Efficient trading with restriction

In a classical paper by Cramton, Gibbons, and Klemperer (CGK) (Econometrica 55:615–632, 1987), it is shown that an efficient trading mechanism exists if traders’ initial endowments are not too asymmetric. In this paper, we extend the CGK model by assuming that traders are not allowed to consume more than a given amount (upper bound) of the good. In the CGK model, instead the only restriction is that no agent can consume more than the entire endowment in the economy. By varying this upper bound, we characterize the set of endowments (efficient region) in which efficient trading mechanisms exist in terms of this upper bound. We show that the efficient region becomes smaller when the upper bound decreases. On the other hand, when this upper bound becomes the entire endowment of the economy, we obtain the result in CGK as a special case.