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 Fighting It Out

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0007
Subject:
Economics and Finance, Microeconomics

This chapter describes the theory of two-person, zero-sum games invented by John Von Neumann in 1928. It begins with an application to the computation of economic shadow prices. It shows that a ... More


SELF-CONSISTENT FIELD THEORY

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the topic of self-consistent field theory, a mean-field approximation method for analyzing the statistical field models constructed in Chapter 4. The mean-field approximation ... More


Intersections and Fixed Points

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0031
Subject:
Economics and Finance, Microeconomics

This is the last of three chapters on general mathematics as applied to economics, and presents a treatment of intersections and fixed points. The eight sections of the chapter are: simplices and ... More


Saddle Points

Michael Veseth

in Mountains of Debt: Crisis and Change in Renaissance Florence, Postwar Britain, and Postwar America

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195064209
eISBN:
9780199854998
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195064209.003.0010
Subject:
Economics and Finance, Economic History

This chapter develops the idea of the “saddle point,” where changes in economic and social policy are critical to the future. It looks back at Florence and Britain to see why they failed when they ... More


 Backing Up

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0002
Subject:
Economics and Finance, Microeconomics

This chapter's title signifies not only that backward induction is introduced, but that some backing up is necessary to put the material of the previous chapter on a more solid foundation. The game ... More


Changing Directions

Michael Veseth

in Mountains of Debt: Crisis and Change in Renaissance Florence, Postwar Britain, and Postwar America

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195064209
eISBN:
9780199854998
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195064209.003.0011
Subject:
Economics and Finance, Economic History

It is one thing to identify the problem of the saddle point and point out the need for policies to move the economy in a new direction. It is another thing actually to conceive of policies that might ... More


Some Applications

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0009
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Some recent applications of wavelet methods are shown. The chapter starts with the numerical realization of the WEM and consider the L-shaped domain as a model for a non-separable domain. The chapter ... More


Games in Extensive Form

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0007
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a number of key concepts for extensive form game representation. It first considers a matrix that defines a zero-sum matrix game for which the minimizer has two actions and the ... More


A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily

Harald Uhlig

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0003
Subject:
Economics and Finance, Macro- and Monetary Economics

An extensive treatment is provided of methods that use log‐linear approximations to solve nonlinear dynamic discrete‐time stochastic models. These methods, based on their linear counterparts, have ... More


Stochastic Policies for Games in Extensive Form

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses two types of stochastic policy for extensive form game representation as well as the existence and computation of saddle-point equilibrium. For games in extensive form, a mixed ... More


MATRIX MODELS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter starts with explaining some basic aspects and techniques of matrix models. Matrix models are the simplest examples of quantum gauge theories; they are quantum gauge theories in zero ... More


Potential energy surfaces

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the ... More


Mixed Policies

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0004
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions ... More


Ballistic electron transport in quantum point contacts

Thomas Ihn

in Semiconductor Nanostructures: Quantum states and electronic transport

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199534425
eISBN:
9780191715297
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534425.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter contrasts the results of Chapter 10 with the theory of ballistic transport through quantum point contacts. It discusses the experimental observation of conductance quantization based on ... More


Zero-Sum Matrix Games

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0003
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a number of key concepts for zero-sum matrix games. A zero-sum matrix game is played by two players, each with a finite set of actions. Player 1 wants to minimize the outcome ... More


Computation of Mixed Saddle-Point Equilibrium Policies

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the computation of mixed saddle-point equilibrium policies. In view of the Minimax Theorem, the mixed saddle-point equilibria can be determined by computing the mixed security ... More


NUMERICAL APPROXIMATION OF ONE-FLUID PROBLEMS

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.003.0003
Subject:
Mathematics, Mathematical Physics

This chapter addresses the discretization of the one-fluid magnetohydrodynamics equations. At the numerical level, the difficulties due to nonlinearities (coming both from the hydrodynamics equations ... More


State-Feedback Zero-Sum Differential Games

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0018
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum continuous time dynamic game in a state-feedback policy. It begins by considering the solution for two-player ... More


State-Feedback Zero-Sum Dynamic Games

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0017
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum discrete time dynamic game in a state-feedback policy. It begins by considering solution methods for two-player ... More


More complex systems

Gert D. Billing (ed.)

in The Quantum Classical Theory

Published in print:
2003
Published Online:
November 2020
ISBN:
9780195146196
eISBN:
9780197561836
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195146196.003.0009
Subject:
Chemistry, Quantum and Theoretical Chemistry

By more complex systems we mean systems containing on the order of hundreds or thousands of atoms, or molecules with less atoms but with “complicated” motions, the latter being the case when ... More


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