Oligopoly dynamic pricing: A repeated game with incomplete information

We consider an oligopoly dynamic pricing problem where the demand model is unknown and the sellers have different marginal costs. We formulate the problem as a repeated game with incomplete information. We develop a dynamic pricing strategy that leads to a Pareto-efficient and subgame-perfect equilibrium and offers a bounded regret over an infinite horizon, where regret is defined as the expected cumulative profit loss as compared to the ideal scenario with a known demand model. The resulting equilibrium also reveals a spontaneous collusion among a subset of sellers due to the difference in marginal costs among the sellers.