Manipulation via Endowments

A competitive allocation in an exchange economy has several desirable properties; it is (with minimal assumptions) Pareto optimal and it guarantees that each trader doesn't lose utility in the trade. Besides these properties of efficiency and individual rationality, however, there are undesirable properties such as its manipulability. There is the possibility that an agent can behave as though his utility function is other than the true utility function and achieve a better outcome (higher utility for him) than at a true competitive outcome. Hurwicz (1972) has shown that this manipulability isn't unique to the competitive process, but in fact is common to any reallocation scheme which achieves Pareto optimal, individually rational outcomes. Besides manipulation via the agent's utility function, there is another type of manipulation, namely of the agent's endowment. In theory, an agent's endowment can be known to all people through inspection and therefore undetectable manipulation is impossible. In practice, however, it is often impossible to determine an agent's true endowment. Even if it were possible to determine true endowments, given a private ownership structure, there is no way of preventing an agent from destroying all or some portion of his endowment. In economies in which there are many agents, each of whom initially owns (at most) a small share of the total amount of a commodity the advantages of these types of manipulation would be small. It is straightforward to apply the techniques used by Roberts and Postlewaite (1976) to show (with similar assumptions as used there) that as an economy gets large agents have diminishing incentive to manipulate endowments. However, in economies in which there are small numbers of agents, large agents, or coalitions of agents the manipulation of the competitive mechanism is theoretically possible. Situations in which farmers withhold from market or destroy portions of their crops are possible instances of coalitional attempts to manipulate via endowments. In international trade we normally must consider agents who are not insignificant and potentially can upset " competitive " allocations through manipulation. Because of this possible manipulation of the competitive mechanism, it becomes interesting to investigate the possibility of designing alternative mechanisms which are not manipulable. In this paper we will show that the problem of manipulation by withholding endowments is not unique to the competitive mechanism, but rather is shared by any Pareto optimal, individually rational scheme of reallocating resources. We show that manipulation via destruction of endowments, however, can be avoided and give an example of a resource reallocation scheme which cannot be manipulated in this way. Finally, we consider manipulation by coalitions and show that if coalitions can " pre-trade ", that is, form a submarket among themselves, they may be able to enter the larger market in an improved position. We show that all Pareto optimal individually rational reallocation schemes are susceptible to this form of manipulation and discuss stability problems which therefore arise. 2. MODEL