# Learning Deceptive Strategies in Adversarial Settings:
## 5 Results and Simulations
### Experiment 1: Two-Goal Environment  
In this baseline scenario--a \(7\times 7\) grid with one true and one decoy goal--the trained DQN police officer (\(\pi^{\textsc{DQN}}_{\text{P}}\)) dramatically reduces misallocation compared to naive strategies. Table 2 reports the PFA, where \(\pi^{\textsc{DQN}}_{\text{P}}\) lowers the percentage of resources sent to the decoy by up to 40%. The results demonstrate the effectiveness of our DQN-based approach compared to baseline strategies Table 3. The trained DQN police officer (\(\pi^{\textsc{DQN}}_{\text{P}}\)) consistently outperforms the game-theoretic baseline (\(\pi^{\textsc{baseline}}_{\text{P}}\)), achieving identical or better performance across all robber policies. Notably, \(\pi^{\textsc{DQN}}_{\text{P}}\) maintains the same 28.57% PFA as \(\pi^{\textsc{baseline}}_{\text{P}}\) against the shortest-path (\(\pi^{\textsc{shortest path}}_{\text{R}}\)), naive deceptive (\(\pi^{\textsc{naive}}_{\text{R}}\)), and trained DQN (\(\pi^{\textsc{DQN}}_{\text{P}}\)) robbers while also handling the random robber (\(\pi^{\textsc{random}}_{\text{R}}\)) more effectively. The DQN robber (\(\pi^{\textsc{DQN}}_{\text{R}}\)) shows competitive performance against the baseline (\(\pi^{\textsc{baseline}}_{\text{P}}\)), achieving 28.57% PFA against \(\pi^{\textsc{DQN}}_{\text{P}}\) compared to \(\pi^{\textsc{baseline}}_{\text{P}}\)'s 25.00% against \(\pi^{\textsc{baseline}}_{\text{P}}\), demonstrating that learned policies can match or exceed theoretical equilibrium strategies in practice. The ablation study reveals the critical contribution of each component to our framework's performance. The full MARL-DQN approach achieves the best performance with 28.6% PFA and 78% interception rate, significantly outperforming all ablated variants. Removing reward shaping degrades performance substantially (46.6% PFA, 62% interception), demonstrating that game-theoretic incentives are essential for learning effective deception strategies. The absence of intent inference also hurts performance (39.6% PFA, 68% interception), confirming that opponent modeling is crucial for counter-deception. Training on static layouts only results in the worst performance (53.6% PFA, 54% interception), highlighting the importance of dynamic environment training for generalization. These results validate that our integrated approach combining reward shaping, intent inference, and dynamic training is necessary for achieving robust deception and counter-deception capabilities. \begin{table}
\begin{tabular}{l l} \hline \hline
**Abbreviation** & **Description** \\ \hline \(\pi^{\textsc{random}}_{\text{P}}\) & Random Police Officer: allocates resources uniformly at random. \\ \(\pi^{\textsc{DQN}}_{\text{P}}\) & Fully Informed Police Officer: all resources are allocated to the true exit. \\ \(\pi^{\textsc{DQN}}_{\text{P}}\) & Trained DQN Police Officer: learns to infer intent and counter deception via deep Q-learning. \\ \(\pi^{\textsc{baseline}}_{\text{P}}\) & Baseline Game-Theoretic Police Officer: allocates according to the equilibrium strategy from [26]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \cline{3-6} \multicolumn{1}{c}{} & \multicolumn{5}{c|}{P’s Policy} \\ \cline{3-6} \multicolumn{1}{c}{} & & \(\pi^{\textsc{random}}_{\text{P}}\) & \(\pi^{\textsc{Fully Informed}}_{\text{P}}\) & \(\pi^{\textsc{DQN}}_{\text{P}}\) & \(\pi^{\textsc{Baseline}}_{\text{P}}\) \\ \hline \multirow{5}{*}{
\begin{tabular}{c} **C.1** \\ **C.2** \\ \end{tabular} } & \(\pi^{\textsc{random}}_{\text{R}}\) & 52.00 & 0.00 & 52.00 & 48.00 \\ \cline{2-6}  & \(\pi^{\textsc{shortest path}}_{\text{R}}\) & 46.00 & 0.00 & 28.57 & 24.50 \\ \cline{2-6}  & \(\pi^{\textsc{naive}}_{\text{R}}\) & 52.00 & 0.00 & 34.00 & 32.00 \\ \cline{2-6}  & \(\pi^{\textsc{DQN}}_{\text{R}}\) & 38.89 & 0.00 & 28.57 & 26.00 \\ \cline{2-6}  & \(\pi^{\textsc{baseline}}_{\text{P}}\) & 46.00 & 0.00 & 28.57 & 25.00 \\ \hline \end{tabular}
\end{table} 
Table 2: PFA (%) in the two-goal environment.