Tipping in Service Systems: The Role of a Social Norm

Abstract

We study the impact of tipping in a service facility on the server's tipping wage, in the presence of an endogenously formed social norm. The problem is modeled as a two-stage tipping game: In the first stage, delay-sensitive customers arrive at an M/M/1 facility and decide whether to join or not, and if so, how much to tip. In the second stage customers who joined meet in a social market, compare their tip amounts, and are penalized on tipping differently from one another. All customers are homogeneous in terms of their valuation of the service and waiting cost rate. Yet, some customers visit the facility repeatedly and can therefore obtain a shorter waiting time by tipping more. Other customers visit only once and hence, cannot influence their waiting time via their tip. We find that in the presence of a social norm, the server cannot extract the optimal social welfare through tipping, because of (i) rents that the repeat customers can accrue and (ii) the variability in tips, introduced by repeat customers, which causes the social costs to be strictly positive. Nevertheless, in some limiting cases, the tipping wage approaches the optimal welfare when (i) the social norm is weak and there are many repeat customers such that no one-time customers join; or when (ii) the social norm is strong and there are few repeat customers who join.