Interior collective optimum in a voluntary contribution to a public-goods game

Abstract

This study shows a public good experiment with four different treatments. The payoff function is chosen so that the Nash equilibrium (NE) and the collective optimum (CO) are both in the interior of the strategy space. This study tries to test the effect of varying the level of the collective optimum, which changes the ‘social dilemma’, involved in the decision as to how much to contribute to the public good. The results show that contributions increase with the level of the interior CO. There is overcontribution in comparison to the NE and undercontribution in comparison to the CO. But contributions are as far from the CO as the level of the former increases. An overcontribution index that takes into account the effective contribution relative to both the NE and the CO, shows that subjects adopt a constant behaviour while passing from one treatment to another: they contribute a constant share of the CO.

AcknowledgEments

I am indebted to Alan Kirman for the supervision of this work. I’m grateful to Sylvie Thoron, Marc Willinger and Jordi Brandts for their very helpful comments. I also thank Antoni Bosh for making the LeeX available for me and the participants to the Workshop on Economics and Heterogeneous Interacting Agents (WEHIA, Italy), the European Science Association (ESA, Strasbourg) and the “6èmes Journées d’Economie Expérimentale” (JEE, Paris).

Notes

¹ In Willinger and Ziegelmeyer (2001), the ‘social dilemma’ refers to the difference between the equilibrium contribution level and the social optimum.

² Sec Isaac et al. (1984).

³ These are approximate values. The exact values are respectively: 4, 5.6568542, 6.9282032 and 8.9442719. These values are chosen such that the CO corresponds respectively to 64, 128, 192 and 280.

⁴ Experimental Currency Unit.