Dynamical properties of entry games with firms adopting different adjustment mechanisms

Li, Xiaoliang and Zhang, Ally Quan (2026) Dynamical properties of entry games with firms adopting different adjustment mechanisms. Physica A: Statistical Mechanics and its Applications, 690: 131440. ISSN 0378-4371

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Abstract

This paper investigates the dynamical properties of three entry games in a market initially composed of N gradient-adjusting firms. The entrant may adopt one of three output adjustment mechanisms: gradient adjustment, best response, or local monopolistic approximation (LMA). Under the assumptions that the entrant’s marginal cost does not differ significantly from the average marginal cost of the incumbents and that the number of incumbent firms is no less than four, we establish an ordering of the stability regions, indicating that less information in the adjustment mechanism may lead to stronger market stability. With respect to dynamics, we find that the entry model of a best response firm differs qualitatively from the other two. Furthermore, numerical simulations reveal that this model may exhibit 1:3, 1:4, and 1:5 resonance bifurcations, and may also display the coexistence of multiple attractors.