Same Game, Different Story: A Minimal Conservative Strategic Robustness Benchmark for Large Language Model Agents

Large language model agents are increasingly deployed in settings where the value of an action depends on what other agents do. This creates a strategic reliability problem: the same game may be described as a business negotiation, a friendly compromise, a diplomatic exchange, or an abstract payoff matrix, and the model may choose different actions even when the incentives are unchanged. This paper introduces Same Game, Different Story, a benchmark for strategic robustness: invariance of model-induced action distributions under payoff-preserving language changes. The empirical analysis uses a deliberately narrow, literature-calibrated comparison from Lor`e and Heydari's peer-reviewed study: business framing versus friend-sharing framing across GPT-3.5, GPT-4, and LLaMa-2 in four social-dilemma games, with 300 initializations per retained model-game-context cell. The retained design comprises 24 of the source study's 60 cells, representing 7,200 decisions. Because trial-level files were not available from the article, the analysis is presented as a secondary calibration based on reconstructed published rates, not as new model runs. As a conservative sensitivity analysis, effect magnitudes are attenuated by 30% toward the null: action shifts are multiplied by 0.70, and non-robustness, defined as one minus the robustness score, is multiplied by 0.70. Under this attenuation, pooled strategic robustness is 0.783 with a 95% bootstrap interval from 0.774 to 0.790, and friend-sharing framing raises cooperation by 0.307 with a 95% bootstrap interval from 0.297 to 0.316 relative to business framing. The analysis supports the narrower claim that social-relational framing can change strategic choices even when incentives are held fixed, without extending the analysis to a broader suite of contextual or cross-benchmark comparisons.