Discrete CATS Seminar
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U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

2011 - 2012

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"Evolutionary dynamics and efficient equilibria in games"

Robert Molzon

University of Kentucky

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Monday, November 14, 2011

4:00 pm

845 POT

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Abstract:

Classical Game Theory as developed by von Neumann and Morgenstern
relies in a fundamental way on the assumption of rational behavior by
players or agents. In 1973 the biologist John Maynard Smith developed
an approach to the evolution of strategic behavior in animals that
helped explain certain traits that could not be based on an assumption
of rational behavior. It is now generally recognized that homo sapiens
(in spite of the name) are no great shakes when it comes to rational
behavior either. This enlightenment prompted the application of
evolutionary game theory to the study of social behavior of humans in
fields such as economics, linguistics, and political science.

Evolutionary game theory studies the dynamics and equilibria of
strategies of agents who interact in a manner that generally involves
a stochastic component. Because the resulting stochastic dynamical
systems are often complex to the point of intractability, it is often
assumed that population size large enough so that the random factors
somehow cancel out through a "Law of Large Numbers". I study this
assumption in the context of a well known model for learning in
games. The model consists of a large number of players who are
pairwise matched to play a two strategy game that has two Nash
equilibria. Players update their strategy by imitation. I show that
the limiting distribution of strategies as population size becomes
arbitrarily large is quite diferent than it would be for an infinite
population. The primary mathematical tools needed to obtain the
resuls are discrete probability, stochastic processes, and estimates
for combinatorial expressions.