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Equilibrium Play and Learning in a Stochastic Public Goods Experiment

The public goods problem or the “tragedy of the commons,” (Hardin, 1968) either viewed as a problem of extraction or that of contribution has had a rich history in Economics and indeed in other social sciences like Anthropology, Sociology and Political Science. Our research examines free riding in an environment slightly different from that used in experimental studies thus far. In the game we use, the benefit received from the public good is not linear in effort or contribution as in most Voluntary Contribution Mechanism (VCM) or Common Property Resource (CPR) games but varies stochastically with effort (Banerjee, 2007). We specifically examine the effect of a quality bound (for the public good provided) below which very negligible benefits are received by community members. Our theory predicts that the presence of such a “pass mark” on quality of the good ultimately provided may under certain conditions reduce the incidence of free-riding in these games. This result has very significant implications for the design of mechanisms and institutions that provide public goods and services. We obtain very mixed support for the hypothesis that the presence of a pass mark on quality significantly lowers the incidence of free riding in the laboratory. In most sessions, the presence of this pass mark may actually significantly increase the incidence of free-riding, even when the theory predicts the opposite. In general, the mixed strategy Nash equilibrium (MSNE) prediction performs very poorly in the laboratory. A noisy theoretical model, the Quantal Response Equilibrium (QRE) is then used and is a better predictor of laboratory play than the MSNE. We then use the Roth-Erev (RE, Erev and Roth, 1995) reinforcement learning model in both its one-parameter as well as three-parameter forms which generate predictions that fit observed play in the laboratory much better than the earlier “steady state” theory predictions.