The Volunteer's Dilemma
Three people witness a problem. Each simultaneously decides whether to volunteer to fix it. If at least one person volunteers, everyone receives a benefit of 1. A volunteer additionally pays a private cost of 1/9. If nobody volunteers, everyone receives 0. In the symmetric Nash equilibrium in which each person volunteers independently with the same probability p strictly between 0 and 1, what is the probability that exactly one person volunteers? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Hawk-Dove 6.0/10
- Making the Other Side Indifferent 6.0/10
- A Three-by-Three Value 6.0/10
Source: Volunteer's dilemma, introduced by Diekmann (1985). Numbers written for AxiomIQ.