We evaluate whether LLMs adapt their strategic behavior when familiar games are counterfactually modified. We introduce a repeated-game evaluation framework covering Prisoner’s Dilemma and Rock–Paper–Scissors under default, label-perturbed, payoff-perturbed, and joint counterfactual variants. This design separates surface robustness to renamed actions from deeper sensitivity to changed incentives. Across multiple frontier LLMs, we find that label perturbations usually cause moderate degradation, whereas payoff perturbations expose stronger failures: LLMs often preserve canonical strategies even when the equilibrium structure changes. In RPS, several LLMs remain close to uniform play despite a payoff-counterfactual equilibrium requiring a biased mixed strategy. Behavioral and efficiency metrics further show that stronger or reasoning-enabled LLMs are not uniformly more strategic: some deliberate more without adapting faster. Overall, counterfactual repeated games provide a compact diagnostic for distinguishing robust incentive-sensitive behavior from brittle template-based strategic execution.

The advent of Large Language Models (LLMs) has revolutionized product recommenders, yet their susceptibility to adversarial manipulation poses critical challenges, particularly in real-world commercial applications. Our approach is the first one to tap into human psychological principles, seamlessly modifying product descriptions, making such manipulations hard to detect. In this work, we investigate cognitive biases as black-box adversarial strategies, drawing parallels between their effects on LLMs and human purchasing behavior. Through extensive evaluation across models of varying scale, we find that certain biases, such as social proof, consistently boost product recommendation rate and ranking, while others, like scarcity and exclusivity, surprisingly reduce visibility. Our results demonstrate that cognitive biases are deeply embedded in state-of-the-art LLMs, leading to highly unpredictable behavior in product recommendations and posing significant challenges for effective mitigation.