## 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