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Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
 IN PROCEEDINGS OF THE ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2004
"... The LemkeHowson algorithm is the classical algorithm for the problem NASH of finding one Nash equilibrium of a bimatrix game. It provides a constructive, elementary proof of existence of an equilibrium, by a typical "directed parity argument", which puts NASH into the complexity class PPA ..."
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Cited by 47 (1 self)
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PPAD. This paper presents a class of bimatrix games for which the LemkeHowson algorithm takes, even in the best case, exponential time in the dimension d of the game, requiring #((# 3=4 ) d ) many steps, where # is the Golden Ratio. The "parity argument" for NASH is thus explicitly shown
Finding Nash Equilibria of Bimatrix Games
"... This thesis concerns the computational problem of finding one Nash equilibrium of a bimatrix game, a twoplayer game in strategic form. Bimatrix games are among the most basic models in noncooperative game theory, and finding a Nash equilibrium is important for their analysis. The Lemke–Howson algo ..."
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Cited by 3 (1 self)
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–Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. In this thesis, we present a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games
The complexity of computing a Nash equilibrium
, 2006
"... We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability of n ..."
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Cited by 324 (23 self)
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We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability
Automobile prices in market equilibrium
 Econometrica
, 1995
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 510 (18 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
The Cyclical Behavior of Equilibrium Unemployment and Vacancies
 American Economic Review
, 2005
"... This paper argues that a broad class of search models cannot generate the observed businesscyclefrequency fluctuations in unemployment and job vacancies in response to shocks of a plausible magnitude. In the U.S., the vacancyunemployment ratio is 20 times as volatile as average labor productivity ..."
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Cited by 839 (20 self)
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that wages are determined by Nash bargaining. ∗ This is a major revision of ‘Equilibrium Unemployment Fluctuations’. I thank Daron Acemoglu, Olivier
Polynomial algorithms for approximating Nash equilibria of bimatrix games
 In: Proceedings of the 2nd Workshop on Internet and Network Economics (WINE’06
, 2006
"... 1 PROBLEM DEFINITION Nash [13] introduced the concept of Nash equilibria in noncooperative games and proved that any game possesses at least one such equilibrium. A wellknown algorithm for computing a Nash equilibrium of a 2player game is the LemkeHowson algorithm [11], however it has exponentia ..."
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Cited by 26 (5 self)
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exponential worstcase running time in the number of available pure strategies [15]. Recently, Daskalakis et al [4] showed that the problem of computing a Nash equilibrium in a game with 4 or more players is PPADcomplete; this result was later extended to games with 3 players [7]. Eventually, Chen and Deng
Risk, Return and Equilibrium: Empirical Tests
 Journal of Political Economy
, 1973
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 1445 (10 self)
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A Simple Model of Capital Market Equilibrium with Incomplete Information
 JOURNAL OF FINANCE
, 1987
"... The sphere of modern financial economics encompases finance, micro investment theory and much of the economics of uncertainty. As is evident from its influence on other branches of economics including public finance, industrial organization and monetary theory, the boundaries of this sphere are both ..."
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Cited by 720 (2 self)
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. But for all its mathematical refinement, the research has nevertheless had a direct and significant influence on practice. It was not always thus. Thirty years ago, finance theory was little more than a collection of anecdotes, rules of thumb, and manipulations of accounting data with an almost exclusive
Results 1  10
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227,346