Price condition with communication constraints

The traditional description of coordination assumes noise free messages and in inifinite sequence of iterations converging to the optimum price vector p. It is shown that when communications are constrained to finite bit length messages the price mechanism converges only to a ball surrounding p. The size of this ball depends on the size of the message truncation noise. For a given specification of the maximum size of the ball, one can find an "optimum" message length in the sense of minimizing the total number of bits transmitted.