We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption characterize Markovian equilibria for ﬁnite and inﬁnite horizon versions of the model and show that the stationary inﬁnite horizon version of the model possesses an equilibrium where all the sellers receive an equilibrium payoﬀ equal to their marginal contribution to the social welfare.
Bergemann, Dirk and Välimäki, Juuso, "Dynamic Price Competition" (2003). Cowles Foundation Discussion Papers. 1681.