Working and Shirking: Equilibrium in Public Goods Games with Overlapping Generations of Players

Abstract

In overlapping-generations models of public gods provision, in which the contribution decision is binary and lifetimes are finite, the set of symmetric subgame-perfect equilibria can be categorized into three types: seniority equilibria in which players contribute (effort) until a predetermined age and then shirk thereafter; dependency equilibria in which players initially shirk, then contribute for a set number of periods, then shirk for the remainder of their lives; and sabbatical equilibria in which players alternately contribute and shirk for periods of varying length before entering a final stage of shirking. In a world without discounting we establish conditions for equilibrium and demonstrate that for any dependency equilibrium there is a seniority equilibrium that Pareto-dominates it ex ante. We proceed to characterize generational preferences over alternative seniority equilibria. We explore the aggregation of these preferences by embedding the public goods provision game in a voting framework and solving for the majority-rule equilibria. In this way we can think of political processes as providing one natural framework for equilibrium selection in the original public-goods provision game.