  A dynamical model of capital exchange is introduced in which a specified
amount of capital is exchanged between two individuals when they meet. The
resulting time dependent wealth distributions are determined for a variety of
exchange rules. For ``greedy'' exchange, an interaction between a rich and a
poor individual results in the rich taking a specified amount of capital from
the poor. When this amount is independent of the capitals of the two traders, a
mean-field analysis yields a Fermi-like scaled wealth distribution in the
long-time limit. This same distribution also arises in greedier exchange
processes, where the interaction rate is an increasing function of the capital
difference of the two traders. The wealth distribution in multiplicative
processes, where the amount of capital exchanged is a finite fraction of the
capital of one of the traders, are also discussed. For random multiplicative
exchange, a steady state wealth distribution is reached, while in greedy
multiplicative exchange a non-steady power law wealth distribution arises, in
which the support of the distribution continuously increases. Finally,
extensions of our results to arbitrary spatial dimension and to growth
processes, where capital is created in an interaction, are presented.
