“…The realization theory studies the question of how much communication must be provided to realize a given performance, or more precisely, studies the minimal informational cost of operating a given performance in terms of the size of the message space and determines which economic system or social choice rule is informationally the most efficient in the sense that the minimal informational cost is used to operate the system. Since the pioneering work of Hurwicz (1960), there has been a lot of work on studying the informational requirements of decentralized resource allocation mechanisms over various classes of economies such as those in Calsamiglia (1977), Calsamiglia and Kirman (1993), Hurwicz (1972, 1977, 1999), Hurwicz, Reiter, and Saari (1985), Mount and Reiter (1974), Sato (1981), Tian (1990, 1994, 2000a, 2000b) among others.…”