Naor's (1969) celebrated paper studies customer decisions in an observable M/M/1 queue where joining-customers utility is linearly decreasing with the joining position. Naor derives the optimal threshold strategies for the individuals, social planner and monopolist, and proves the monopoly...

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...