  We consider n agents located on the vertices of a connected graph. Each agent
v receives a signal X_v(0)~N(s, 1) where s is an unknown quantity. A natural
iterative way of estimating s is to perform the following procedure. At
iteration t + 1 let X_v(t + 1) be the average of X_v(t) and of X_w(t) among all
the neighbors w of v.
  In this paper we consider a variant of simple iterative averaging, which
models "greedy" behavior of the agents. At iteration t, each agent v declares
the value of its estimator X_v(t) to all of its neighbors. Then, it updates
X_v(t + 1) by taking the maximum likelihood (or minimum variance) estimator of
s, given X_v(t) and X_w(t) for all neighbors w of v, and the structure of the
graph.
  We give an explicit efficient procedure for calculating X_v(t), study the
convergence of the process as t goes to infinity and show that if the limit
exists then it is the same for all v and w. For graphs that are symmetric under
actions of transitive groups, we show that the process is efficient. Finally,
we show that the greedy process is in some cases more efficient than simple
averaging, while in other cases the converse is true, so that, in this model,
"greed" of the individual agents may or may not have an adverse affect on the
outcome.
  The model discussed here may be viewed as the Maximum-Likelihood version of
models studied in Bayesian Economics. The ML variant is more accessible and
allows in particular to show the significance of symmetry in the efficiency of
estimators using networks of agents.
