Efficiency in a forced contribution threshold public good game

What is it about?

A threshold public good is provided if and only if sufficiently many people contribute towards its production. In this paper we study a particular type of threshold public good game called a forced contribution game. The key thing about this game is that if sufficiently many people ‘voluntarily’ contribute towards the public good then everyone else is ‘forced’ to contribute. This removes any incentive to try and free-ride on the contributions of others. Note, however, that if the public good is not provided then those that voluntarily contributed do not receive a refund. Hence, people may choose not to contribute in the fear that others will not contribute. This could result in the public good not being provided. In the paper we contrast the predictions of three theoretical models. A model based on ordinal potential gives the very optimistic prediction that the public good will always be provided. A model based on quantal response gives a far more pessimistic prediction that the public good will only be provided if the returns on the public good are high. Finally, a model based on impulse balance theory gives a middle ground prediction that the public good will be provided unless the returns on the public good are relatively low. In the paper we also report the results of an experiment designed to test the predictions of the respective models. We find that impulse balance best fits our experimental results. For instance, in a ‘many-small’ treatment, with many players and small returns to the public good, we observed very low success in providing the public good. This is inconsistent with the predictions based on ordinal potential. In the remaining treatments, however, we observed high efficiency. This is hard to reconcile with the predictions based on quantal response. Our results allow us to derive a simple expression detailing when success at providing the public good is likely to be high. Essentially, success will be high unless the returns to the public good are low or the threshold is high. This corroborates a claim in the existing literature that greed rather than fear drives inefficiency in the production of threshold public goods. Our results also provide further evidence that impulse balance theory is a good predictor of behaviour in games.

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Why is it important?

Accepted wisdom seemed to be that a money back guarantee is a good way (and maybe the best way) to enhance efficiency in the provision of threshold public goods. Our work is challenging that idea. There is no doubt that a money back guarantee works sometimes. But we are seeing that in many situations something else is needed. And in this paper we show that enforcing contributions can work.