Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction - Softcover

Gintis, Herbert

Softcover

ISBN 10: 0691140510 ISBN 13: 9780691140513

Verlag: Princeton University Press, 2009

Inhaltsangabe

Since its original publication in 2000, Game Theory Evolving has been considered the best textbook on evolutionary game theory. This completely revised and updated second edition of Game Theory Evolving contains new material and shows students how to apply game theory to model human behavior in ways that reflect the special nature of sociality and individuality. The textbook continues its in-depth look at cooperation in teams, agent-based simulations, experimental economics, the evolution and diffusion of preferences, and the connection between biology and economics.


Recognizing that students learn by doing, the textbook introduces principles through practice. Herbert Gintis exposes students to the techniques and applications of game theory through a wealth of sophisticated and surprisingly fun-to-solve problems involving human and animal behavior. The second edition includes solutions to the problems presented and information related to agent-based modeling. In addition, the textbook incorporates instruction in using mathematical software to solve complex problems. Game Theory Evolving is perfect for graduate and upper-level undergraduate economics students, and is a terrific introduction for ambitious do-it-yourselfers throughout the behavioral sciences.

• Revised and updated edition relevant for courses across disciplines


• Perfect for graduate and upper-level undergraduate economics courses


• Solutions to problems presented throughout


• Incorporates instruction in using computational software for complex problem solving


• Includes in-depth discussions of agent-based modeling

Über diesen Titel

Über die Autorin bzw. den Autor

Herbert Gintis holds faculty positions at the Santa Fe Institute, Central European University, and University of Siena. He has coedited numerous books, including Moral Sentiments and Material Interests, Unequal Chances (Princeton), and Foundations of Human Sociality.

Von der hinteren Coverseite

"Mathematically rigorous, computationally adroit, rich in illuminating problems, and engagingly written, Game Theory Evolving will be invaluable to students and researchers across the social sciences."--Joshua M. Epstein, Brookings Institution and Santa Fe Institute

"An inspiring introduction to the potential and various applications of game theory."--Jan Ekman, Ecological Economics

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Game Theory Evolving

A Problem-Centered Introduction to Modeling Strategic InteractionBy Herbert Gintis

Princeton University Press

Copyright © 2009 Princeton University Press
All right reserved.
ISBN: 978-0-691-14051-3

Contents

Preface...................................................................xv1 Probability Theory....................................................12 Bayesian Decision Theory..............................................183 Game Theory: Basic Concepts...........................................324 Eliminating Dominated Strategies......................................525 Pure-Strategy Nash Equilibria.........................................806 Mixed-Strategy Nash Equilibria........................................1167 Principal-Agent Models................................................1628 Signaling Games.......................................................1799 Repeated Games........................................................20110 Evolutionarily Stable Strategies......................................22911 Dynamical Systems.....................................................24712 Evolutionary Dynamics.................................................27013 Markov Economies and Stochastic Dynamical Systems.....................29714 Table of Symbols......................................................31915 Answers...............................................................321Sources for Problems......................................................373References................................................................375Index.....................................................................385

Chapter One

Probability Theory

Doubt is disagreeable, but certainty is ridiculous.

Voltaire

1.1 Basic Set Theory and Mathematical Notation

A set is a collection of objects. We can represent a set by enumerating its objects. Thus,

A = {1, 3, 5, 7, 9, 34}

is the set of single digit odd numbers plus the number 34. We can also represent the same set by a formula. For instance,

A = {x|x [member of] N [conjunction] (x < 10 [conjunction] x is odd) [disjunction] (x = 34)}.

In interpreting this formula, N is the set of natural numbers (positive integers), "|" means "such that," "[member of]" means "is a element of," [conjunction] is the logical symbol for "and," and [disjunction] is the logical symbol for "or." See the table of symbols in chapter 14 if you forget the meaning of a mathematical symbol.

The subset of objects in set X that satisfy property p can be written as

{x [member of] X|p(x)}.

The union of two sets A, B [subset] X is the subset of X consisting of elements of X that are in either A or B:

A [union] B = {x|x [member of] A [disjunction] x [member of] B}.

The intersection of two sets A, B [subset] X is the subset of X consisting of elements of X that are in both A or B:

A [intersection] B = {x|x [member of] A [conjunction] x [member of] B}.

If a [member of] A and b [member of] B, the ordered pair (a,b) is an entity such that if (a, b) = (c, d), then a = c and b = d. The set {(a, b)|a [member of] A [conjunction] b [member of] B} is called the product of A and B and is written A x B. For instance, if A = B = R, where R is the set of real numbers, then A x B is the real plane, or the real two-dimensional vector space. We also write

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

A function f can be thought of as a set of ordered pairs (x, f(x)). For instance, the function f(x) = [chi square] is the set

{(x, y)|(x, y [member of] R) [conjunction] (y = [chi square])}

The set of arguments for which f is defined is called the domain of f and is written dom (f). The set of values that f takes is called the range of f and is written range (f). The function f is thus a subset of dom(f) x range(f). If f is a function defined on set A with values in set B, we write f : A -> B.

1.2 Probability Spaces

We assume a finite universe or sample space [OMEGA] and a set X of subsets A, B, C, ... of [OMEGA], called events. We assume X is closed under finite unions (if [A.sub.1], [A.sub.2], ... [A.sub.n] are events, so is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), finite intersections (if [A.sub.1], ..., [A.sub.n] are events, so is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), and complementation (if A is an event so is the set of elements of [OMEGA] that are not in A, which we write [A.sup.c]). If A and B are events, we interpret A [intersection] B = AB as the event "A and B both occur," A [intersection] B as the event "A or B occurs," and [A.sup.c] as the event "A does not occur."

For instance, suppose we flip a coin twice, the outcome being HH (heads on both), HT (heads on first and tails on second), TH (tails on first and heads on second), and TT (tails on both). The sample space is then [OMEGA] = {HH, TH, HT, TT}. Some events are {HH, HT} (the coin comes up heads on the first toss), {TT} (the coin comes up tails twice), and {HH, HT, TH} (the coin comes up heads at least once).

The probability of an event A [member of] X is a real number P[A] such that 0 [less than or equal to] P[A] [less than or equal to] 1. We assume that P[[OMEGA]] = 1, which says that with probability 1 some outcome occurs, and we also assume that if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [A.sub.i] [member of] X and the {[A.sub.i]} are disjoint (that is, [A.sub.i] [intersection] [A.sub.j] = 0 for all i [not equal to] j), then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which says that probabilities are additive over finite disjoint unions.

1.3 De Morgan's Laws

Show that for any two events A and B, we have

[(A [intersection] B).sup.c] = [A.sup.c] [intersection] [B.sup.c]

and

[(A [intersection] B).sup.c] = [A.sup.c] [intersection] [B.sup.c].

These are called De Morgan's laws. Express the meaning of these formulas in words.

Show that if we write p for proposition "event A occurs" and q for "event B occurs," then

not (p or q) [??] (not p and not q);

not (p and q) [??] (not p or not q).

The formulas are also De Morgan's laws. Give examples of both rules.

1.4 Interocitors

An...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 0691140510
• ISBN 13: 9780691140513
• Einband: Taschenbuch
• Auflage: 2
• Anzahl der Seiten: 408
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar