Abstract

Autonomous agents are the new inhabitants of the digital marketplace, yet the nature of their “rationality” remains elusive. While research has focused on how Large Language Models (LLMs) might mutually conspire to inflate prices, we uncover a more insidious phenomenon: unilateral cooperation driven by extortion. This paper investigates the interaction between an LLM-based pricing agent and an opponent employing a Zero-Determinant (ZD) extortionate strategy. By mapping a multinomial logit demand model onto a Prisoner’s Dilemma framework, we represent the strategic choice between a low-price Nash Equilibrium and high-price collusion. Our experimental results reveal a significant strategic vulnerability, as the LLM agent consistently chooses high prices to maximize its own expected utility, thereby falling under the linear payoff control of the extortioner. We demonstrate that as the extortion factor χ increases, the ratio of the players’ surplus payoffs, measured as the gain above the low-price baseline, converges toward the theoretical value of 1/χ. This suggests that the LLM’s rational pursuit of payoff maximization enables an extortionate opponent to unilaterally fix the market into a state of high-price exploitation. These findings highlight the susceptibility of autonomous pricing agents to algorithmic control, where a rational pursuit of profit leads to a state of unilateral cooperation, a subjugation of the market by a hegemonic competitor.

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