Strategic Concealment of Environment Representations in Competitive Games

TL;DR

Simulations show that purposeful concealment naturally emerges: the Attacker randomizes its trajectory to manipulate the Defender’s belief, inducing suboptimal barrier selections and thereby gaining a strategic advantage.

Abstract

This paper investigates the strategic concealment of environment representations used by players in competitive games. We consider a defense scenario in which one player (the Defender) seeks to infer and exploit the representation used by the other player (the Attacker). The interaction between the two players is modeled as a Bayesian game: the Defender infers the Attacker's representation from its trajectory and places barriers to obstruct the Attacker's path towards its goal, while the Attacker obfuscates its representation type to mislead the Defender. We solve for the Perfect Bayesian Nash Equilibrium via a bilinear program that integrates Bayesian inference, strategic planning, and belief manipulation. Simulations show that purposeful concealment naturally emerges: the Attacker randomizes its trajectory to manipulate the Defender's belief, inducing suboptimal barrier selections and thereby gaining a strategic advantage.

Figures (5)

• Figure 1: An example of the proposed two-phase defense game. In Phase I, the Attacker navigates the grid while the Defender passively observes the state-action trajectory. The middle panel illustrates the two available barrier configurations for the Defender to protect the target. The Defender selects barrier configuration $\omega = 2$ to obstruct the Attacker’s path. In Phase II, the Attacker continues toward the goal under the modified environment induced by the selected barrier.
• Figure 2: Example of two representations and trajectories under different barrier placement. The solid line shows the trajectory segment that can be achieved with deterministic strategies, while the dashed ones need to be achieved with randomized strategy due to coarse resolution. The randomized strategies are illustrated via the red arrows in the corresponding superstates. Subplots (a) and (b) show different realizations of trajectories from the same mixed strategy.
• Figure 3: Left: Attacker trajectories under each representation type. Right: Observed trajectories from the Defender’s perspective.
• Figure 4: Trajectories in Phase II. Subplots (a)–(c) show the trajectories under the type-1 representation, while (d)–(e) correspond to the type-2 representation. The dashed segments indicate portions of the trajectory that require a randomized strategy; they represent the intended path, but the actual realized trajectory may differ due to stochasticity.
• Figure 5: Value heatmaps of the Phase II constrained MDP for states reachable within $T = 6$.

Theorems & Definitions (13)

• Remark 1
• Definition 1
• Remark 2
• Definition 2
• Proposition 0
• proof
• Remark 3
• Definition 3
• Lemma 1
• proof