THE OPTIMAL OFFER DEADLINE WHEN FACING A BAYESIAN-LEARNING SEARCHER

Abstract

This thesis studies the optimal offer deadline for a responder with learning behavior in a Stackelberg game involving a proposer who makes offers and a responder who decides which offer to accept. The responder follows a discrete-time finite-horizon search process with zero search cost for alternative offers (zero deadline) whose size is a random variable drawn from an identical but unknown probability distribution. Such unknown underlying distribution is assumed to be a n-point discrete distribution, and it is learnt in the Bayesian fashion. The case when the underlying unknown distribution is a two-point distribution is analyzed first. It can be shown that the shortest acceptable deadline (SAD), the shortest deadline that is acceptable to the responder, is the optimal offer deadline for this case, and we also show that it is no longer than the optimal deadline in the perfect information environment (the size distribution is perfectly known). For the case when n is at least three is discussed as well, and it can be proved that it is never optimal to set a deadline strictly shorter than the SAD. Finally, the numerical results for the multi-point case are discussed at the end.