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.
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