Complainer’s Dilemma

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In assessing complaint policy, it is important to understand the strategic environment facing complainers. Complaining is costly, and there is incentive to free-ride. I model complainer’s incentives as a generalization of the Volunteer’s Dilemma. Any who complain pay a cost c, if at least m complain, all receive benefit b. The equilibria of this game have interesting implications for complaint policy. Even without being able to observe the benefit of addressing particular problems, the administrator can prevent complaints that are not worth addressing by carefully setting the cost and required number of complaints. I present the properties of this family of policies, including novel results for large constituencies. Notably, policies which minimize the cost of complaining while requiring a suitably large number of complaints are most efficient. This result relies on a useful transcendental function known as Lambert-W, and, in proving the result, I generalize a Poisson tail inequality originally due to Teicher (1955). Because these two aspects of the proof may be of broader interest, I discuss the use of Lambert-W in economics and applications of this Poisson tail inequality in separate appendix sections. (JEL C72, C73, D82)

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