Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Sequential Binary Hypothesis Testing with Competing Agents under Information Asymmetry

Aneesh Raghavan, M. Umar B. Niazi, Karl H. Johansson

TL;DR

The study addresses sequential binary hypothesis testing with two competitive agents under information asymmetry and potentially manipulated signals. It develops a formal model featuring private observations, belief signaling, and belief fusion, and establishes that the optimal signaling policy is a random 50/50 mix between truthful and inverted beliefs, while belief updates rely on private data and signals only to predict stopping. The analysis reveals a first-mover advantage where the initiator achieves a bounded error and the rival may incur higher error, with an entropy-based interpretation of why randomization is optimal. Numerical results show that larger KL divergence between an agent's observations under the two states yields faster and more accurate decisions, and that information sharing reduces stopping time despite strategic manipulation. These findings offer practical guidance for robust, fast sequential decision-making in competitive, information-limited environments and point to extensions to multi-agent networks and adaptive learning.

Abstract

This paper concerns sequential hypothesis testing in competitive multi-agent systems where agents exchange potentially manipulated information. Specifically, a two-agent scenario is studied where each agent aims to correctly infer the true state of nature while optimizing decision speed and accuracy. At each iteration, agents collect private observations, update their beliefs, and share (possibly corrupted) belief signals with their counterparts before deciding whether to stop and declare a state, or continue gathering more information. The analysis yields three main results: (1)~when agents share information strategically, the optimal signaling policy involves equal-probability randomization between truthful and inverted beliefs; (2)~agents maximize performance by relying solely on their own observations for belief updating while using received information only to anticipate their counterpart's stopping decision; and (3)~the agent reaching their confidence threshold first cause the other agent to achieve a higher conditional probability of error. Numerical simulations further demonstrate that agents with higher KL divergence in their conditional distributions gain competitive advantage. Furthermore, our results establish that information sharing -- despite strategic manipulation -- reduces overall system stopping time compared to non-interactive scenarios, which highlights the inherent value of communication even in this competitive setup.

Sequential Binary Hypothesis Testing with Competing Agents under Information Asymmetry

TL;DR

The study addresses sequential binary hypothesis testing with two competitive agents under information asymmetry and potentially manipulated signals. It develops a formal model featuring private observations, belief signaling, and belief fusion, and establishes that the optimal signaling policy is a random 50/50 mix between truthful and inverted beliefs, while belief updates rely on private data and signals only to predict stopping. The analysis reveals a first-mover advantage where the initiator achieves a bounded error and the rival may incur higher error, with an entropy-based interpretation of why randomization is optimal. Numerical results show that larger KL divergence between an agent's observations under the two states yields faster and more accurate decisions, and that information sharing reduces stopping time despite strategic manipulation. These findings offer practical guidance for robust, fast sequential decision-making in competitive, information-limited environments and point to extensions to multi-agent networks and adaptive learning.

Abstract

This paper concerns sequential hypothesis testing in competitive multi-agent systems where agents exchange potentially manipulated information. Specifically, a two-agent scenario is studied where each agent aims to correctly infer the true state of nature while optimizing decision speed and accuracy. At each iteration, agents collect private observations, update their beliefs, and share (possibly corrupted) belief signals with their counterparts before deciding whether to stop and declare a state, or continue gathering more information. The analysis yields three main results: (1)~when agents share information strategically, the optimal signaling policy involves equal-probability randomization between truthful and inverted beliefs; (2)~agents maximize performance by relying solely on their own observations for belief updating while using received information only to anticipate their counterpart's stopping decision; and (3)~the agent reaching their confidence threshold first cause the other agent to achieve a higher conditional probability of error. Numerical simulations further demonstrate that agents with higher KL divergence in their conditional distributions gain competitive advantage. Furthermore, our results establish that information sharing -- despite strategic manipulation -- reduces overall system stopping time compared to non-interactive scenarios, which highlights the inherent value of communication even in this competitive setup.

Paper Structure

This paper contains 13 sections, 4 theorems, 28 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Our Contributions
  4. Problem Formulation
  5. Setup
  6. Belief Signaling and Decision Policies
  7. Problem Definition
  8. Analysis
  9. Optimal Signaling
  10. Optimal Belief Fusion and Stopping Time
  11. Conditional Probability of Error
  12. Numerical Example
  13. Conclusion and Future Work

Key Result

Proposition 1

Consider the belief signaling policy eq:signaling parametrized by $0\leq \alpha^i\leq 1$. Then, for any belief fusion parameter sequence, $\{w^{ {\sim} i}_{n}\}$ and thresholds $T^{ {\sim} i}_{U}, T^{ {\sim} i}_{L}$ of agent ${\sim} i$, $\alpha^i = 0.5$ is optimal with respect to Problem 3.

Figures (4)

  • Figure 1: The two-agent binary hypothesis testing setup.
  • Figure 2: Steps executed by agents at each iteration of sequential binary hypothesis testing.
  • Figure 3: Entropy of the Bernoulli Distribution.
  • Figure 4: Decay of conditional probability of error with time

Theorems & Definitions (9)

  • Proposition 1
  • proof
  • Remark 1
  • Lemma 1
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Remark 2