Multiplicity and Uniqueness of Equilibria in Continuous-Time Dynamic Discrete Choice Games

Jason R. Blevins and Youngjae Jeong.
The Ohio State University, Department of Economics
Working paper.

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Abstract. This paper studies the determinants of equilibrium multiplicity and uniqueness in continuous-time dynamic discrete choice games. We focus on a simple dynamic duopoly model of entry and exit where firms make decisions at stochastic sequential times governed by independent Poisson processes following Arcidiacono, Bayer, Blevins, and Ellickson (2016, Review of Economic Studies). We derive two sufficient conditions for uniqueness based on establishing contractivity of the equilibrium Bellman system. The first applies to the general model when the discount rate is sufficiently high. The second focuses on the case of symmetric switching costs and yields a sharper contraction condition. To evaluate the practical implications of these conditions and to explore the sources of multiplicity, we conduct a large-scale numerical search for equilibria across 10 million uniformly drawn parameter vectors. We find a unique equilibrium in over 90\% of configurations. Our results show empirically how multiplicity is related to strategic incentives in dynamic duopoly models such as patience, competition intensity, and switching costs. In particular, multiplicity arises when competition is intense enough that duopoly is not viable.

Keywords: Continuous-time games, dynamic discrete choice, entry and exit, equilibrium uniqueness, equilibrium multiplicity, Markov perfect equilibrium.

JEL Classification: C35, C57, C62, C73, L13.

BibTeX Record:

@TechReport{blevins-jeong-wp,
    author      = {Jason R. Blevins and Youngjae Jeong},
    title       = {Multiplicity and Uniqueness of Equilibria in
                   Continuous-Time Dynamic Discrete Choice Games},
    type        = {Working Paper},
    institution = {The Ohio State University},
    year        = 2026
}