  Simple stochastic exchange games are based on random allocation of finite
resources. These games are Markov chains that can be studied either
analytically or by Monte Carlo simulations. In particular, the equilibrium
distribution can be derived either by direct diagonalization of the transition
matrix, or using the detailed balance equation, or by Monte Carlo estimates. In
this paper, these methods are introduced and applied to the
Bennati-Dragulescu-Yakovenko (BDY) game. The exact analysis shows that the
statistical-mechanical analogies used in the previous literature have to be
revised.
