Skip to Main Content
HBS Home
  • About
  • Academic Programs
  • Alumni
  • Faculty & Research
  • Baker Library
  • Giving
  • Harvard Business Review
  • Initiatives
  • News
  • Recruit
  • Map / Directions
Faculty & Research
  • Faculty
  • Research
  • Featured Topics
  • Academic Units
  • …→
  • Harvard Business School→
  • Faculty & Research→
Publications
Publications
  • January 1987
  • Article
  • Econometrica

Posterior Implementability in a Two-person Decision Problem

By: Jerry R. Green and Jean-Jacques Laffont
  • Format:Print
ShareBar

Abstract

When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publicly observable, the players' information is augmented by their observation of each others' strategies. In this paper we study the set of Bayesian implementable decision rules which have the further property that the information conveyed in the process of their implementation does not invalidate the optimality of the players' strategies. We call such rules posterior implementable.
We concentrate on a two-person problem with two possible decisions, and, for this problem, we obtain a complete characterization of the set of posterior implementable decision rules. Our main result entails that a posterior implementable social decision rule can take essentially only two values throughout the range of observations of the two players. The domains over which each of these two outcomes is realized can be characterized by the fact that the boundary between them is a step function satisfying a cetain set of equations.
The motivation for studying posterior implementable rules is that they represent the outcomes of a two-stage cooperative process. In the first stage, communication takes place but no binding commitments can be made. The second stage consists of ratifying ("signing") the agreement obtained at the first stage. At this state, no further information is conveyed. Both parties must be satisfied with the nonbinding commitments obtained at the first stage, so that these actions are actually carried out.
Possible applications of this theory are given. A constructive method for finding the posterior implementable rules is presented and the set of such rules is contrasted, in an example, with the full set of Bayesian implementable rules.

Keywords

Incentives; Commitment; Mechanism Design; Decision Making; Information

Citation

Green, Jerry R., and Jean-Jacques Laffont. "Posterior Implementability in a Two-person Decision Problem." Econometrica 55, no. 1 (January 1987): 69–94.
  • Find it at Harvard
  • Read Now

About The Author

Jerry R. Green

Negotiation, Organizations & Markets
→More Publications

More from the Authors

    • December 2022
    • Decisions in Economics and Finance

    Two Representations of Information Structures and Their Comparisons

    By: Jerry R. Green and Nancy L. Stokey
    • Social Choice and Welfare

    Assent-maximizing Social Choice

    By: Katherine A. Baldiga and Jerry R. Green
    • January 2011
    • American Naturalist

    Let the Right One In: A Microeconomic Approach to Partner Choice in Mutualisms

    By: Marco Archetti, Francisco Ubeda, Drew Fudenberg, Jerry R. Green, Naomi E. Pierce and Douglas W. Yu
More from the Authors
  • Two Representations of Information Structures and Their Comparisons By: Jerry R. Green and Nancy L. Stokey
  • Assent-maximizing Social Choice By: Katherine A. Baldiga and Jerry R. Green
  • Let the Right One In: A Microeconomic Approach to Partner Choice in Mutualisms By: Marco Archetti, Francisco Ubeda, Drew Fudenberg, Jerry R. Green, Naomi E. Pierce and Douglas W. Yu
ǁ
Campus Map
Harvard Business School
Soldiers Field
Boston, MA 02163
→Map & Directions
→More Contact Information
  • Make a Gift
  • Site Map
  • Jobs
  • Harvard University
  • Trademarks
  • Policies
  • Accessibility
  • Digital Accessibility
Copyright © President & Fellows of Harvard College.