A Modeling Framework for Tipping in the Presence of a Social Norm

We introduce a game in which a firm offers service at a price to a set of potential customers, who choose whether or not to consume it, and if so, how much to tip the server after having received service. By tipping, customers wish to signal their appreciation for the server, but also wish to comply with the recommended tip. For a given recommended tip, we characterize the unique equilibrium tip distribution and the firm's optimal price. To study the evolution of the tipping norm over time, we consider a sequence of such games in which the average tip in each period determines the recommended tip for the next period. This dynamic process is shown to converge to an invariant tip distribution. When customers are highly sensitive to social pressure, this process results in an unnecessarily-aggressive tipping behavior -- a phenomenon we refer to as a ``tipping war''. Building on this dynamic framework we study a stylized model of a large industry of firms, each firm either legitimatizes or abolishes tipping, thereby collectively shaping customers' perception of the norm. Labor is mobile across firms, forcing the tip-abolishing firm to offer servers a wage competitive to that of a tipped firm. We show that in this industry, only two evolutionary-stable outcomes are possible: either all firms universally abolish or they all permit tipping. The stability of tipping is attributed to strong social pressure, but in some special cases also occurs when this pressure is weak and the customers are sufficiently snobbish