Szanowni Państwo,
We wtorek 12 stycznia 2009
Dr David M. Ramsey z Universytetu w Limerik wygłosi referat na temat

A Large Population Mate Choice Game with Age Preferences

Abstract
This talk considers a mate choice problem in which individuals aim to
obtain a partner so as to maximize the length of time for which both
partners are fertile. It is assumed that individuals mate only once.

First, a discrete time model will be presented. It is assumed that
males are fertile for m moments of time and females are fertile for n
moments. It is assumed that the population is large and males enter
the adult population at a rate r times the rate at which females enter
the adult population. The parameter r is known as the incoming sex
ratio. At each moment in time an unmated individual from the rarer sex
in the mating pool is presented with a prospective partner. This
prospective partner is chosen at random from the set of individuals of
the opposite sex in the mating pool. If such a pair is mutually
acceptable, then they form a breeding pair and leave the mating pool.
The payoff they obtain is the number of moments for which both remain
fertile. Otherwise, both individuals continue searching. At the next
moment in time they are one time unit older. If an individual has not
previously found a mate, on becoming infertile he/she leaves the
mating pool and thus obtains a reward of zero.
The steady state distributions of the ages of fertile males and
females, as well as the ratio of the number of males to the number of
females in the mating pool (the operational sex ratio, denoted R)
depend on the strategy profile used by the population as a whole. The
calculation of such a steady state distribution is outlined.
Conditions that an evolutionary stable strategy profile must satisfy
are given and an example is considered.
A continuous time model is then defined by using a discrete time model
with “inefficient” matching. Under such a model an individual of the
rarer sex in the mating pool (assumed, for convenience, to be females)
is presented with a prospective partner at a given moment with
probability δ. The continuous time model is obtained by simultaneously
allowing δ → 0 and n → ∞ such that δn → λ. We consider a problem which
is symmetric with respect to sex (i.e. r = 1). The form of a symmetric
equilibrium profile is given. A coupled pair of differential equations
for the equilibrium strategy profile and the corresponding age
distribution is derived. An iterative procedure deriving the
equilibrium profile is given.

This work has been carried out with Prof. Steve Alpern and Dr. Ioanna
Katranzi (London School of Economics).

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