Complainer's Dilemma

Technological innovations have made complaining easier. Often, when it is easy to complain, only problems that meet a high threshold of complaints are addressed. We present a novel model of the strategic environment facing complainers and demonstrate that the properties of the resulting games' equilibria justify the existence of high complaint thresholds. By setting the thresholds appropriately, an administrator can prevent complaints that are not worth addressing. Policies that minimize the cost of complaining while requiring a large threshold are universally more efficient for large constituencies. Our results regarding the equilibrium for large constituencies are facilitated by the application of the Lambert-W function, demonstrating how this tool can be employed to analyze games with a large number of players. We motivate the model using a rich data set of complaints from New York City.