The Volunteer’s Dilemma with Cost Synergies

Abstract

This paper revisits the well-known volunteer’s dilemma on the production of a public good when a single participant is sufficient for the task. We propose a cost-sharing model with a volunteering cost that decreases exponentially in the number of volunteers. We show that, at the unique mixed-strategy equilibrium, the probability of production may increase in the number of players for sufficiently low volunteering costs. This provides an alternative account of the fit of the model with some political-military conflict situations: A larger group does erode the individual incentive to volunteer but in an offsetting way that favors the production of the public good. A second result is that the mixed-strategy Nash equilibrium may be more socially efficient than the pure-strategy Nash equilibrium for some parameter values, which is a major reversal with respect to the standard dilemma and many other coordination games.