DP13542 Optimal Selling Mechanisms with Endogenous Proposal Rights
We study a model of optimal pricing where the right to propose a mechanism is determined endogenously: a privately informed buyer covertly invests to increase the probability of offering a mechanism. We establish the existence of equilibrium and show that higher types get to propose a mechanism more often than lower types allowing the seller to learn from the trading process. In any equilibrium, the seller either offers the price he would have offered if he was always the one to make an offer or randomises over prices. Pure strategy equilibria may fail to exist, even when types are continuously distributed. A full characterization of equilibria is provided in the model with two types, where notably the seller's profit is shown to be non-monotonic in the share of high-value buyers.