How Learning Selects Equilibria and When It Leads to Collusion
Hanzhang Wang, Manxi Wu
We study how learning algorithm design shapes equilibrium selection in infinite-horizon discounted Markov games with finite states and actions. Each episode, players choose smooth best responses to beliefs about opponents' policies, test them using noisy observations, and resample rejected beliefs or explore at rates determined by increasing transformations of their discounted values. We show that stochastically stable states induce approximate stationary Nash equilibria maximizing the minimum transformed discounted value across players, with transformations governing which players selection favors. In repeated games with bounded recall of noisy public signals, longer recall weakly increases the selected minimum transformed value. In repeated Cournot games, every stochastically stable state induces an approximate public perfect equilibrium whose minimum discounted profit across firms exceeds the Cournot-Nash benchmark. Collusion is therefore inevitable under these conditions and learning dynamics. For symmetric firms, selected profits can approach the monopoly benchmark arbitrarily closely. These results offer a novel equilibrium-selection perspective on algorithmic collusion.
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