  This paper considers a problem where multiple users make repeated decisions
based on their own observed events. The events and decisions at each time step
determine the values of a utility function and a collection of penalty
functions. The goal is to make distributed decisions over time to maximize time
average utility subject to time average constraints on the penalties. An
example is a collection of power constrained sensor nodes that repeatedly
report their own observations to a fusion center. Maximum time average utility
is fundamentally reduced because users do not know the events observed by
others. Optimality is characterized for this distributed context. It is shown
that optimality is achieved by correlating user decisions through a commonly
known pseudorandom sequence. An optimal algorithm is developed that chooses
pure strategies at each time step based on a set of time-varying weights.
