Dynamic Monopoly Pricing With Multiple Varieties: Trading Up

📅 2021-08-16
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This paper investigates dynamic pricing mechanisms for a monopolist offering durable goods, rental services, or hybrid products across multiple categories. The central problem addresses the drivers and convergence conditions of dynamic pricing. Methodologically, the study integrates game theory and mechanism design, introducing the first systematic distinction between Coasian and non-Coasian environments. It demonstrates that dynamic pricing arises if and only if the static optimal solution admits exploitable “trade-up” opportunities—i.e., incentives for consumers to upgrade from lower- to higher-valued options. Based on this insight, the paper establishes an existence theorem for dynamic pricing, using trade-up possibility as the decisive criterion: in Coasian settings, it derives an explicit price evolution path; in non-Coasian settings, it proves the absence of incentive to dynamically adjust prices. The results unify theoretical tractability, empirical testability, and economic intuition.
📝 Abstract
This paper studies dynamic monopoly pricing for a broad class of Coasian and Non-Coasian settings. We show that the driving force behind pricing dynamics is the seller’s incentive to trade up consumers to higher-valued consumption options. In Coasian settings, consumers can be traded up from the static optimum, and pricing dynamics arise until all trading-up opportunities are exhausted. In Non-Coasian settings, consumers cannot be traded up from the static optimum, and no pricing dynamics arise. Hence, dynamic monopoly pricing can be characterized by checking for trading-up opportunities in the static optimum. We are grateful to Alia Gizatulina, Paul Heidhues, Igor Letina, Marc Moeller, Georg Noeldeke, Armin Schmutzler, Philipp Zahn, and seminar audiences at DICE, the University of Southampton, the University of St. Gallen, and several conferences, for helpful discussions and comments. We gratefully acknowledge financial support from the Swiss National Science Foundation through grant No. 100018-178836. Stefan Buehler: University of St.Gallen, Institute of Economics, Varnbüelstrasse 19, 9000 St.Gallen, Switzerland (stefan.buehler@unisg.ch); Nicolas Eschenbaum: University of St.Gallen, Institute of Economics, Varnbüelstrasse 19, 9000 St.Gallen, Switzerland (nicolas.eschenbaum@unisg.ch)
Problem

Research questions and friction points this paper is trying to address.

Dynamic pricing for multiple durable or rental varieties
Impact of trading-up opportunities on pricing dynamics
Conditions for pricing dynamics to end in finite time
Innovation

Methods, ideas, or system contributions that make the work stand out.

Dynamic pricing with multiple product varieties
Trading-up opportunities drive pricing dynamics
Lower bounds for prices and profits characterized
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Stefan Buehler
University of St. Gallen, Department of Economics, Rosenbergstr. 22, 9000 St. Gallen, Switzerland
Nicolas Eschenbaum
Nicolas Eschenbaum
University of St Gallen, Swiss Economics
algorithmic pricinggame theorycomputational economicsweb3ai