The value allocation of an economy with differential information

Summary

We analyze the Shapley value allocation of an economy with differential information. Since the intent of the Shapley value is to measure the sum of the expected marginal contributions made by an agent to any coalition that he/she belongs to, the value allocation of an economy with differential information provides an interesting way to measure the information advantage of an agent. This feature of the Shapley value allocation is not necessarily shared by the rational expectation equilibrium. Thus, we analyze the informational structure of an economy with differential information from a different and new viewpoint.

In particular we address the following questions: How do coalitions of agents share their private information? How can one measure the information advantage or superiority of an agent? Is each agent’s private information verifiable by other members of a coalition? Do coalitions of agents pool their private information? Do agents have an incentive to report their true private information? What is the correct concept of a value allocation in an economy with differential information? Do value allocations exist in an economy with differential information? We provide answers to each of these questions.

We wish to thank David Ballard, Leonidas Koutsougeras, Wayne Shafer, Anne Villamil and three referees for useful comments, discussions and suggestions. We are also very indebted to Andreu Mas-Colell whose thoughtful suggestions inspired Section 4.2.As usual we are responsible for any remaining shortcomings.