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542
Replicator Equations, Maximal Cliques, and Graph Isomorphism
, 1999
"... We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to fo ..."
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Cited by 53 (11 self)
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We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear onetoone correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the socalled replicator equations—a class of straightforward continuous and discretetime dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate meanfield annealing heuristics.
Computing Equilibria in MultiPlayer Games
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... We initiate the systematic study of algorithmic issues involved in finding equilibria (Nash and correlated) in games with a large number of players; such games, in order to be computationally meaningful, must be presented in some succinct, gamespecific way. We develop a general framework for obta ..."
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Cited by 53 (3 self)
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We initiate the systematic study of algorithmic issues involved in finding equilibria (Nash and correlated) in games with a large number of players; such games, in order to be computationally meaningful, must be presented in some succinct, gamespecific way. We develop a general framework for obtaining polynomialtime algorithms for optimizing over correlated equilibria in such settings, and show how it can be applied successfully to symmetric games (for which we actually find an exact polytopal characterization), graphical games, and congestion games, among others. We also present complexity results implying that such algorithms are not possible in certain other such games. Finally, we present a polynomialtime algorithm, based on quantifier elimination, for finding a Nash equilibrium in symmetric games when the number of strategies is relatively small.
Measuring social norms and preferences using experimental games: a guide for social scientists
 In
, 2004
"... The purpose of this chapter is to describe a menu of experimental games that are useful for measuring aspects of social norms and social preferences. Economists use the term “preferences ” to refer to the choices people make, and particularly to tradeoffs between different collections (“bundles”) of ..."
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Cited by 52 (0 self)
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The purpose of this chapter is to describe a menu of experimental games that are useful for measuring aspects of social norms and social preferences. Economists use the term “preferences ” to refer to the choices people make, and particularly to tradeoffs between different collections (“bundles”) of things they value—food, money, time, prestige, and
Exploring bidding strategies for marketbased scheduling
 DECISION SUPPORT SYSTEMS
, 2005
"... ..."
On the evolution of overconfidence and entrepreneurs
 Journal of Economics & Management Strategy
, 2001
"... This paper explains why seemingly irrational overconfident behavior can persist. Information aggregation is poor in groups in which most individuals herd. By ignoring the herd, the actions of overconfident individuals (“entrepreneurs”) convey their private information. However, entrepreneurs make mi ..."
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Cited by 51 (2 self)
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This paper explains why seemingly irrational overconfident behavior can persist. Information aggregation is poor in groups in which most individuals herd. By ignoring the herd, the actions of overconfident individuals (“entrepreneurs”) convey their private information. However, entrepreneurs make mistakes and thus die more frequently. The socially optimal proportion of entrepreneurs trades off the positive information externality against high attrition rates of entrepreneurs, and depends on the size of the group, on the degree of overconfidence, and on the accuracy of individuals ’ private information. The stationary distribution trades off the fitness of the group against the fitness of overconfident individuals. Starting any company is really hard to do, so you can’t be so smart that it occurs to you that it can’t be done.
Adaptive Heuristics
 Econometrica
, 2005
"... We exhibit a large class of simple rules of behavior, which we call adaptive heuristics, and show that they generate rational behavior in the long run. These adaptive heuristics are based on natural regret measures, and may be viewed as a bridge between rational and behavioral viewpoints. Taken toge ..."
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Cited by 51 (4 self)
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We exhibit a large class of simple rules of behavior, which we call adaptive heuristics, and show that they generate rational behavior in the long run. These adaptive heuristics are based on natural regret measures, and may be viewed as a bridge between rational and behavioral viewpoints. Taken together, the results presented here establish a solid connection between the dynamic approach of adaptive heuristics and the static approach of correlated equilibria.
The Contributions of the Economics of Information to Twentieth
 Century Economics.” Quarterly Journal of Economics
"... In the �eld of economics, perhaps the most important break with the past—one that leaves open huge areas for future work—lies in the economics of information. It is now recognized that information is imperfect, obtaining information can be costly, there are important asymmetries of information, and ..."
