Dynamic Price Competition and Evolutionary Behavior with Search

Posted: 5 Nov 2023 Last revised: 19 Jan 2024


This paper studies a model of undirected consumer search with boundedly-rational agents. Consumers observe one price, can engage in costly search to learn the other prices, and then purchase from the firm with the lowest observed price. Each consumer searches only if the observed price exceeds their reservation price, which they dynamically update through one of two revision protocols: myopic best responses or imitation. Firms myopically optimize given the current distribution of consumer thresholds. The short run pricing is characterized by Edgeworth cycles. Each cycle ends when the firm with the larger installed base relents and monopolizes its residual demand. These price cycles persist in the long run except under restrictive conditions. Convergence to the Diamond paradox occurs only if consumers adapt to search sufficiently infrequently. The Bertrand paradox can emerge temporarily when the search cost becomes arbitrarily small, but cannot persist.

Keywords: Bertrand paradox, Bounded Rationality, Diamond paradox, Edgeworth cycles, undirected search

Suggested Citation

Allison, Blake and Sacks, Michael, Dynamic Price Competition and Evolutionary Behavior with Search. Available at SSRN: https://ssrn.com/abstract=4623774 or http://dx.doi.org/10.2139/ssrn.4623774

Blake Allison

Emory University ( email )

201 Dowman Drive
Atlanta, GA 30322
United States

Michael Sacks (Contact Author)

Clarkson University ( email )

Potsdam, NY 13699
United States

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