Instability in the Voluntary Contribution Mechanism with a Quasi-linear Payoff Function: An Experimental Analysis

We conduct experiments to investigate the convergence of contributions in the voluntary contribution mechanism (VCM) with two quasi-linear payoff functions. One is linear with respect to private goods and nonlinear with respect to public goods; we call it "QL1." The other is linear with respect to public goods and nonlinear with respect to private goods; we call it "QL2." The system with QL1, built on the assumption of self-interested players and myopic Cournot best response dynamics, is not stable, but the system with QL2 has a dominant Nash equilibrium. This theoretical result predicts a "pulsing" of contributions in the VCM with QL1. Our experimental observations demonstrate that individual contributions are certainly converging to the dominant Nash equilibrium in the experiment with QL2. In the experiments with QL1, however, the dispersion of individual contributions increases progressively with repeated trials, and the contributions are still volatile in the experiments’ last periods, although we do not find a clearly unstable pulsing in the group's total contribution.