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Information Design for Adaptive Organizations

Wataru Tamura

TL;DR

A Bayesian persuasion problem is formulated to determine the optimal public signal and it is shown that it comprises a set of statistics on local states, necessarily including their average, which serves as the organizational goal.

Abstract

This paper examines the optimal design of information sharing in organizations. Organizational performance depends on agents adapting to uncertain external environments while coordinating their actions, where coordination incentives and synergies are modeled as graphs (networks). The equilibrium strategies and the principal's objective function are summarized using Laplacian matrices of these graphs. I formulate a Bayesian persuasion problem to determine the optimal public signal and show that it comprises a set of statistics on local states, necessarily including their average, which serves as the organizational goal. When the principal benefits equally from the coordination of any two agents, the choice of disclosed statistics is based on the Laplacian eigenvectors and eigenvalues of the incentive graph. The algebraic connectivity (the second smallest Laplacian eigenvalue) determines the condition for full revelation, while the Laplacian spectral radius (the largest Laplacian eigenvalue) establishes the condition for minimum transparency, where only the average state is disclosed.

Information Design for Adaptive Organizations

TL;DR

A Bayesian persuasion problem is formulated to determine the optimal public signal and it is shown that it comprises a set of statistics on local states, necessarily including their average, which serves as the organizational goal.

Abstract

This paper examines the optimal design of information sharing in organizations. Organizational performance depends on agents adapting to uncertain external environments while coordinating their actions, where coordination incentives and synergies are modeled as graphs (networks). The equilibrium strategies and the principal's objective function are summarized using Laplacian matrices of these graphs. I formulate a Bayesian persuasion problem to determine the optimal public signal and show that it comprises a set of statistics on local states, necessarily including their average, which serves as the organizational goal. When the principal benefits equally from the coordination of any two agents, the choice of disclosed statistics is based on the Laplacian eigenvectors and eigenvalues of the incentive graph. The algebraic connectivity (the second smallest Laplacian eigenvalue) determines the condition for full revelation, while the Laplacian spectral radius (the largest Laplacian eigenvalue) establishes the condition for minimum transparency, where only the average state is disclosed.
Paper Structure (17 sections, 12 theorems, 17 equations)

This paper contains 17 sections, 12 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. Related literature
  3. Model
  4. Preliminaries
  5. The Laplacian spectrum of graphs
  6. Equilibrium and efficient strategies
  7. Optimal public signal characterization
  8. General results
  9. Average state as a fundamental information component
  10. Conditions for full revelation optimality
  11. Determining the dimension of the optimal public signal
  12. Optimal signal for uniform synergy graphs
  13. Characterization
  14. Examples
  15. Star graphs
  16. ...and 2 more sections

Key Result

Theorem 1

Suppose that each $x_{i}$ is independent and identically distributed according to a normal distribution. Let $\omega_j$ denote an eigenvalue of $V$ and let $\bm{z}_j$ denote the corresponding eigenvector. Assume that $V$ has $r$ nonnegative eigenvalues and $n-r$ negative eigenvalues. Then, the optim

Theorems & Definitions (12)

  • Theorem 1: tamura2018bayesian
  • Proposition 1
  • Proposition 2
  • Corollary 1
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Proposition 6
  • Corollary 2
  • Proposition 7
  • ...and 2 more