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Cited by 49 (0 self)
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In the �eld of economics, perhaps the most important break with the past—one that leaves open huge areas for future work—lies in the economics of information. It is now recognized that information is imperfect, obtaining information can be costly, there are important asymmetries of information, and the extent of information asymmetries is affected by actions of �rms and individuals. This recognition deeply affects the understanding of wisdom inherited from the past, such as the fundamental welfare theorem and some of the basic characterization of a market economy, and provides explanations of economic and social phenomena that otherwise would be hard to understand. I.
A New GraphTheoretic Approach to Clustering, with Applications to Computer Vision
, 2004
"... This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given ..."
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Cited by 44 (4 self)
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This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given dataset. Many problems of computer vision have precisely this goal, namely to find which visual entities belong to an inherent structure, e.g. in an image or in a database of images. For example, a meaningful structure in the context of image segmentation is a set of pixels which correspond to the same object in a scene. Clustering algorithms can be used to partition the pixels of an image into meaningful parts, which may correspond to different objects. In this work we focus on the problems of image segmentation and image database organization. The visual entities to consider are pixels and images, respectively. Our first contribution in this work is a novel partitional (flat) clustering algorithm. The algorithm uses pairwise representation, where the visual objects (pixels,
Fast convergence to Wardrop equilibria by adaptive sampling methods
 in Proc. 38th Ann. ACM. Symp. on Theory of Comput. (STOC
, 2006
"... We study rerouting policies in a dynamic roundbased variant of a well known game theoretic traffic model due to Wardrop. Previous analyses (mostly in the context of selfish routing) based on Wardrop’s model focus mostly on the static analysis of equilibria. In this paper, we ask the question whethe ..."
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Cited by 43 (8 self)
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We study rerouting policies in a dynamic roundbased variant of a well known game theoretic traffic model due to Wardrop. Previous analyses (mostly in the context of selfish routing) based on Wardrop’s model focus mostly on the static analysis of equilibria. In this paper, we ask the question whether the population of agents responsible for routing the traffic can jointly compute or better learn a Wardrop equilibrium efficiently. The rerouting policies that we study are of the following kind. In each round, each agent samples an alternative routing path and compares the latency on this path with its current latency. If the agent observes that it can improve its latency then it switches with some probability depending on the possible improvement to the better path. We can show various positive results based on a rerouting policy using an adaptive sampling rule that implicitly amplifies paths that carry a large amount of traffic in the Wardrop equilibrium. For general asymmetric games, we show that a simple replication protocol in which agents adopt strategies of more successful agents reaches a certain kind of bicriteria equilibrium within a time bound that is independent of the size and the structure of the network but only depends on a parameter of the latency functions, that we call the relative slope. For symmetric games, this result has an intuitive interpretation: Replication approximately satisfies almost everyone very quickly. In order to achieve convergence to a Wardrop equilibrium besides replication one also needs an exploration component discovering possibly unused strategies. We present a
Evolutionary dynamics of social dilemmas in structured heterogeneous populations
 Proc. Natl. Acad. Sci. USA
, 2006
"... Abbreviations frequently used: T – Payoff for defecting on a cooperator R – Payoff for mutual cooperation P – Payoff for mutual defection S – Payoff for cooperating with a defector NoC – Network of Contacts SI – Supporting Information Real populations have been shown to be heterogeneous, in which so ..."
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Cited by 41 (15 self)
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Abbreviations frequently used: T – Payoff for defecting on a cooperator R – Payoff for mutual cooperation P – Payoff for mutual defection S – Payoff for cooperating with a defector NoC – Network of Contacts SI – Supporting Information Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which heterogeneity ranges from singlescale graphs, where it is small and associated degree distributions exhibit a Gaussian tail, to scalefree graphs, where it is large with degreedistributions exhibiting a powerlaw behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that longterm cooperative behavior easily resists shortterm noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scalefree populations. accepted 15dec2005 in the Proceedings of the National Academy of Sciences; published online 16feb2006 2 1.