A Theoretical Analysis of Cooperation Incentives for Non-Mutually Dependent Sellers

Lorenzo Ferrari, Werner Güth, Vittorio Larocca and Luca Panaccione ()
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Lorenzo Ferrari: Italian Competition Authority, 00198 Rome, Italy
Werner Güth: Max Planck Institute for Research on Collective Goods, 53113 Bonn, Germany
Vittorio Larocca: Department of Economics and Business, University of Sassari, 07100 Sassari, Italy
Luca Panaccione: Department of Economics and Law, Sapienza University of Rome, 00161 Rome, Italy

Games, 2025, vol. 16, issue 5, 1-21

Abstract: This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. In each game of this class, both sellers simultaneously choose prices that determine their endogenous threats, i.e., conflict profits. The sellers are aware of the cooperation probability but cannot condition prices on whether or not there is cooperation. We characterize the equilibrium prices and the sellers’ expected profits. Our main result shows that the independent seller earns higher expected profits when cooperation is more likely. In contrast, the dependent seller earns lower expected profits when the likelihood of cooperation is below a threshold that we characterize explicitly, and higher profits are earned thereafter. These findings suggest that, within our framework, antitrust concerns may be mitigated. Since dependent sellers can incur losses from cooperation, collusion attempts become less viable in markets with one-sided dependency.

Keywords: one-sided dependency; stochastic bargaining; incentives to cooperate (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
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