Search results for "Theorem"
showing 10 items of 1250 documents
Consensus in Noncooperative Dynamic Games: a Multi-Retailer Inventory Application
2008
We focus on Nash equilibria and Pareto optimal Nash equilibria for a finite horizon noncooperative dynamic game with a special structure of the stage cost. We study the existence of these solutions by proving that the game is a potential game. For the single-stage version of the game, we characterize the aforementioned solutions and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multistage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately, not necessarily Pareto op…
Noncooperative dynamic games for inventory applications: A consensus approach
2008
We focus on a finite horizon noncooperative dynamic game where the stage cost of a single player associated to a decision is a monotonically nonincreasing function of the total number of players making the same decision. For the single-stage version of the game, we characterize Nash equilibria and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multi-stage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately not necessarily Pareto optimal. The algorithm returns a seque…
Bounded Computational Capacity Equilibrium
2010
We study repeated games played by players with bounded computational power, where, in contrast to Abreu and Rubisntein (1988), the memory is costly. We prove a folk theorem: the limit set of equilibrium payoffs in mixed strategies, as the cost of memory goes to 0, includes the set of feasible and individually rational payoffs. This result stands in sharp contrast to Abreu and Rubisntein (1988), who proved that when memory is free, the set of equilibrium payoffs in repeated games played by players with bounded computational power is a strict subset of the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded c…
Aging effects in simple models for glassy relaxation
2006
Aging effects in the two-time correlation function and the response function after a quench from a high temperature to some low temperature are considered for a simple kinetic random energy model exhibiting stretched exponential relaxation. Because the system reaches thermal equilibrium for long times after the quench, all aging effect are of a transient nature. In particular, the violations of the fluctuation-dissipation theorem are considered and it is found that the relation between the response and the two-time correlation function depends on another function, the so-called asymmetry. This asymmetry vanishes in equilibrium but cannot be neglected in the aging regime. It is found that pl…
Thermalization and condensation in an incoherently pumped passive optical cavity
2011
International audience; We study theoretically and numerically the condensation and the thermalization of classical optical waves in an incoherently pumped passive Kerr cavity. We show that the dynamics of the cavity exhibits a turbulent behavior that can be described by the wave turbulence theory. A mean-field kinetic equation is derived, which reveals that, in its high finesse regime, the cavity behaves essentially as a conservative Hamiltonian system. In particular, the intracavity turbulent field is shown to relax adiabatically toward a thermodynamic equilibrium state of energy equipartition. As a consequence of this effect of wave thermalization, the incoherent optical field undergoes …
Online Sparse Collapsed Hybrid Variational-Gibbs Algorithm for Hierarchical Dirichlet Process Topic Models
2017
Topic models for text analysis are most commonly trained using either Gibbs sampling or variational Bayes. Recently, hybrid variational-Gibbs algorithms have been found to combine the best of both worlds. Variational algorithms are fast to converge and more efficient for inference on new documents. Gibbs sampling enables sparse updates since each token is only associated with one topic instead of a distribution over all topics. Additionally, Gibbs sampling is unbiased. Although Gibbs sampling takes longer to converge, it is guaranteed to arrive at the true posterior after infinitely many iterations. By combining the two methods it is possible to reduce the bias of variational methods while …
On Słowikowski, Raíkov and De Wilde Closed Graph Theorems
1986
Publisher Summary This chapter focuses on the Slowikowski, Raikov and De Wilde closed graph theorems. The vector spaces used in the chapter, are defined over the field Ղ of real or complex numbers. The term, “space” means separated topological vector space, unless the contrary is specifically stated. If Ω is a non-empty open subset of the n -dimensional euclidean space, then the Schwartz space ҟ′(Ω) endowed with the strong topology belongs to this class. The chapter also studies the classes of spaces related with this conjecture. The class of Slowikowski spaces contains the F-spaces and it is stable with respect to the operations that include: countable topological direct sums, closed subsp…
Extension theory and the calculus of butterflies
2016
Abstract This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H 2 -actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier–M…
Ultimate Order Statistics-Based Prototype Reduction Schemes
2013
Published version of a chapter in the book: AI 2013: Advances in Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-319-03680-9_42 The objective of Prototype Reduction Schemes (PRSs) and Border Identification (BI) algorithms is to reduce the number of training vectors, while simultaneously attempting to guarantee that the classifier built on the reduced design set performs as well, or nearly as well, as the classifier built on the original design set. In this paper, we shall push the limit on the field of PRSs to see if we can obtain a classification accuracy comparable to the optimal, by condensing the information in the data set into a single tr…
Highly transitive actions of free products
2013
We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group $\PSL_2(\Z)\simeq (\Z/2\Z)*(\Z/3\Z)$ admits a faithful and highly transitive action on a countable set.