共查询到20条相似文献,搜索用时 15 毫秒
1.
We continue in this Note our study of the notion of mean field games that we introduced in a previous Note. We consider here the case of Nash equilibria for stochastic control type problems in finite horizon. We present general existence and uniqueness results for the partial differential equations systems that we introduce. We also give a possible interpretation of these systems in term of optimal control. To cite this article: J.-M. Lasry, P.-L. Lions, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
2.
We introduce here a general approach to model games with a large number of players. More precisely, we consider N players Nash equilibria for long term stochastic problems and establish rigorously the ‘mean field’ type equations as N goes to infinity. We also prove general uniqueness results and determine the deterministic limit. To cite this article: J.-M. Lasry, P.-L. Lions, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
3.
Lawrence C. Evans 《Calculus of Variations and Partial Differential Equations》2009,35(4):435-462
We introduce and make estimates for several new approximations that in appropriate asymptotic limits yield the key PDE for
weak KAM theory, namely a Hamilton–Jacobi type equation for a potential u and a coupled transport equation for a measure σ. We revisit as well a singular variational approximation introduced in Evans (Calc Vari Partial Differ Equ 17:159–177, 2003)
and demonstrate “approximate integrability” of certain phase space dynamics related to the Hamiltonian flow. Other examples
include a pair of strongly coupled PDE suggested by the Lions–Lasry theory (Lasry and Lions in Japan J Math 2:229–260, 2007)
of mean field games and a new and extremely singular elliptic equation suggested by sup-norm variational theory.
Supported in part by NSF Grant DMS-0500452. 相似文献
4.
《Stochastic Processes and their Applications》2019,129(9):3174-3206
A class of singular stochastic control problems whose value functions satisfy an invariance property was studied by Lasry and Lions (2000). They have shown that, within this class, any singular control problem is equivalent to the corresponding standard stochastic control problem. The equivalence is in the sense that their value functions are equal. In this work, we clarify their idea and extend their work to allow Lévy type noise. In addition, for the purpose of application, we apply our result to an optimal trade execution problem studied by Lasry and Lions (2007). 相似文献
5.
P. Cardaliaguet G. Carlier B. Nazaret 《Calculus of Variations and Partial Differential Equations》2013,48(3-4):395-420
In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savaré. We first prove the existence of a potential function and then give necessary and sufficient optimality conditions that take the form of a coupled system of PDEs somehow similar to the Mean-Field-Games system of Lasry and Lions. We also consider an equivalent formulation posed in a set of probability measures over curves. 相似文献
6.
We study the existence and asymptotics for large time of the solutions to a one dimensional evolution equation with non-standard
right-hand side. The right-hand side involves the derivative of the solution computed at a given point. Existence is proven
through a fixed point argument. When the problem is considered in a bounded interval, it is shown that the solution decays
exponentially to the stationary state. This problem is a particular case of a mean-field free boundary model proposed by Lasry
and Lions on price formation and dynamic equilibria.
Maria P. Gualdani is supported by the NSF Grant DMS-0807636. 相似文献
7.
D. T. Allemang 《International Journal of Game Theory》2002,30(4):539-556
Two approaches have been used to solve impartial games with misère play; genus theory, which has resulted in a number of results summarized in [2], and Sibert-Conway decomposition [9], which has been used to solve the octal game 0.77 (known as Kayles). The main aim of this paper is to publish (for the
first time) the results archived in [1], extending genus theory beyond the applications to which it has previously been applied.
In addition, we extend a result from [6] to misère play by adapting it to use the extended genus theory. The resulting theorems
require extensive calculations to verify that their preconditions hold for any particular games. These calculations have been
carried out by computer for all two-digit octal games. For many of these games, this has resulted in complete solutions. Complete
solutions are presented for four games listed in [8] as unsolved.
Received: September 2001 相似文献
8.
Luis A. Caffarelli Peter A. Markowich Jan-F. Pietschmann 《Comptes Rendus Mathematique》2011,349(11-12):621-624
We discuss global existence and asymptotic behaviour of a price formation free boundary model introduced by Lasry and Lions in 2007. Our results are based on a construction which transforms the problem into the heat equation with specially prepared initial datum. The key point is that the free boundary present in the original problem becomes the zero level set of this solution. Using the properties of the heat operator we can show global existence, regularity and asymptotic results of the free boundary. 相似文献
9.
