Incentive compatibility and information superiority of the core of an economy with differential information

Abstract

: We analyse the coarse, the fine, and the private information core allocation of an exchange economy with differential information. The basic questions that we address are whether the above concepts are: (i) coalitionally incentive compatible, i.e., does truthful revelation of information in each coalition occur; and (ii) take into account the information superiority or information advantage of an agent. Moreover, the above three concepts are examined in the presence of externalities and a comparison and interpretation of all of these core notions is provided.We wish to thank Stefan Krasa and Anne Villamil for several useful suggestions. Obviously we are responsible for all errors.

Incentives and the core of an exchange economy: a survey

“…The equilibrium notion introduced in Radner (1968) modifies the notion of an Arrow-Debreu equilibrium precisely by incorporating such measurability restrictions on agents' trades. An analogous ex ante core concept, the private core, is studied in Allen (1993) and Koutsougeras and Yannelis (1993), and a similar interim concept in Yannelis (1991). 6 The private core is related to equilibrium allocations in the sense of Radner (1968) in the same way as the core of the Arrow-Debreu economy is related to Arrow-Debreu equilibrium allocations.…”

“…Of course, strategic considerations cannot be ignored in considering such a contract and incentive compatibility is therefore an important consideration. A possible rationale for requiring measurability with respect to private information is that, in an exchange economy, (under appropriate assumptions) it implies incentive compatibility; see Allen (1993), Koutsougeras and Yannelis (1993) and Section 4.1.1. But the converse is not true.…”

“…A possible rationale for private measurability is that, under appropriate assumptions, it implies incentive compatibility (see, e.g. Allen, 1993;Koutsougeras and Yannelis, 1993). We turn to a clarification of this point in the next section.…”

“…As we pointed out in Section 1.1.1, the corresponding core is then the core of an Arrow-Debreu economy with complete contingent markets, to which all classical (existence, convergence) results apply. Restricting coalition S's feasible allocations to F m S just reduces the set of objections (while F m = F), so that the associated core is still non-empty (this core corresponds to the "fine core" in Allen, 1993 and to the "weak fine core" in Koutsougeras and Yannelis, 1993). 18 Alternative measurability restrictions have been considered in the literature.…”

“…For instance, agents in a coalition may be forbidden to communicate information in any way, leading to feasible sets for coalitions which are even more restricted than F m S . 19 More interestingly, every individual can be restricted to allocations that are measurable with respect to his own private information, which generates the "private core" (using the terminology of Yannelis, 1991; see also Allen, 1993;Ichiishi and Idzik, 1996;Hahn and Yannelis, 1997;Koutsougeras and Yannelis, 1993). A possible rationale for private measurability is that, under appropriate assumptions, it implies incentive compatibility (see, e.g.…”