An analysis of tipping

From a waiter's perspective, there are two types of customers.

a) Customers who always tip the same percentage. It could be the standard 15%, or it could be less from the bad tippers. They are indifferent to the quality of service and there's nothing a waiter can do to change the tip amount.

b) Customers who tip an amount correlated positively with the quality of service. Better service means more satisfied customers, which brings in a bigger tip. The correlation function might not be linear at all, and it probably has lower and upper limits.

Note that there are no bizzaro customers who tip more for worse service. Assuming the percent of B type customers is non-zero, waiters will always have an economic incentive to provide better service.

However, if the service-tip correlation function resembles a logistic curve, then the waiter would have to commit significant effort before any noticeable increase in the amount of tip received. This model might discourage many waiters from investing into the relationship.

Even worse, if the service-tip correlation is a step function, then the waiters would see no benefits at all until they overcome a threshold of service quality. The result of this model will be a segmentation of waiter behavior:

a) Some waiters will decide not to invest any additional effort into their service quality, because they don't expect any returns. They treat all customers as type A.

b) Other waiters will do their very best to satisfy their customers, because they believe that reward will follow quality. 

On the other side of the table, the customer's perspective is quite different. There is no economic benefit at all for tipping a greater amount. Disregarding any social, moral, or karmic influences, the customer has no incentive to tip. Since the service has already been provided, the customer can not affect the quality of service by varying the amount of the tip, not in the way that a waiter can affect the reciprocal relationship.

However, from a macroscopic point of view, there is benefit to tipping more for better service. Each type B customer helps to reinforce the proactive mentality of the waiters who work harder. In this way, the customers are all contributing to the system of rewards that encourages better service. Though the customer may not be able to retroactively improve his experience, but he may find consolation in the thought that he may convert a type A waiter to a type B waiter.

Of course, if the customer plans to return to that particular establishment, he would benefit from building up a good reputation there by tipping more. On the other hand, the customer is more likely to return if the service was excellent. Successful business relationships take advantage of this positive feedback between the type B groups for mutual benefit. Better service leads to more tips, which leads better service. The flip side of this is increasing apathy among waiters and decline of repeat business.

Though the restaurant can not control the type of customers coming in, it can control what type of waiters to hire. The only way to build up positive customer relationships is to staff only waiters who are reward-minded and willing to put effort into their service.

For the customers, indifference in tipping can never help increase the quality of service they receive, no matter if they always tip 20% or 0%. If they reward good service and punish bad service, they may be able to reduce apathy from the waiters and ensure better experience in the future.