  This paper is concerned with general spatially explicit versions of three
stochastic models for the dynamics of money that have been introduced and
studied numerically by statistical physicists: the uniform reshuffling model,
the immediate exchange model and the model with saving propensity. All three
models consist of systems of economical agents that consecutively engage in
pairwise monetary transactions. Computer simulations performed in the physics
literature suggest that, when the number of agents and the average amount of
money per agent are large, the distribution of money at equilibrium approaches
the exponential distribution for the first model, the gamma distribution with
shape parameter two for the second model and a gamma distribution whose shape
parameter depends on the saving propensity for the third model. The main
objective of this paper is to give rigorous proofs of and extend these
conjectures to generalizations of the first two models and a variant of the
third model that include local rather than global interactions, i.e., instead
of choosing the two interacting agents uniformly at random from the system, the
agents are located on the vertex set of a general connected graph and can only
interact with their neighbors.
