Alexander Mehlmann, Vienna University of Technology, Austria
The Game's Afoot! Game Theory in Myth and Paradox
Description
It all started with von Neumann and Morgenstern half a century ago. Their Theory of Games and Economic Behavior gave birth to a whole new area of mathematics concerned with the formal problems of rational decision as experienced by multiple agents. Now, game theory is all around us, making its way even into
regular conversations. In the present book, Mehlmann presents mathematical foundations and concepts illustrated via social quandaries, mock political battles, evolutionary confrontations, economic struggles, and literary conflict. Most of the standard models--the prisoners' dilemma, the arms race, evolution, duels, the game of chicken, etc.--are here. Many non-standard examples are also here: the Legend of Faust, shootouts in the movies, the Madness of Odysseus, to name a few.
The author uses familiar formulas, fables, and paradoxes to guide readers through what he calls the "hall of mirrors of strategic decision-making". His light-hearted excursion into the world of strategic calculation shows that even deep insights into the nature of strategic thought can be elucidated by games, puzzles and diversions.
Originally written in German and published by Vieweg-Verlag, this AMS edition is a translation tailored for the English-speaking reader. It offers an intriguing look at myths and paradoxes through the lens of game theory, bringing the mathematics into sharper focus at the same time. This book is a must for those who wish to
consider game theory from a different perspective: one that embraces science, literature, and real-life conflict.
The Game's Afoot! would make an excellent book for an undergraduate course in game theory. It can also be used for independent study or as supplementary course reading. The connections to literature, films and everyday life also make it highly suitable as a text for a challenging course for non-majors. Its refreshing style
and amusing combination of game theoretic analysis and cultural issues even make it appealing as recreational reading.
Contents
The glass bead game
Introduction
Games, form(ula)s, and scholars
Equilibrium and game as metaphor
In the forest of game trees
Games against time
The myths of game theory
Introduction
The prisoner's dilemma
Paradoxes of backward induction
Strategic accents of game-theoretic scholasticism
Odysseus goes to war
A postlude in rhyme
Games in the network of networks
References
Index
Details:
Series: Student Mathematical Library, Volume: 5
Publication Year: 2000
ISBN: 0-8218-2121-0
Paging: 159 pp.
Binding: Softcover
Edited by:
Luis G. Gorostiza, Centro de Investigacion y de Estudios Avanzados, Mexico City, Mexico,
and B. Gail Ivanoff, University of Ottawa, ON,Canada
Stochastic Models
Description
This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right.
A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work.
This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.
Contents
D. A. Dawson -- Stochastic models of evolving information systems
M. Birkner and A. Wakolbinger -- A comparison of free branching and stepping stone models
D. Blount and A. Bose -- Fourier analysis applied to super stable and related processes
J. T. Cox, A. Klenke, and E. A. Perkins -- Convergence to equilibrium and linear systems duality
M. Csg・and B. Szyszkowicz -- Weighted quantile processes and their applications to change-point analysis
C. D. Cutler -- Embedding theorems, scaling structures and determinism in time series
S. N. Evans -- Kingman's coalescent as a random metric space
S. Feng -- The behaviour near the boundary of some degenerate diffusions under random perturbation
K. Fleischmann and C. Mueller -- Finite time extinction of catalytic branching processes
J. G舐tner and S. A. Molchanov -- Moment asymptotics and Lifshitz tails for the parabolic Anderson model
L. G. Gorostiza and Z.-H. Li -- High-density fluctuations of immigration branching particle systems
A. Greven -- On phase-transitions in spatial branching systems with interaction
A. Greven and K. J. Hochberg -- New behavioral patterns for two-level branching systems
B. G. Ivanoff and E. Merzbach -- Set-indexed Markov processes
I. Jeon and P. March -- Condensation transition for zero range invariant measures
A. Klenke -- A review on spatial catalytic branching
M. A. Kouritzin -- Exact infinite dimensional filters and explicit solutions
R. J. Kulperger -- SDE estimation: Effects of misspecified diffusion functions
T. G. Kurtz -- Particle representations for measure-valued population processes with spatially varying birth rates
B. MacGibbon, E. Gourdin, B. Jaumard, and P. Kempthorne -- Minimax estimation of exponential family means over $\ell_p$ bodies under quadratic loss
W. A. Massey and R. Srinivasan -- Steady state analysis with heavy traffic limits for semi-open networks
R. Norvaisa and D. M. Salopek -- Estimating the Orey index of a Guassian stochastic process with stationary increments: An application to financial data set
B. Remillard -- Large deviations estimates for occupation time integrals of Brownian motion
D. Sankoff and M. Blanchette -- Comparitive genomics via phylogenetic invariants for Jukes-Cantor semigroups
B. Schmuland -- Some exceptional configurations
V. Vinogradov -- On a conjecture of B. Jgensen and A. D. Wentzell: From extreme stable laws to Tweedie exponential dispersion models
H. Wang -- Valuation of a barrier European option on jump-diffusion underlying stock price
Details:
Series: Conference Proceedings, Canadian Mathematical Society, Volume: 26
Publication Year: 2000
ISBN: 0-8218-1063-4
Paging: 450 pp.
