This paper introduces the Minimum Price Markov Game (MPMG), a theoretical model that reasonably approximates real-world first-price markets following the minimum price rule, such as public auctions. 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, amid growing concerns about algorithmic collusion in online markets. Using multi-agent reinforcement learning-driven artificial agents, we demonstrate that (i) the MPMG is a reliable model for first-price market dynamics, (ii) the minimum price rule is generally resilient to non-engineered tacit coordination among rational actors, and (iii) when tacit coordination occurs, it relies heavily on self-reinforcing trends. These findings contribute to the ongoing debate about algorithmic pricing and its implications.

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