A Two Stage Core with Applications to Asset Markets and Differential Information Economies

This paper focuses on the coalitional approach to sequential trading processes. We study the allocation of resources through sequential trading, when individuals have the option to form coalitions and make group decisions. We introduce a new core concept, called the two stage core, which is appropriate for analyzing asset market and differential information economies, with sequential trade. The two stage core characterizes fully optimal allocations. vVe show that the two stage core always exists under standard continuity and concavity assumptions. We derive the two stage core of an asset markets economy as a specification of the two stage core. In order to capture the case of arbitrary short sales we provide a core existence proof for the case of consumption sets with no lower bound. Further, we show that the two stage core is non empty in the Hart (1975) example where a rational expectations equilibrium fails to exist. Finally, we apply this core concept to differential information economies and show that the two stage core is incentive compatible in the sense that no coalition of agents can misreport the true state and provide improvements to all its members, even by redistributing the benefits from misreporting. Thus, our core notion results in allocations that are both fully optimal and incentive compatible.