Luis A. Caffarelli Peter A. Markowich Marie-Therese Wolfram 《Comptes Rendus Mathematique》2011,349(15-16):841-844
We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry and Lions in 2007. The results are based on a transformation of the problem to the heat equation with nonstandard boundary conditions. The free boundary becomes the zero level set of the solution of the heat equation. The transformation allows us to construct an explicit solution and discuss the behavior of the free boundary. Global existence can be verified under certain conditions on the free boundary and examples of non-existence are given. 相似文献
10.
The starting point of this work is a paper by Alvarez, Lasry and Lions (1997) concerning the convexity and the partial convexity of solutions of fully nonlinear degenerate elliptic equations. We extend their results in two directions. First, we deal with possibly sublinear (but epi-pointed) solutions instead of 1-coercive ones; secondly, the partial convexity of C2 solutions is extended to the class of continuous viscosity solutions. A third contribution of this paper concerns C1,1 estimates for convex viscosity solutions of strictly elliptic nonlinear equations. To finish with, all the tools and techniques introduced here permit us to give a new proof of the Alexandroff estimate obtained by Trudinger (1988) and Caffarelli (1989). 相似文献
11.
V. V. Chichagov 《Journal of Mathematical Sciences》1995,75(1):1461-1468
The limit behavior of Markov chains with discrete time and a finite number of states (MCDT) depending on the number n of its
steps has been almost completely investigated [1–4]. In [5], MCDT with forbidden transitions were investigated, and in [6],
the sum of a random number of functionals of random variables related by a homogeneous Markov chain (HMC) was considered.
In the present paper, we continue the investigation of the limit behavior of the MCDT with random stopping time which is determined
by a Markov walk plan II with a fixed number of certain transitions [7, 8]. Here we apply a method similar to that of [6],
which allows us to obtain, together with some generalizations of the results of [6], a number of new assertions.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 119–130, Perm, 1990. 相似文献
12.
Consider two discrete time Markov chains on a finite state space with ±1 win or lose payoff subject to transition between the states. We introduce a class of processes whose cumulative expected payoffs are decreasing in time but, whenever the processes are chosen at random by flipping a fair coin, the expected payoff for the randomized process becomes increasing in time. The seemingly counterintuitive long time run mean reversal generalizes the idea of combining two losing games into a winning one, known as Parrondo’s Paradox. 相似文献
13.
In this paper we consider second order scalar elliptic boundary value problems posed over three–dimensional domains and their
discretization by means of mixed Raviart–Thomas finite elements [18]. This leads to saddle point problems featuring a discrete
flux vector field as additional unknown. Following Ewing and Wang [26], the proposed solution procedure is based on splitting
the flux into divergence free components and a remainder. It leads to a variational problem involving solenoidal Raviart–Thomas
vector fields. A fast iterative solution method for this problem is presented. It exploits the representation of divergence
free vector fields as s of the –conforming finite element functions introduced by Nédélec [43]. We show that a nodal multilevel splitting of these finite
element spaces gives rise to an optimal preconditioner for the solenoidal variational problem: Duality techniques in quotient
spaces and modern algebraic multigrid theory [50, 10, 31] are the main tools for the proof.
Received November 4, 1996 / Revised version received February 2, 1998 相似文献
14.
Summary. In shape optimization problems, each computation of
the cost function by the finite element method
leads to an expensive analysis. The use of the second order derivative
can help to reduce the number of analyses. Fujii ([4], [10])
was the first to study this problem. J. Simon [19] gave the second order
derivative for the Navier-Stokes
problem, and the authors describe in [8], [11], a method which gives an
intrinsic expression of the first and second order derivatives on the
boundary
of the involved domain.
In this paper we study higher order derivatives. But one can ask
the following questions:
-- are they expensive to calculate?
-- are they complicated to use?
-- are they imprecise?
-- are they useless?
\medskip\noindent
At first sight, the answer seems to be positive, but classical results of
V. Strassen [20] and J. Morgenstern [13] tell us that the higher order
derivatives are not expensive to calculate, and can be computed
automatically. The purpose of this paper is to give an answer to the third
question by proving that the higher order derivatives of a function can be
computed with the same precision as the function itself.
We prove also that the derivatives so computed are
equal to the derivatives of the discrete problem (see Diagram 1). We
call the discrete
problem the finite dimensional problem processed by the computer. This result
allows the use of automatic differentiation ([5], [6]), which works only on
discrete problems.
