Tipping as a strategic investment in service quality: An optimal-control analysis of repeated interactions in the service industry

We present an optimal-control model where tipping behavior creates reputation that affects future service. Tipping and reputation can evolve in four path prototypes: converging to an interior equilibrium; converging to minimum tips and reputation; and two prototypes that start differently but end with tips and reputation increasing indefinitely. Analyzing the interior equilibrium suggests that when reputation erodes more quickly (capturing lower patronage frequency), equilibrium reputation is lower. Interestingly, however, tips may be higher. Increasing the minimal tip raises tips by the same increase, and does not change reputation. A more patient customer leaves higher tips and reaches a higher reputation.