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On Team Decision Problems with Nonclassical Information Structures

Andreas A. Malikopoulos

Abstract

In this paper, we consider sequential dynamic team decision problems with nonclassical information structures. First, we address the problem from the point of view of a ``manager" who seeks to derive the optimal strategy of the team in a centralized process. We derive structural results that yield an information state for the team which does not depend on the control strategy, and thus it can lead to a dynamic programming decomposition where the optimization problem is over the space of the team's decisions. We, then, derive structural results for each team member that yield an information state which does not depend on their control strategy, and thus it can lead to a dynamic programming decomposition where the optimization problem for each team member is over the space of their decisions. Finally, we show that the solution of each team member is the same as the one derived by the manager. We present an illustrative example of a dynamic team with a delayed sharing information structure.

On Team Decision Problems with Nonclassical Information Structures

Abstract

In this paper, we consider sequential dynamic team decision problems with nonclassical information structures. First, we address the problem from the point of view of a ``manager" who seeks to derive the optimal strategy of the team in a centralized process. We derive structural results that yield an information state for the team which does not depend on the control strategy, and thus it can lead to a dynamic programming decomposition where the optimization problem is over the space of the team's decisions. We, then, derive structural results for each team member that yield an information state which does not depend on their control strategy, and thus it can lead to a dynamic programming decomposition where the optimization problem for each team member is over the space of their decisions. Finally, we show that the solution of each team member is the same as the one derived by the manager. We present an illustrative example of a dynamic team with a delayed sharing information structure.

Paper Structure

This paper contains 33 sections, 16 theorems, 110 equations.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contributions of This Paper
  5. Comparison with Related Work
  6. Organization of This Paper
  7. Problem Formulation
  8. Notation
  9. Modeling Framework
  10. Nonclassical Information Structures
  11. $n$-step delayed information sharing
  12. Periodic information sharing with period $\omega\ge1$
  13. $n$-step delayed observation sharing
  14. $n$-step delayed control sharing
  15. No sharing information
  16. ...and 18 more sections

Key Result

Lemma 1

For any control strategy $\textbf{g}\in\mathcal{G}$ of the team, for all $t=0,1,\ldots, T-1.$

Theorems & Definitions (36)

  • Definition 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 1
  • Theorem 1: Information State -- Team
  • proof
  • ...and 26 more