  We study a repeated game between a supplier and a retailer who want to
maximize their respective profits without full knowledge of the problem
parameters. After characterizing the uniqueness of the Stackelberg equilibrium
of the stage game with complete information, we show that even with partial
knowledge of the joint distribution of demand and production costs, natural
learning dynamics guarantee convergence of the joint strategy profile of
supplier and retailer to the Stackelberg equilibrium of the stage game. We also
prove finite-time bounds on the supplier's regret and asymptotic bounds on the
retailer's regret, where the specific rates depend on the type of knowledge
preliminarily available to the players. In the special case when the supplier
is not strategic (vertical integration), we prove optimal finite-time regret
bounds on the retailer's regret (or, equivalently, the social welfare) when
costs and demand are adversarially generated and the demand is censored.
