarchy in the Bayesian setting, when valuations are drawn independently, and the valuation is known only to the bidder and only the distributions used are common knowledge. Our proof exhibits a combinatorial structure of Nash equilibria and uses this structure to bound the price of Anarchy. While establishing the structure is simple in the case of pure and mixed Nash equilibria, the extension to the Bayesian setting requires the use of novel combinatorial techniques that can be of independent interest.
Edward Peter Stringham - One of the best experts on this subject based on the ideXlab platform.
-
Anarchy, State and Public Choice
2018Co-Authors: Edward Peter StringhamAbstract:1. Introduction 2. Individual Welfare in Anarchy 3. Jungle or Just Bush? Anarchy and the Evolution of Cooperation 4. The Edge of the Jungle 5. Social Interaction without the State 6. Towards a Theory of the Evolution of Government 7. Do Contracts Require Formal Enforcement? 8. Before Public Choice 9. Public Choice and Leviathan 10. Cases in Anarchy 11. Defining Anarchy as Rock-n-Roll: Rethinking Hogarty's Three Cases 12. Private Property Anarchism: An American Variant 13. Anarchism and the Theory of Power 14. Polycentrism and Power 15. Reflections After Three Decades 16. Anarchy 17. Tullock on Anarchy 18. Anarchism as a Progressive Research Program in Political Economy.
-
Public choice and the economic analysis of Anarchy: a survey
Public Choice, 2009Co-Authors: Benjamin Powell, Edward Peter StringhamAbstract:Public choice economists began studying the economics of Anarchy in the 1970s. Since then, the amount of research on Anarchy has burgeoned. This article surveys the important public choice contributions to the economics of Anarchy. Following the lead of the early public choice economists, many current economists are researching and analyzing how individuals interact without government. From their non-ublic-interested explanations of the creation of government law enforcement to their historical studies of attempts to internalize externalities under Anarchy, public choice scholars are arriving at a more realistic perspective on government and how people interact when government law enforcement is lacking. Although the economics of politics often receives more attention, the economics of Anarchy is an important area of research in public choice.
-
Public choice and the economic analysis of Anarchy: a survey
Public Choice, 2009Co-Authors: Benjamin Powell, Edward Peter StringhamAbstract:Public choice economists began studying Anarchy in the 1970s. Since then, the amount of research on Anarchy has burgeoned. This article surveys the important public choice contributions to the economics of Anarchy. Following early public choice economists, many economists are researching how individuals interact without government. From non-public-interested explanations of the creation of government to historical studies of internalizing externalities under Anarchy, public choice scholars are arriving at a more realistic perspective of human interaction with and without government. Although the economics of politics receives more attention, the economics of Anarchy is an important area of research in public choice.
-
public choice and the economic analysis of Anarchy a survey
MPRA Paper, 2009Co-Authors: Benjamin Powell, Edward Peter StringhamAbstract:Public choice economists began studying the economics of Anarchy in the 1970s. Since then, the amount of research on Anarchy has burgeoned. This article surveys the important public choice contributions to the economics of Anarchy. Following the lead of the early public choice economists, many current economists are researching and analyzing how individuals interact without government. From their non-ublic-interested explanations of the creation of government law enforcement to their historical studies of attempts to internalize externalities under Anarchy, public choice scholars are arriving at a more realistic perspective on government and how people interact when government law enforcement is lacking. Although the economics of politics often receives more attention, the economics of Anarchy is an important area of research in public choice.
-
Is Government Inevitable
2006Co-Authors: Peter T. Leeson, Edward Peter StringhamAbstract:Inspired by Holcombe's (2004) argument that government is inevitable, this paper reconsiders some of his claims. We contend that his argument fails on two counts: it both fails to show that Anarchy must break down and that limited government will not. The arguments Holcombe raises against the viability of Anarchy can be applied to the viability of limited government, and the arguments he uses for the viability of limited government can be applied to the viability of Anarchy. We discuss the problems with Holcombe's theoretical arguments as well as historical evidence that casts doubt on his claims.
Renato Paes Leme - One of the best experts on this subject based on the ideXlab platform.
-
pure and bayes nash price of Anarchy for generalized second price auction
Foundations of Computer Science, 2010Co-Authors: Renato Paes Leme, Éva TardosAbstract:The Generalized Second Price Auction has been the main mechanism used by search companies to auction positions for advertisements on search pages. In this paper we study the social welfare of the Nash equilibria of this game in various models. In the full information setting, socially optimal Nash equilibria are known to exist (i.e., the Price of Stability is 1). This paper is the first to prove bounds on the price of Anarchy, and to give any bounds in the Bayesian setting. Our main result is to show that the price of Anarchy is small assuming that all bidders play un-dominated strategies. In the full information setting we prove a bound of 1.618 for the price of Anarchy for pure Nash equilibria, and a bound of 4 for mixed Nash equilibria. We also prove a bound of 8 for the price of Anarchy in the Bayesian setting, when valuations are drawn independently, and the valuation is known only to the bidder and only the distributions used are common knowledge. Our proof exhibits a combinatorial structure of Nash equilibria and uses this structure to bound the price of Anarchy. While establishing the structure is simple in the case of pure and mixed Nash equilibria, the extension to the Bayesian setting requires the use of novel combinatorial techniques that can be of independent interest.
-
FOCS - Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction
2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 2010Co-Authors: Renato Paes Leme, Éva TardosAbstract:The Generalized Second Price Auction has been the main mechanism used by search companies to auction positions for advertisements on search pages. In this paper we study the social welfare of the Nash equilibria of this game in various models. In the full information setting, socially optimal Nash equilibria are known to exist (i.e., the Price of Stability is 1). This paper is the first to prove bounds on the price of Anarchy, and to give any bounds in the Bayesian setting. Our main result is to show that the price of Anarchy is small assuming that all bidders play un-dominated strategies. In the full information setting we prove a bound of 1.618 for the price of Anarchy for pure Nash equilibria, and a bound of 4 for mixed Nash equilibria. We also prove a bound of 8 for the price of Anarchy in the Bayesian setting, when valuations are drawn independently, and the valuation is known only to the bidder and only the distributions used are common knowledge. Our proof exhibits a combinatorial structure of Nash equilibria and uses this structure to bound the price of Anarchy. While establishing the structure is simple in the case of pure and mixed Nash equilibria, the extension to the Bayesian setting requires the use of novel combinatorial techniques that can be of independent interest.
Avrim Blum - One of the best experts on this subject based on the ideXlab platform.
-
regret minimization and the price of total Anarchy
Symposium on the Theory of Computing, 2008Co-Authors: Avrim Blum, Mohammadtaghi Hajiaghayi, Katrina Ligett, Aaron RothAbstract:We propose weakening the assumption made when studying the price of Anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total Anarchy" matches the Nash price of Anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of Anarchy and the recently introduced price of sinking, which require all players to behave in a prescribed manner, we show that the price of total Anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total Anarchy is an upper bound on the price of Anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of Anarchy in mixed strategies.
-
STOC - Regret minimization and the price of total Anarchy
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08, 2008Co-Authors: Avrim Blum, Mohammadtaghi Hajiaghayi, Katrina Ligett, Aaron RothAbstract:We propose weakening the assumption made when studying the price of Anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total Anarchy" matches the Nash price of Anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of Anarchy and the recently introduced price of sinking, which require all players to behave in a prescribed manner, we show that the price of total Anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total Anarchy is an upper bound on the price of Anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of Anarchy in mixed strategies.