This paper introduces the Minimum Price Markov Game (MPMG), a dynamic variant of the Prisoner's Dilemma. The MPMG serves as a theoretical model and reasonable approximation of real-world first-price sealed-bid public auctions that follow the minimum price rule. The goal is to provide researchers and practitioners with a framework to study market fairness and regulation in both digitized and non-digitized public procurement processes, amidst growing concerns about algorithmic collusion in online markets. We demonstrate, using multi-agent reinforcement learning-driven artificial agents, that algorithmic tacit coordination is difficult to achieve in the MPMG when cooperation is not explicitly engineered. Paradoxically, our results highlight the robustness of the minimum price rule in an auction environment, but also show that it is not impervious to full-scale algorithmic collusion. These findings contribute to the ongoing debates about algorithmic pricing and its implications.

翻译：本文介绍了最低价格马尔可夫博弈（MPMG），它是囚徒困境的一种动态变体。MPMG作为一种理论模型，能够合理近似现实世界中遵循最低价规则的第一价格密封投标公开拍卖。其目标是为研究者和从业者提供一个框架，用以研究数字化与非数字化公共采购过程中的市场公平性与监管问题，尤其是在当前对在线市场中算法合谋日益担忧的背景下。我们通过采用多智能体强化学习驱动的人工智能体进行实验，证明在MPMG中，若未显式设计合作机制，算法间的默契协调难以实现。矛盾的是，我们的结果既凸显了最低价规则在拍卖环境中的鲁棒性，同时也表明该规则并非完全免疫于全面算法合谋。这些发现为当前关于算法定价及其影响的讨论提供了新的见解。