Abstract
The paper considers tacit collusion in markets that are not fully transparent on both sides. Consumers only detect prices with some probability before deciding which firm to purchase from, and each firm only detects the other firm’s price with some probability. Increasing transparency on the producer side facilitates collusion, while increasing transparency on the consumer side makes collusion more difficult. Conditions are given under which increases in a common factor that affects transparency positively on both sides are pro-competitive. With two standard information technologies, this holds when firms are easier to inform than are consumers.
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Notes
It is straightforward to check that the second-order condition for a maximum is fulfilled. In deriving the equilibrium, we assumed that the market is covered and the second line of (3) is relevant; hence it should not be advantageous to undercut the other firm by t and gain the whole informed market. This requires that \(\left( \frac{t}{\phi }-t\right) \left( \phi +\frac{1-\phi }{2}\right) <\frac{t}{2\phi }\), which is fulfilled for all positive \(\phi\) and t. Under assumption (2) the market is covered in the Nash equilibrium.
We abuse notation slightly by designating the expected profit \(\pi ^{N}\) in the pure as well as in the mixed-strategy equilibrium.
\(\gamma \le 2\phi\) for all \(\phi\) if \(u/t{<}5/2\) and otherwise for \(\phi \le 1/(u/t-5/2)\).
For the case of a uniform distribution of demand, one can show that the optimal deviation is the solution to a third-degree polynomial.
Coate (2004) uses this function.
In fact, colluding firms in the vitamins industry used magazines to announce price changes to the public/competitors (Marshall, Marx, and Raif, 2008). I am grateful to a referee for pointing to this example.
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I have benefitted from discussions with Joe Harrington, Morten Hviid, Kai-Uwe Kühn, and Thomas Rønde and with seminar audiences in Aarhus, Copenhagen, Boston, Norwich, and Reykjavik. I am grateful to comments and suggestions of two referees and the editor.
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Schultz, C. Collusion in Markets with Imperfect Price Information on Both Sides. Rev Ind Organ 50, 287–301 (2017). https://doi.org/10.1007/s11151-016-9539-7
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DOI: https://doi.org/10.1007/s11151-016-9539-7