Furthermore, the computations of Taylor's expansions
which are proposed at the end of this paper, could be a partial answer to
the last question.
Received January 27, 1993/Revised version received July 20, 1993 相似文献
15.
A well known and major drawback of standard time integration schemes in the field of non-linear elastodynamics is their unstable behavior in the case of stiff material behaviour. Even second order accurate implicit time integration schemes are unable to resolve the problem under consideration effectively. To remedy this drawback, structure preserving integrators have been developed. Therefore, the goal of this paper is to compare recently developed integrators. In particular, an energy and momentum conserving scheme, based on a publication by Betsch & Steinmann [1], as well as a symplectic variational integrator, proposed by Lew et al. [4] and Wendlandt & Marsden [3], based on a mid-point evaluation of the discrete Lagrangian, are presented. Two representative numerical examples will outline the characteristics of the different approaches. In particular, a stiff non-linear spring pendulum and a finite element model of non-linear structural dynamics are considered. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
拟牛顿流的一种三变量域模型的有限元方法的数值分析 总被引:1,自引:0,他引:1
0.引言目前,涉及高温条件下材料蠕变性质的粘弹性流动问题已引起人们广泛的研究兴趣,不少文章讨论了如何对其进行数值求解(见[1]--[41),首先,人们研究了较简单的仅以速度,压力两个变量来表述此现象的模型问题(如[1,2])等.鉴于应力变量在材料性质方面的特殊重要性,最近J.Baxanzer等人在[3]中首次对应力满足幂函数规律的蠕变流研究了包含应力、速度和压力三种变量的模型问题的有限元逼近,当粘性的牛顿部分为零时(详见下述)在假定速度与应力、速度与压力有限元空间之间同时满足两种**B条件以后,证明了有限元解… 相似文献
17.
We consider a class of quasilinear elliptic systems of PDEs consisting of N Hamilton–Jacobi–Bellman equations coupled with N divergence form equations, generalising to N > 1 populations the PDEs for stationary Mean-Field Games first proposed by Lasry and Lions. We provide a wide range of sufficient conditions for the existence of solutions to these systems: either the Hamiltonians are required to behave at most linearly for large gradients, as it occurs when the controls of the agents are bounded, or they must grow faster than linearly and not oscillate too much in the space variables, in a suitable sense. We show the connection of these systems with the classical strongly coupled systems of Hamilton–Jacobi–Bellman equations of the theory of N-person stochastic differential games studied by Bensoussan and Frehse. We also prove the existence of Nash equilibria in feedback form for some N-person games. 相似文献
18.
《中国科学 数学(英文版)》2010,(6)
By introducing state payoff vector to every state node on the connected graph in this paper,dynamic game is researched on finite graphs.The concept of simple strategy about games on graph defined by Berge is introduced to prove the existence theorem of absolute equilibrium about games on the connected graph with state payoff vector.The complete algorithm and an example in the three-dimensional connected mesh-like graph are given in this paper. 相似文献
19.
Andreas Meister 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(6):1010-1049
In [43] a finite volume method for
reliable simulations of inviscid fluid flows at high as well as
low Mach numbers based on a preconditioning technique proposed by
Guillard and Viozat [14] is presented. In this paper
we describe an extension of the numerical scheme for computing
solutions of the Euler and Navier-Stokes equations. At first we
show the high resolution properties, accuracy and robustness of
the finite volume scheme in the context of a wide range of
complicated transonic and supersonic test cases whereby both
inviscid and viscous flow fields are considered. Thereafter, the
validity of the method in the low Mach number regime is proven by
means of an asymptotic analysis as well as numerical simulations.
Whereas in [43] the asymptotic analysis of the
scheme is focused on the behaviour of the continuous and discrete
pressure distribution for inviscid low speed simulations we prove
both the physical sensible discrete pressure field for viscous low
Mach number flows and the divergence free condition of the
discrete velocity field in the limit of a vanishing Mach number
with respect to the simulation of inviscid fluid flow. 相似文献
20.
The existence theorem of absolute equilibrium about games on connected graph with state payoff vecto
By introducing state payoff vector to every state node on the connected graph in this paper, dynamic game is researched on finite graphs. The concept of simple strategy about games on graph defined by Berge is introduced to prove the existence theorem of absolute equilibrium about games on the connected graph with state payoff vector. The complete algorithm and an example in the three-dimensional connected mesh-like graph are given in this paper. 相似文献