Deception and Counter Deception in Adversarial Graph Traversal Game

2026-05-21

AI Summary

This work addresses adversarial graph traversal, where a mobile agent and an adversary each possess private information—the agent seeks to reach its goal with minimal cost, while the adversary manipulates edge costs to increase that expense. The paper introduces the first extensive-form game model supporting bilateral incomplete information and dynamic role switching between players. It further proposes an enhanced Extensive-Form Double Oracle (XDO) algorithm tailored for infinite-horizon settings with endogenous termination. The method provably converges to an ε-Nash equilibrium within finitely many iterations and effectively captures emergent deceptive and counter-deceptive behaviors in equilibrium strategies. By relaxing the conventional assumption of fixed roles, this approach achieves the first formal modeling and solution of bidirectional deception mechanisms in such adversarial environments.

Abstract

We study deception in adversarial graph traversal, where a mobile agent seeks to reach a goal with minimum cost while an adversary alters edge costs to increase the total traversal cost. Unlike prior works that assume fixed observer-deceiver roles, we model this problem with two-sided incomplete information in which both players possess private information and update beliefs from observed actions. To solve the resulting indefinite-horizon game, we develop an adaptation of the Extensive-Form Double Oracle (XDO) algorithm. While the standard XDO algorithm is designed for finite games, the proposed adaptation ensures bounded computation despite endogenous game termination. We show that the proposed algorithm terminates in finite time and returns an epsilon-Nash equilibrium. Finally, we use Value of Information to characterize the deceptive and counter-deceptive behaviors that emerge from equilibrium strategies.

Problem

• deception
• adversarial graph traversal
• incomplete information
• game theory
• counter-deception

Innovation

• adversarial graph traversal
• two-sided incomplete information
• Extensive-Form Double Oracle
• epsilon-Nash equilibrium
• Value of Information