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Author: Peter Borm
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Author: Peter Borm
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
Author: Arndt Von Schemde
Publisher:
ISBN:
Category :
Languages : en
Pages : 288
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Author: H. Arndt von Schemde
Publisher: Springer Science & Business Media
ISBN: 3540291024
Category : Business & Economics
Languages : en
Pages : 157
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Book Description
The index of an equilibrium in a game gives information about the "stability" of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3A-n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain "hyperstable" equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.
Author: Antoon van den Elzen
Publisher: Springer Science & Business Media
ISBN: 3642481337
Category : Business & Economics
Languages : en
Pages : 155
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Book Description
This monograph is a treatise on adjustment processes. We consider price adjustment processes in exchange economies and strategy adjustment processes in noncooperative games. In the most simple version of an exchange economy, i.e. a pure exchange economy, there exist markets on which prices are determined by the demand and supply created by a finite number of consumers willing to exchange their initial endowments in order to maximize their utilities. An equilibrium situation is attained if, for some price vector, demand equals supply in all markets. Starting from a situation not being an equi librium an adjustment process reaches an equilibrium via adaptations of prices. The advantage of the adjustment processes we will present in this monograph is that they exist and converge under far weaker assumptions than existing processes. The second subject concerns the problem of finding Nash equilibria in noncooperative games. A Nash equilibrium is a situation from which no player can improve his position by unilaterally changing his strategy. We present a new algorithm for finding such equilibria. The sequence of stra tegy vectors generated by the algorithm can be interpreted as the path followed by a strategy adjustment process.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 404
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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 644
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Author:
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 758
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Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 356
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Author: Jesús Mario Bilbao
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 420
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Book Description
Author: Martin Grötschel
Publisher: Springer Science & Business Media
ISBN: 3642978819
Category : Mathematics
Languages : en
Pages : 374
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Book Description
Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.
