Keep ’Em Coming: Detecting and Nurturing Loyalty
AbstractWe consider a continuous-time game between a buyer and a seller.
The buyer privately knows how often he needs to trade. When he does,
he can choose to either engage with the seller, who chooses what utility
to supply, or search for an alternative. Because time is informative, the
seller learns and adjusts her behavior over time. Without commitment,
in the Markov perfect equilibrium, the seller starts with a pooling offer,
before experimenting with occasional separating offers. Her payoff is
non-monotone –in fact, quasi-convex– in her belief about the buyer’s
type. With commitment, the seller can take advantage of limited-time
offers to extract all the buyer’s surplus.