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Information Compression in Dynamic Information Disclosure Games

Dengwang Tang, Vijay G. Subramanian

TL;DR

This work tackles dynamic information design between a principal and a receiver on a Markovian system, where the principal can publicly perform experiments and truthfully disclose results to influence actions. It introduces Canonical Belief Based (CBB) strategies and proves the existence of Perfect Bayesian Equilibria in which both players operate on compressed beliefs rather than full histories, accompanied by a backward-inductive procedure to compute such equilibria. The main technical contribution is a dynamic programming framework that relies on piecewise-linear value functions, concave closures, and triangulation-based interpolation to construct equilibrium strategies. The results offer insight into credible, long-horizon information disclosure and highlight both the theoretical structure and practical computation of equilibria, with implications for public health, cybersecurity, and other dynamic settings where information sharing shapes outcomes.

Abstract

We consider a two-player dynamic information design problem between a principal and a receiver -- a game is played between the two agents on top of a Markovian system controlled by the receiver's actions, where the principal obtains and strategically shares some information about the underlying system with the receiver in order to influence their actions. In our setting, both players have long-term objectives, and the principal sequentially commits to their strategies instead of committing at the beginning. Further, the principal cannot directly observe the system state, but at every turn they can choose randomized experiments to observe the system partially. The principal can share details about the experiments to the receiver. For our analysis we impose the truthful disclosure rule: the principal is required to truthfully announce the details and the result of each experiment to the receiver immediately after the experiment result is revealed. Based on the received information, the receiver takes an action when its their turn, with the action influencing the state of the underlying system. We show that there exist Perfect Bayesian equilibria in this game where both agents play Canonical Belief Based (CBB) strategies using a compressed version of their information, rather than full information, to choose experiments (for the principal) or actions (for the receiver). We also provide a backward inductive procedure to solve for an equilibrium in CBB strategies.

Information Compression in Dynamic Information Disclosure Games

TL;DR

This work tackles dynamic information design between a principal and a receiver on a Markovian system, where the principal can publicly perform experiments and truthfully disclose results to influence actions. It introduces Canonical Belief Based (CBB) strategies and proves the existence of Perfect Bayesian Equilibria in which both players operate on compressed beliefs rather than full histories, accompanied by a backward-inductive procedure to compute such equilibria. The main technical contribution is a dynamic programming framework that relies on piecewise-linear value functions, concave closures, and triangulation-based interpolation to construct equilibrium strategies. The results offer insight into credible, long-horizon information disclosure and highlight both the theoretical structure and practical computation of equilibria, with implications for public health, cybersecurity, and other dynamic settings where information sharing shapes outcomes.

Abstract

We consider a two-player dynamic information design problem between a principal and a receiver -- a game is played between the two agents on top of a Markovian system controlled by the receiver's actions, where the principal obtains and strategically shares some information about the underlying system with the receiver in order to influence their actions. In our setting, both players have long-term objectives, and the principal sequentially commits to their strategies instead of committing at the beginning. Further, the principal cannot directly observe the system state, but at every turn they can choose randomized experiments to observe the system partially. The principal can share details about the experiments to the receiver. For our analysis we impose the truthful disclosure rule: the principal is required to truthfully announce the details and the result of each experiment to the receiver immediately after the experiment result is revealed. Based on the received information, the receiver takes an action when its their turn, with the action influencing the state of the underlying system. We show that there exist Perfect Bayesian equilibria in this game where both agents play Canonical Belief Based (CBB) strategies using a compressed version of their information, rather than full information, to choose experiments (for the principal) or actions (for the receiver). We also provide a backward inductive procedure to solve for an equilibrium in CBB strategies.
Paper Structure (11 sections, 7 theorems, 41 equations, 5 figures)

This paper contains 11 sections, 7 theorems, 41 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. A Motivating Example
  3. PROBLEM FORMULATION
  4. BACKGROUND: DISCRETE GEOMETRY
  5. MAIN RESULTS
  6. Extension
  7. EXAMPLES
  8. DISCUSSION
  9. CONCLUSION AND FUTURE WORK
  10. Proofs of Discrete Geometric Results
  11. Proof of Main Results

Key Result

Lemma 1

Let $\Omega_1, \Omega_2$ be polytopes. Let $\ell:\Omega_1\mapsto \Omega_2$ be an affine function and $f:\Omega_2\mapsto \mathbb{R}$ be a piecewise linear function. Then the composite function $f\circ \ell: \Omega_1\mapsto \mathbb{R}$ is piecewise linear.

Figures (5)

  • Figure 1: Left: 2-D Polytope $\Omega$; Center: A triangulation; Right: NOT a triangulation.
  • Figure 2: Left: A triangulation $\gamma$ labeled with the values of a function $f$ on the vertices. Right: 3-D plot of $\mathbb{I}(f, \gamma)$.
  • Figure 3: Top-left: 3-D plot of a function $f$ (an upper semi-continuous piecewise constant function taking values in $\{0, 1, 2\}$). Top-right: Concave closure of $f$. Bottom-left and bottom-right: 2-D visualization of two different triangulations in $\arg\mathrm{cav}(f)$.
  • Figure 4: The $q_t^B$ and $V_t^A$ functions for Example \ref{['ex:did:farhadi']} with $p = 0.2, c = 0.1$ at times $t=T:T-13$.
  • Figure 5: The $q_t^B$ and $V_t^A$ functions for Example \ref{['ex:did:2']} with $p = 0.2, c = 0.15$ at times $t=T:T-13$.

Theorems & Definitions (29)

  • Example 1
  • Definition 1: PBE
  • Definition 2
  • Lemma 1
  • proof
  • Definition 3
  • Lemma 2
  • proof
  • Definition 4
  • Lemma 3
  • ...and 19 more