Technical Note–Dynamic Duopolistic Competition with Sticky Prices

Steven L. Heston () and Bo Hu ()
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Steven L. Heston: Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742
Bo Hu: Costello College of Business, George Mason University, Fairfax, Virginia 22030

Operations Research, 2025, vol. 73, issue 5, 2627-2635

Abstract: A paradoxical conclusion arises in a series of game-theoretic models: the limit equilibria retain frictional qualities even as frictions seemingly vanish. This originates in textbook models, such as the differential game by Fershtman and Kamien [Fershtman C, Kamien MI (1987) Dynamic duopolistic competition with sticky prices. Econometrica 55(5):1151–1164] on duopolistic competition with sticky prices. We show that this paradox is an artifact of the type of limit restricted by continuous-time modeling. Fershtman and Kamien find that the closed-loop equilibrium remains surprisingly distinct from the static Cournot equilibrium as price adjustment becomes infinitely fast. We formulate and solve a discrete-time analog that nests their continuous-time model. Contrary to their conclusion, we show that the frictionless closed-loop equilibrium converges to the static Cournot equilibrium. Price stickiness persists instantaneously in the continuous-time setting because this approach cannot control the extent of price adjustment per period. Because of this subtle limitation, limit results differ between continuous- and discrete-time formulations of the model.

Keywords: Decision; Analysis; differential games; discrete-time games; closed-loop equilibrium; frictionless limits (search for similar items in EconPapers)
Date: 2025
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