Mathematical Tools
(do not be discouraged: we shall cover only a very small subset
of this; but one should know that some sharp tools are there and ready
for use)
E. Akin, "The General Topology of
Dynamical Systems", AMS.
B. Hasselblatt, A. Katok,
Introduction to the
Modern Theory of Dynamical Systems , Cambridge University
Press, 1995
M. I. Friedlin, Functional Integration and Partial
Differential Equations, Annals of Mathematical Studies,
Princeton University Press, 1985
M. I. Friedlin, AD Wentzell, Random Perturbations of Dynamical Systems, Russian Math. Surveys, 1970
Y.
Kifer, A Discrete-Time Version of the
Wentzell-Friedlin Theory, The Annals of Probability, Vol. 18,
No. 4. (Oct., 1990), pp. 1676-1692
Y. Kifer, Large deviations in dynamical systems
and stochastic processes, Transactions of the American
Mathematical Society 321:22, 505-524,
Books on
Evolutionary Game theory
Josef Hofbauer Karl Sigmund,
Evolutionary Games and Population Dynamics , Cambridge University
Press 1998
.
K.
Ritzberger,
"Foundations of
Non-Cooperative Game Theory", Oxford University Press.
L. Samuelson,
Evolutionary
Games and Equilibrium Selection, MIT Press.
B.
Sandholm, "
Deterministic
Evolutionary Dynamics". Forthcoming, The New Palgrave
Dictionary of Economics , 2nd edition.
Available
on
http://www.ssc.wisc.edu/~whs/research/ded.pdf.
B. Sandholm,
Population Games and Evolutionary Dynamics,
MIT press, forthcoming
J.
Weibull,
"Evolutionary Game
Theory" ,
MIT
Press 1995.
H. Peyton Young, Strategic Learning and Its Limits , Oxford Univ. Press
Some articles (preliminary
list, to be completed)
Bena¨ım
M. and J. Weibull (2003): “Deterministic
approximation of stochastic
evolutionary in games”, Econometrica 71, 873-903
van Damme,
Eric & Weibull, Jorgen W., 2002."Evolution in Games with Endogenous Mistake
Probabilities," Journal of
Economic Theory, Elsevier, vol. 106(2), pages 296-315, October.
S. Demichelis, K.
Ritzberger, J.
Swinkels: "The Simple Geometry of Perfect
Information
Games." ,
IJGT,
vol. 32, nr. 3, 2003, 315-338.
Reprint
here .
S. Demichelis, K.
Ritzberger, "From
Evolutionary
to Strategic Stability."
JET,
vol. 113, nr. 1, 2003, 51-75.
Reprint available here
S.
Demichelis, F.
Germano: "On
knots and dynamics in games.",
GEB,
Volume 41, Number 1, October 2002, pp. 46-60(15).
Reprint
in
KnotsandGames.pdf.
J. Hofbauer
W.H. Sandholm Evolution in games with randomly perturbed
payoffs . J. Economic Theory 132 (Jan 2007), 47–69.
Josef Hofbauer Bill Sandholm
On the global convergence of stochastic fictitious play.
Econometrica 70 (Nov 2002) 2265-2294.
Josef Hofbauer,
Bill Sandholm:
"Survival of Dominated Strategies under Evolutionary Dynamics"
Klaus
Ritzberger, Joergen Weibull: "Evolutionary
selection in normal-form games", Econometrica 63, 1371-1399, 1995.
Saez-Marti,
Maria & Weibull, Jorgen W., 1999. "Clever Agents in Young's
Evolutionary Bargaining Model," Journal of Economic Theory, Elsevier,
vol. 86(2), pages 268-279, June.
K. Binmore, L. Samuelson,
Evolutionary Drift and
Equilibrium Selection
K.
Binmore, L. Samuelson, Drift
Young, H Peyton,
1993. "The Evolution of Conventions," Econometrica, Econometric
Society, vol. 61(1), pages 57-84, January.
Some more articles on social
networks (preliminary
list, to be completed)
Banerjee, Abhijit, and Drew Fudenberg. 2004.
“Word-of-mouth learning.” Games
and Economic Behavior, 46: 1-22.
Ellison, Glenn, and Drew Fudenberg. 1993. “Rules of thumb for social
learning.”
Journal of Political Economy, 101: 612-643.
Ellison, Glenn, and Drew Fudenberg. 1995. “Word of mouth communication
and
social learning.” Quarterly Journal of Economics, 110: 93-125.
Golub, Benjamin, and Matthew O. Jackson. 2007. “Naive learning in social
networks: convergence, influence, and the wisdom of crowds.” Stanford
University Department of Economics Working Paper.
Kirman, Alan. 1993. “Ants, rationality, and recruitment.” Quarterly
Journal of
Economics, 108: 137-156.
Granovetter, Mark. 1978. “Threshold models of collective behavior.”
American
Journal of Sociology, 83: 1420-1443.
H. Peyton Young, 2007. "Innovation Diffusion in Heterogeneous
Populations,"Economics Series Working Papers 303,
University of Oxford, Department of Economics.
