The Nature of Equilibria Under Noncollusive Product Design and Collusive Pricing

Kali P. Rath and Gongyun Zhao ()
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Kali P. Rath: Department of Economics, University of Notre Dame, Notre Dame, IN 46556, USA
Gongyun Zhao: Department of Mathematics, National University of Singapore, 117543, Singapore

International Game Theory Review (IGTR), 2022, vol. 24, issue 02, 1-28

Abstract: The basic framework is Hotelling’s model of product choice with quadratic transportation cost. Duopolists choose locations in the initial period and compete in prices in subsequent infinite periods. The firms share profits on the profit possibility frontier. It is shown that under very general conditions, both the firms locating at the center is an equilibrium. It is not necessarily unique and multiple symmetric equilibria can exist. Thus, the products are not necessarily minimally differentiated. How the profits are shared when the firms are located together off the center has a critical bearing on the nature of equilibria. If the firms share profits equally at those locations, then all the equilibria are symmetric. Otherwise, asymmetric equilibria can appear. The equilibria can be classified into three types: a unique equilibrium at the center of the market, multiple symmetric equilibria and multiple asymmetric agglomerated equilibria. The second case entails nonminimal product differentiation. Sufficient conditions for each of these equilibria are given. Necessary conditions for multiple symmetric equilibria off the center are also obtained.

Keywords: Minimal product differentiation; profit possibility frontier; subgame perfect Nash equilibrium; transportation cost; unique equilibrium (search for similar items in EconPapers)
JEL-codes: C72 C73 L10 L13 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0219198921500134

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