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Integrated Resource Allocation and Strategy Synthesis in Safety Games on Graphs with Deception

Abhishek N. Kulkarni, Matthew S. Cohen, Charles A. Kamhoua, Jie Fu

TL;DR

The paper develops a hypergame-on-graphs framework to study deception in two-player reachability games with one-sided incomplete information. It models P1's allocation of traps and fake targets and synthesizes stealthy deceptive strategies that steer P2 toward decoys while preserving P2's perception, yielding two solution notions: stealthy deceptive sure winning and stealthy deceptive almost-sure winning. It proves structural properties (monotonicity, sub/supermodularity) that enable a scalable greedy decoy-placement algorithm with a (1 − 1/e) approximation under suitable conditions, and shows that, in the almost-sure setting, fake targets and traps are equally valuable. Experiments on gridworlds and random graphs illustrate the value of deception and the efficacy of the compositional approach, highlighting practical implications for security contexts where deception resources are constrained. The work links subjective rationalizability from one-shot games to qualitative ω-regular game analysis on graphs and proposes a flexible, scalable methodology for defense planning under information asymmetry.

Abstract

Deception plays a crucial role in strategic interactions with incomplete information. Motivated by security applications, we study a class of two-player turn-based deterministic games with one-sided incomplete information, in which player 1 (P1) aims to prevent player 2 (P2) from reaching a set of target states. In addition to actions, P1 can place two kinds of deception resources: "traps" and "fake targets" to disinform P2 about the transition dynamics and payoff of the game. Traps "hide the real" by making trap states appear normal, while fake targets "reveal the fiction" by advertising non-target states as targets. We are interested in jointly synthesizing optimal decoy placement and deceptive defense strategies for P1 that exploits P2's misinformation. We introduce a novel hypergame on graph model and two solution concepts: stealthy deceptive sure winning and stealthy deceptive almost-sure winning. These identify states from which P1 can prevent P2 from reaching the target in a finite number of steps or with probability one without allowing P2 to become aware that it is being deceived. Consequently, determining the optimal decoy placement corresponds to maximizing the size of P1's deceptive winning region. Considering the combinatorial complexity of exploring all decoy allocations, we utilize compositional synthesis concepts to show that the objective function for decoy placement is monotone, non-decreasing, and, in certain cases, sub- or super-modular. This leads to a greedy algorithm for decoy placement, achieving a $(1 - 1/e)$-approximation when the objective function is sub- or super-modular. The proposed hypergame model and solution concepts contribute to understanding the optimal deception resource allocation and deception strategies in various security applications.

Integrated Resource Allocation and Strategy Synthesis in Safety Games on Graphs with Deception

TL;DR

The paper develops a hypergame-on-graphs framework to study deception in two-player reachability games with one-sided incomplete information. It models P1's allocation of traps and fake targets and synthesizes stealthy deceptive strategies that steer P2 toward decoys while preserving P2's perception, yielding two solution notions: stealthy deceptive sure winning and stealthy deceptive almost-sure winning. It proves structural properties (monotonicity, sub/supermodularity) that enable a scalable greedy decoy-placement algorithm with a (1 − 1/e) approximation under suitable conditions, and shows that, in the almost-sure setting, fake targets and traps are equally valuable. Experiments on gridworlds and random graphs illustrate the value of deception and the efficacy of the compositional approach, highlighting practical implications for security contexts where deception resources are constrained. The work links subjective rationalizability from one-shot games to qualitative ω-regular game analysis on graphs and proposes a flexible, scalable methodology for defense planning under information asymmetry.

Abstract

Deception plays a crucial role in strategic interactions with incomplete information. Motivated by security applications, we study a class of two-player turn-based deterministic games with one-sided incomplete information, in which player 1 (P1) aims to prevent player 2 (P2) from reaching a set of target states. In addition to actions, P1 can place two kinds of deception resources: "traps" and "fake targets" to disinform P2 about the transition dynamics and payoff of the game. Traps "hide the real" by making trap states appear normal, while fake targets "reveal the fiction" by advertising non-target states as targets. We are interested in jointly synthesizing optimal decoy placement and deceptive defense strategies for P1 that exploits P2's misinformation. We introduce a novel hypergame on graph model and two solution concepts: stealthy deceptive sure winning and stealthy deceptive almost-sure winning. These identify states from which P1 can prevent P2 from reaching the target in a finite number of steps or with probability one without allowing P2 to become aware that it is being deceived. Consequently, determining the optimal decoy placement corresponds to maximizing the size of P1's deceptive winning region. Considering the combinatorial complexity of exploring all decoy allocations, we utilize compositional synthesis concepts to show that the objective function for decoy placement is monotone, non-decreasing, and, in certain cases, sub- or super-modular. This leads to a greedy algorithm for decoy placement, achieving a -approximation when the objective function is sub- or super-modular. The proposed hypergame model and solution concepts contribute to understanding the optimal deception resource allocation and deception strategies in various security applications.
Paper Structure (13 sections, 16 theorems, 19 equations, 7 figures, 2 algorithms)

This paper contains 13 sections, 16 theorems, 19 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Main Results
  5. Hypergames for Deception
  6. Effect of Decoys on P2's Subjectively Rationalizable Strategy
  7. Synthesis of P1's Deceptive Sure Winning Strategy
  8. Compositional Synthesis for Decoy Placement
  9. Synthesis of P1's Deceptive Almost-sure Winning Strategy
  10. Experiments
  11. Decoy Placement in a Gridworld
  12. Effectiveness of Decoy Placement under Sure and Almost-sure Winning Conditions
  13. Conclusion

Key Result

Proposition 1

The following statements are true about the level-sets $Z_0, Z_1, \ldots, Z_K$ constructed by Algorithm alg:zielonka.

Figures (7)

  • Figure 1: Base game considered in the running example.
  • Figure 2: Perceptual games when the state $s_7$ is a fake target. In both sub-figures, the blue-colored states are winning for P1, and the red-colored states are winning for P2. Dotted transitions depict actions that are not subjectively rationalizable for P2 when players use greedy deterministic strategies.
  • Figure 3: Hypergame on graph constructed based on P1 and P2's perceptual games shown in Figure \ref{['fig:running-ex-fake-p2-perception']}. Dotted lines depict P2's subjectively rationalizable actions. The cyan-colored states are stealthy deceptive sure winning states for P1, whereas the red-colored states are sure winning for P2.
  • Figure 4: A scenario where $\mathsf{DASWin}_1(X, Y) \subsetneq \mathsf{DASWin}_1(X, Y)$.
  • Figure 5: Gridworld example with a cat and a mouse with $2$ cheese blocks.
  • ...and 2 more figures

Theorems & Definitions (41)

  • Definition 1: Reachability Game
  • Proposition 1
  • Remark 1
  • Definition 2: True Game
  • Definition 3: P2's Perceptual Game
  • Remark 2
  • Example 1: Running Example
  • Definition 4: Level-1 and Level-2 Hypergame
  • Definition 5: Subjectively Rationalizable Action
  • Definition 6: Subjectively Rationalizable Strategy
  • ...and 31 more