## Pairwise trade, money holdings, and the geometric probability
distribution

Edward Green, Department of Economics, Penn State University

"Random-matching models" in monetary econmomics consider a very
large population (mathematically, a nonatomic measure space) of individuals
who, at each date t = 0, 1, 2..., are randomly matched into pairs. Each
individual carries money, the holding of which at each date is a natural
number. In each pair of individuals at each date, one is randomly selected
to transfer one unit of money to the other--if he possesses a unit to
transfer. Is there a stationary distribution of individuals' money holdings
in this population, and if so, is it approached from an arbitrary initial
distribution? The answer is that a money-holdings distribution is
stationary iff it is geometric, and that (under a mild assumption) an
initial distribution converges to the geometric distribution with the same
expectation. Besides a presentation of this result (due to E. Green and R.
Zhou, Econometrica, 2002), the talk will include a discussion of what sort
of generalization would be helpful to monetary economists.