Sequential Binary Hypothesis Testing with Competing Agents under Information Asymmetry

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.