This paper relates the issue of efficiency in communication to the problem of designing games that implement a given objective in Nash equilibrium. A message process that "realizes" (or computes) the objective is used to construct a game that implements it in Nash equilibrium. Any efficient encoding of information that occurs in the message process causes a reduction in the size of the strategy space of the game that is constructed. Necessary and (stronger) sufficient conditions on the message process are given for this construction.