Monopolists with a Constant Flow of Buyers over Infinite Periods: Subgame Perfect Nash Equilibrium

Abstract

We analyze a dynamic game between consumers and the sole Seller of a durable good. Unlike previous literature, this paper assumes that there are infinitely many buyers in the market, the number of buyers is dynamic, and the buyer types are defined with respect to budget rather than valuation.The paper first de fines a game with one Monopolist Seller where one buyer of one of two types enters the market at each period. The buyers demands a price, and the Seller sequentially decides to reject or accept all of the demands. If accepted the market clears, and otherwise the buyers remain in the market. This game is repeated over infinite horizons. The paper searches for a subgame perfect Nash equilibrium such that the Seller does strictly better than always conceding to the Lowest price to all buyers. The paper finds that under specified parameter restrictions with respect to High and Low budgets, such an equilibrium not only always exists but also that the number of visited states is fi nite. The paper further visualizes its results under different parameters using backwards induction approximations.