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Mini-twistor theory on three-dimensional space forms

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0006
Subject:
Mathematics, Pure Mathematics

This chapter discusses harmonic morphisms from 3-manifolds to surfaces, especially those of constant curvature. First, the local behaviour is considered, showing that the foliation given by its ... More


Game Theory: Basic Concepts

Herbert Gintis

in The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160849
eISBN:
9781400851348
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160849.003.0002
Subject:
Sociology, Economic Sociology

This chapter deals with the basic concepts of game theory. It presents the formulations for the extensive form, normal form, and Nash equilibrium. It concludes with a brief discussion of correlated ... More


Games and Misdemeanors: Game Theory for the Uninitiated

Kaushik Basu

in Prelude to Political Economy: A Study of the Social and Political Foundations of Economics

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198296713
eISBN:
9780191595943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198296711.003.0002
Subject:
Economics and Finance, Microeconomics

This chapter presents a primer on game theory. It provides an overview of its origins and its establishment as an essential methodological tool for economists. It describes the game of Hex, ... More


Rationalizability and Common Knowledge of Rationality

Herbert Gintis

in The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160849
eISBN:
9781400851348
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160849.003.0004
Subject:
Sociology, Economic Sociology

This chapter deals with the implications of rationality in normal form games. It first explores the ramifications of the rationalizability assumption and shows that in many cases rational individuals ... More


Axiomatizations of the Propositional Calculus

A. N. Prior

in Formal Logic

Published in print:
1963
Published Online:
October 2011
ISBN:
9780198241560
eISBN:
9780191680373
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198241560.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

The laws that arise in the logic of truth-functions can be set out as a series of theorems derived from a small set of axioms. This chapter shows how this can be done. The first section discusses the ... More


Calculus of Propositions

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:
10.1093/0198284616.003.0029
Subject:
Economics and Finance, Microeconomics

This is the first of three chapters on general mathematics as applied to economics, and presents a treatment of the calculus of propositions. The seven sections of the chapter are: the Boolean laws; ... More


Acts of Mathematical Creation

Paul Erickson

in The World the Game theorists Made

Published in print:
2015
Published Online:
May 2016
ISBN:
9780226097039
eISBN:
9780226097206
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226097206.003.0002
Subject:
History, History of Science, Technology, and Medicine

Despite the ex post facto identification of a number of “anticipations” of game-theoretic results through history, it is generally agreed that modern game theory’s founding work was mathematician ... More


Quantal Response Equilibrium in Normal-Form Games

Jacob K. Goeree, Charles A. Holt, and Thomas R. Palfrey

in Quantal Response Equilibrium: A Stochastic Theory of Games

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691124230
eISBN:
9781400880928
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691124230.003.0002
Subject:
Economics and Finance, History of Economic Thought

This chapter lays out the general theory of quantal response equilibrium (QRE) for normal-form games. It starts with the reduced-form approach to QR, based on the direct specification of “regular” ... More


Wright-Fisher Geometry

Charles L. Epstein and Rafe1 Mazzeo

in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural ... More


Planning Ahead

Ken Binmore

in Playing for Real Coursepack Edition: A Text on Game Theory

Published in print:
2012
Published Online:
April 2015
ISBN:
9780199924530
eISBN:
9780190261399
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199924530.003.0005
Subject:
Economics and Finance, Microeconomics

This chapter discusses and joins together the ideas of extensive and strategic forms of a game. Von Neumann and Morgenstern invented both the extensive and the strategic forms of a game. The latter ... More


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