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384
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 635 (18 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 Mechanisms of Governance
, 1996
"... The economics of governance is an effort to implement the “study of good order and workable arrangements, ” 1 where good order includes both spontaneous order in the market, which is a venerated tradition in economics ..."
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Cited by 350 (7 self)
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The economics of governance is an effort to implement the “study of good order and workable arrangements, ” 1 where good order includes both spontaneous order in the market, which is a venerated tradition in economics
On the complexity of the parity argument and other inefficient proofs of existence
 JCSS
, 1994
"... We define several new complexity classes of search problems, "between " the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is define ..."
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Cited by 158 (8 self)
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We define several new complexity classes of search problems, "between " the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph. The existence of the solution sought is established via a simple graphtheoretic argument with an inefficiently constructive proof; for example, PLS can be thought of as corresponding to the lemma "every dag has a sink. " The new classes are based on lemmata such as "every graph has an even number of odddegree nodes. " They contain several important problems for which no polynomial time algorithm is presently known, including the computational versions of Sperner's lemma, Brouwer's fixpoint theorem, Chfvalley's theorem, and the BorsukUlam theorem, the linear complementarity problem for Pmatrices, finding a mixed equilibrium in a nonzero sum game, finding a second Hamilton circuit in a Hamiltonian cubic graph, a second Hamiltonian decomposition in a quartic graph, and others. Some of these problems are shown to be complete. © 1994 Academic Press, Inc. 1.
Engineering and economic applications of complementarity problems
 SIAM Review
, 1997
"... Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions f ..."
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Cited by 132 (24 self)
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Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Market equilibrium via a primaldualtype algorithm
 FOCS
, 2002
"... Although the study of market equilibria has occupied center stage within Mathematical Economics for over a century, polynomial time algorithms for such questions have so far evaded researchers. We provide the first such algorithm for the linear version of a problem defined by Irving Fisher in 1891. ..."
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Cited by 99 (22 self)
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Although the study of market equilibria has occupied center stage within Mathematical Economics for over a century, polynomial time algorithms for such questions have so far evaded researchers. We provide the first such algorithm for the linear version of a problem defined by Irving Fisher in 1891. Our algorithm is modeled after Kuhn’s primaldual algorithm for bipartite matching. 1
Randomeffects analysis
 In
, 2004
"... of the structural measures of flexibility and agility using a measurement theoretical framework $ ..."
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Cited by 49 (4 self)
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of the structural measures of flexibility and agility using a measurement theoretical framework $
Dynamics of bid optimization in online advertisement auctions
 In Proceedings of the 16th International World Wide Web Conference
, 2007
"... We consider the problem of online keyword advertising auctions among multiple bidders with limited budgets, and study a natural bidding heuristic in which advertisers attempt to optimize their utility by equalizing their returnoninvestment across all keywords. We show that existing auction mechani ..."
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Cited by 47 (2 self)
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We consider the problem of online keyword advertising auctions among multiple bidders with limited budgets, and study a natural bidding heuristic in which advertisers attempt to optimize their utility by equalizing their returnoninvestment across all keywords. We show that existing auction mechanisms combined with this heuristic can experience cycling (as has been observed in many current systems), and therefore propose a modified class of mechanisms with small random perturbations. This perturbation is reminiscent of the small timedependent perturbations employed in the dynamical systems literature to convert many types of chaos into attracting motions. We show that the perturbed mechanism provably converges in the case of firstprice auctions and experimentally converges in the case of secondprice auctions. Moreover, the point of convergence has a natural economic interpretation as the unique market equilibrium in the case of firstprice mechanisms. In the case of secondprice auctions, we conjecture that it converges to the “supplyaware” market equilibrium. Thus, our results can be alternatively described as a tâtonnement process for convergence to market equilibrium in which prices are adjusted on the side of the buyers rather than the sellers. We also observe that perturbation in mechanism design is useful in a broader context: In general, it can allow bidders to “share ” a particular item, leading to stable allocations and pricing for the bidders, and improved revenue for the auctioneer.
Settling the Complexity of Computing TwoPlayer Nash Equilibria
"... We prove that Bimatrix, the problem of finding a Nash equilibrium in a twoplayer game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building upon the work of Daskalakis, Goldberg, and Papadimitriou on the c ..."
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Cited by 45 (3 self)
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We prove that Bimatrix, the problem of finding a Nash equilibrium in a twoplayer game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building upon the work of Daskalakis, Goldberg, and Papadimitriou on the complexity of fourplayer Nash equilibria [21], settles a long standing open problem in algorithmic game theory. It also serves as a starting point for a series of results concerning the complexity of twoplayer Nash equilibria. In particular, we prove the following theorems: • Bimatrix does not have a fully polynomialtime approximation scheme unless every problem in PPAD is solvable in polynomial time. • The smoothed complexity of the classic LemkeHowson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results also have a complexity implication in mathematical economics: • ArrowDebreu market equilibria are PPADhard to compute.
Auction Algorithms for Market Equilibrium, STOC 2004
, 2004
"... In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of items. The market equilibrium problem is to compute a price vector which ensures market clearing, i.e. the demand of ..."
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Cited by 41 (2 self)
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In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of items. The market equilibrium problem is to compute a price vector which ensures market clearing, i.e. the demand of a good equals its supply, and given the prices, each buyer maximizes its utility. The problem is of considerable interest in Economics. This paper presents a formulation of the market equilibrium problem as a parameterized linear program. We construct the dual of these parametrized linear programs. We show that finding the market equilibrium is the same as finding a linearprogram from the family of programs where the optimal dual solution satisfies certain properties. The market clearing conditions arise naturally from complementary slackness conditions. We then define an auction mechanism which computes prices such that approximate market clearing is achieved. The algorithm we obtain outperforms previously known methods.
An evaluation of the performance of applied general equilibrium models of the impact of NAFTA. Federal
 Model of the Spanish Economy”, Economic Theory
, 1995
"... ABSTRACT __________________________________________________________________________ This paper evaluates the performances of three of the most prominent multisectoral static applied general equilibrium models used to predict the impact of the North American Free Trade Agreement. These models drastic ..."
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Cited by 35 (6 self)
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ABSTRACT __________________________________________________________________________ This paper evaluates the performances of three of the most prominent multisectoral static applied general equilibrium models used to predict the impact of the North American Free Trade Agreement. These models drastically underestimated the impact of NAFTA on North American trade. Furthermore, the models failed to capture much of the relative impacts on different sectors. Expost performance evaluations of applied GE models are essential if policymakers are to have confidence in the results produced by these models. Such evaluations also help make applied GE analysis a scientific discipline in which there are welldefined puzzles with clear successes and failures for competing theories. Analyzing sectoral trade data indicates the need for a new theoretical mechanism that generates large increases in trade in product categories with little or no previous trade. To capture changes in macroeconomic aggregates, the models need to be able to capture changes in productivity.