Dynamic Volunteer's Dilemma With Procrastinators

Abstract

Only one trip planner is needed for a group of friends to enjoy a pleasant trip and only one country is needed to coordinate on international talks that can be beneficial for all participating countries. We study a dynamic volunteering dilemma game in which two players choose to volunteer or wait given there have not been any volunteering actions in the past. The players can be procrastinators and the benefits of volunteering arrive later than the costs. We fully characterize the stationary Markov Strotz-Pollak equilibria. When the cost of volunteering is sufficiently small or agents' present-bias parameters are sufficiently close, there always exists an equilibrium in which both players randomize. This equilibrium features stochastic delay, and the delay is exacerbated if one or both agents become more present-biased. However, if the agents differ significantly in their present-bias parameters, this difference may act as a 'natural coordination device' and the unique stationary equilibrium predicts that only the less severe procrastinator volunteers, and this may result in an even quicker provision compared with the case of two exponential discounters.