Binding: Softcover
Alexander N. Starkov, Moscow State University, Russia
Dynamical Systems on Homogeneous Spaces
Description
A homogeneous flow is a dynamical system generated by the action of a closed subgroup $H$ of a Lie group $G$ on a homogeneous space of $G$. The study of such systems is of great significance because they constitute an algebraic model for more general and more complicated systems. Also, there are abundant
applications to other fields of mathematics, most notably to number theory.
The present book gives an extensive survey of the subject. In the first chapter the author discusses ergodicity and mixing of homogeneous flows. The second chapter is focused on unipotent flows, for which substantial progress has been made during the last 10-15 years. The culmination of this progress was M. Ratner's celebrated proof of far-reaching conjectures of Raghunathan and Dani. The third chapter is devoted to the dynamics of nonunipotent flows. The final chapter discusses applications of homogeneous flows to number theory, mainly to the theory of Diophantine approximations. In particular, the author describes in detail the famous proof of the Oppenheim-Davenport conjecture using ergodic properties of homogeneous flows.
Contents
Preliminaries
Ergodicity and mixing of homogeneous flows
Dynamics of unipotent flows
Dynamics of nonunipotent flows
Applications to number theory
References
Index
Details:
Series: Translations of Mathematical Monographs, Volume: 190
Publication Year: 2000
ISBN: 0-8218-1389-7
Paging: 243 pp.
Binding: Hardcover
D. G. Babbitt (ed.)
Featured Reviews in Mathematical Reviews Set 1995-1999
Contents
Featured Reviews in Mathematical Reviews 1995-1996
Logic, combinatorics, and number theory
D. G. Babbitt -- Algebra and algebraic geometry
D. G. Babbitt -- Analysis
D. G. Babbitt -- Geometry and topology
D. G. Babbitt -- Differential equations and applied mathematics
D. G. Babbitt -- Probability and mathematical physics
Author index
Reviewer index
Featured Reviews in Mathematical Reviews 1997-1999
Reviews in logic, computer science and number theory
Reviews in algebra and algebraic geometry
Reviews in analysis
Reviews in geometry and topology
Reviews in differential equations and applied mathematics
Selected reviews published 1940-69
Author index
Reviews in probability and mathematical physics
Reviewer index
Details:
Publication Year: 2000
ISBN: 0-8218-2631-X
Binding: Softcover
Edited by:
R. A. Minlos, Russian Academy of Sciences, Moscow, Russia,
Senya Shlosman, CPT/CNRS, Marseille, France,
and Yu. M. Suhov, Russian Academy of Sciences, Moscow
On Dobrushin's Way. From Probability Theory to Statistical Physics
Description
R. Dobrushin worked in several branches of mathematics (probability theory, information theory), but his deepest influence was on mathematical physics. He was one of the founders of the rigorous study of statistical physics. When Dobrushin began working in that direction in the early sixties, only a few people worldwide
were thinking along the same lines. Now there is an army of researchers in the field. This collection is devoted to the memory of R.L. Dobrushin. The authors who contributed to this collection knew him quite well and were his colleagues.
The title, "On Dobrushin's Way", is meant to stress the fact that the current development of mathematical physics is evolving along the lines that Dobrushin foresaw. His ideas and methods are extensively employed today.
