Collusion and Coercion with Naive Rivals

30 Pages Posted: 10 Mar 2023

See all articles by Zach Brown

Zach Brown

University of Michigan

Alexander MacKay

Harvard University - Business School (HBS)

Date Written: March 6, 2023


Standard models of collusion require that all firms are forward-looking and strategic. When one firm displays naive behavior—i.e., when it is myopic, memoryless, or non-strategic—typical collusive strategies cannot be supported in equilibrium. Motivated by the increasing adoption of high-speed pricing algorithms that monitor rivals' prices, we consider instead a model in which a single firm can update prices faster than its rivals. We show that this expands the set of strategies that yield prices above the competitive equilibrium. With sufficiently fast pricing, a firm can unilaterally sustain price levels that maximize joint profits even when all of its rivals are naive. We also characterize a coercive equilibrium that maximizes the profits of the faster firm. Overall, faster pricing provides a single firm with the ability to induce market outcomes that yield higher profits and lower consumer surplus.

Keywords: Pricing Frequency, Pricing Algorithms, Online Competition, Collusion

JEL Classification: L40, D43, L81, L13, L86

Suggested Citation

Brown, Zach and MacKay, Alexander, Collusion and Coercion with Naive Rivals (March 6, 2023). Available at SSRN: or

Zach Brown

University of Michigan ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States

Alexander MacKay (Contact Author)

Harvard University - Business School (HBS) ( email )

Soldiers Field Road
Boston, MA 02163
United States


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