Efficient Incentive Compatible Economies Are Perfectly Competitive

No externalities: a characterization of efficiency and incentive compatibility with public goods

“…The characterization is used to derive existence and non-existence results for models with a finite number of individuals and to explain existence results in the continuum. A similar characterization and conclusions are demonstrated for private goods in [7]. However, unlike private goods, elimination of externalities with public goods implies that individuals cannot change the outcome.…”

“…We have not adopted this terminology because sharpening will be used here to introduce the geometry of kinks in convex preferences. We note that the reverse comparison, that we call flattening, plays a parallel role in the characterization of efficiency, anonymity and incentive compatibility with private goods (see [7]). …”

“…Nevertheless, they suggest how the collection a * D(u, a * ) can come closer to filling out U n the larger is n. Using the techniques employed in [7], the set U n \{ a * D(u, a * )} applied to an approximate notion of incentive compatibility can be shown to converge to a closed no-where dense set in the continuum limit.…”

“…Consequently, the exceptional character of the no externalities property is more likely as n approaches infinity and it becomes typical for populations in the continuum. Such an argument is demonstrated in [7] for private goods where the size of the flats can be made arbitrarily small as the number of individuals increases and, in the limit, indifference surfaces can be curved. We shall provide a brief sketch, below, of a parallel construction for public goods implying that there are outcome functions that are generically efficient, anonymous, and incentive compatible in economies with a continuum of agents.…”

Ordinal Efficiency, Fairness, and Incentives in Large Markets

“…The standard reasons to study ordinal mechanisms are (a) real-life no-transfer mechanisms are typically ordinal, (b) learning and reporting one's rankings of sure outcomes is simpler than learning and reporting one's cardinal utilities, and (c) ordinal preferences over sure outcomes do not rely on agents' attitudes towards risk. For analysis that incorporates cardinal utilities see Hylland and Zeckhauser (1979) and Makowski, Ostroy, and Segal (1999). nisms are asymptotically efficient, that is the maximum size of advantageous swaps vanishes as the market becomes large. In particular, many known mechanisms are asymptotically efficient, and there are no efficiency reasons to favor one of them over others in large markets.…”