Question

A traveler dines at a restaurant along an interstate highway. Both he and the waiter who serves him are rational and self-interested in the narrow sense. The waiter must first choose between providing good service or bad service, whereupon the diner must choose between leaving the customary tip or leaving no tip at all. The payoffs for their interaction are as summarized on the accompanying game tree. What is the most the diner would be willing to pay for the right to make a binding commitment (visible to the waiter) to leave the customary tip at the end of the meal in the event of having received good service? Waiter Give bad Give good service service Diner 80 for waiter 30 for diner Don't Tip tip 20 for waiter 200 for diner 100 for waiter 100 for diner

Answer 1

Without any commitment, the SPNE of the sequential game is found by backward induction

SPNE: ( bad service, don't tip)

So diner gets 30, now if he makes the commitment of paying tip, in event of good service, then diner gets 100

thus the maximum he is willing to pay is (100-30) = 70