Product Recommendation and Self-Preferencing

We consider a monopolistic platform's product recommendation as a nonbinding communication message when there is platform encroachment. We show that a partially truth-revealing equilibrium in which the platform sometimes cheats and the consumer sometimes exits from the platform exists even in a stage game, albeit no fully communicative one. We also characterize a partially revealing equilibrium in infinitely repeated games both in cases that the platform's cheating is perfectly monitored and imperfectly monitored. In the case of imperfect monitoring, a consumer's cheap talk can help improve efficiency by conveying some information about her observation to the platform.