  We introduce a system of kinetic equations describing an exchange market
consisting of two populations of agents (dealers and speculators) expressing
the same preferences for two goods, but applying different strategies in their
exchanges. We describe the trading of the goods by means of some fundamental
rules in price theory, in particular by using Cobb-Douglas utility functions
for the exchange. The strategy of the speculators is to recover maximal utility
from the trade by suitably acting on the percentage of goods which are
exchanged. This microscopic description leads to a system of linear
Boltzmann-type equations for the probability distributions of the goods on the
two populations, in which the post-interaction variables depend from the
pre-interaction ones in terms of the mean quantities of the goods present in
the market. In this case, it is shown analytically that the strategy of the
speculators can drive the price of the two goods towards a zone in which there
is a marked utility for their group. Also, the general system of nonlinear
kinetic equations of Boltzmann type for the probability distributions of the
goods on the two populations is described in details. Numerical experiments
then show how the policy of speculators can modify the final price of goods in
this nonlinear setting.
