Asymmetry and Timing in the Volunteer's Dilemma

Abstract

The production of a binary collective good by the contribution of a single volunteer was modeled by Diekmann in 1985. Without a mechanism for selecting a volunteer, the case with homogeneous players has a Pareto inefficient solution. I discuss a variant with asymmetric costs and benefits. Game-theoretic arguments are developed for selecting the equilibrium in which the player with the most favorable costs/benefits volunteers. As a scenario, the volunteer's timing dilemma (VTD) is presented. In a VTD, a player volunteers after some waiting time, given that the other players have not volunteered earlier, or he surely abstains from volunteering. The benefits associated with the delayed production of the collective good decrease with the length of the delay. In the symmetric VTD, players randomize the time at which to volunteer. Here, Pareto inefficiency is due both to a delay in production of the collective good and to the possibility that it is not produced at all. In the asymmetric VTD, there is a unique equilibrium that indeed generates the Pareto efficient focal equilibrium. In an elegant article, Diekmann (1985) provides an insightful analysis of the famous case of Kitty Genovese, a young woman brutally attacked and stabbed to death in New York. The attack happened in front of a building block. At least 38 people witnessed the crime, but nobody came to help her or phoned the police to report the incident. Given a helper's risk of being hurt oneself, it is not surprising that people were reluctant to step in. The fact that people seemed unwilling to apply the minimal resources to phone the police triggered a public response that condemned the indifference of people in our modern anonymous society with respect to the affairs of their fellow citizens.