Beyond research papers, this volume contains a short biography. Recollections from his contemporaries and younger colleagues are also included. This short biographical section sketches for readers a bit of Dobrushin's qpersonality.
Contents
N. Angelescu, R. A. Minlos, and V. A. Zagrebnov -- The lower spectral branch of the generator of the stochastic dynamics for the classical Heisenbergmodel
C. Boldrighini, R. A. Minlos, and A. Pellegrinotti -- Random walk in a fluctuating random environment with markov evolution
S. Brassesco, E. Presutti, V. Sidoravicius, and M. E. Vares -- Ergodicity and exponential convergence of a Glauber+Kawasaki process
A. van Enter, C. Maes, R. H. Schonmann, and S. Shlosman -- The Griffiths singularity random field
A. van Enter, C. Maes, and S. Shlosman -- Dobrushin's program on Gibbsianity restoration: Weakly Gibbs and almost Gibbs random fields
G. L. Eyink and H. Spohn -- Space-time invariant states of the ideal gas with finite number, energy, and entropy density
B. M. Gurevich and A. A. Templeman -- Hausdorff dimension and pressure in the DLR thermodynamic formalism
V. Yu. Kaloshin and Ya. G. Sinai -- Nonsymmetric simple random walks along orbits of ergodic automorphisms
F. I. Karpelevich, E. A. Pechersky, and Yu. M. Suhov -- The Crame transform and large deviations on three-dimensional Lobachevsky space
F. I. Karpelevich and A. N. Rybko -- Thermodynamical limit for symmetric closed queuing networks
V. A. Malyshev -- Random infinite spin graph evolution
F. Martinelli -- An elementary approach to finite size conditions for the decay of covariances in lattice spin models
S. Nanda, C. M. Newman, and D. L. Stein -- Dynamics of Ising spin systems at zero temperature
S. A. Pirogov -- Peierls argument for the anisotropic Ising model
M. Zahradn -- Contour methods and Pirogov-Sinai theory for continuous spin lattice models
R. Minlos, A. M. Vershik, N. D. Vvedenskaya, Yu. D. Apresyan, S. Gindikin, V. M. Tikhomirov, Yu. Suhov, L. N. Vaserstein, M.-F. Chen, and S. Shlosman -- Recollections
Details:
Series: American Mathematical Society Translations--Series 2, Subseries: Advances in the Mathematical Sciences Volume: 198
Publication Year: 2000
ISBN: 0-8218-2150-4
Paging: 243 pp.
Binding: Hardcover
Edited by:
Jerry Bona, University of Texas, Austin, TX,
Katarzyna Saxton, Loyola University, New Orleans, LA,
and Ralph Saxton, University of New Orleans, LA
Nonlinear PDE's, Dynamics and Continuum Physics
Description
This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity,
thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and
fractal solutions.
The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.
Contents
H. Chen -- Travelling-waves for generalized KdV-Burgers equations
S. R. Choudhury -- Some analytical coherent structures of the long-wave equations
W. Domanski -- Weakly nonlinear elastic plane waves in a cubic crystal
M. L. Frankel and V. Roytburd -- On dynamics of exothermic interfaces
P.-A. Gremaud, J. V. Matthews, and M. Shearer -- Similarity solutions for granular flows in hoppers
T. Hagen and M. Renardy -- Stability issues in nonisothermal elongational flow
L. Hsiao and R. Pan -- The damped $P$-system with boundary effects
B. L. Keyfitz and C. A. Mora -- Prototypes for nonstrict hyperbolicity in conservation laws
S. Kichenassamy -- Stability of blow-up patterns for nonlinear wave equations
M. Kovalyov -- Slowly decaying solutions of KdV
I. Rodnianski -- Fractal solutions of the Schringer equation
J. Shatah and W. Strauss -- Spectral condition for abstract instability
A. Tovbis -- On approximation of stable and unstable manifolds and the Stokes phenomenon
S. J. Watson -- A priori bounds in one-dimensional nonlinear thermoviscoelasticity
R. Young -- Periodic solutions to conservation laws
Details:
Series: Contemporary Mathematics, Volume: 255
Publication Year: 2000
ISBN: 0-8218-1052-9
Paging: approximately 264 pp.
Binding: Softcover