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Analysis of a Dynamic Voluntary Contribution Mechanism Public Good Game

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  • Dmytro Bogatov

Abstract

I present a dynamic, voluntary contribution mechanism, public good game and derive its potential outcomes. In each period, players endogenously determine contribution productivity by engaging in costly investment. The level of contribution productivity carries from period to period, creating a dynamic link between periods. The investment mimics investing in the stock of technology for producing public goods such as national defense or a clean environment. After investing, players decide how much of their remaining money to contribute to provision of the public good, as in traditional public good games. I analyze three kinds of outcomes of the game: the lowest payoff outcome, the Nash Equilibria, and socially optimal behavior. In the lowest payoff outcome, all players receive payoffs of zero. Nash Equilibrium occurs when players invest any amount and contribute all or nothing depending on the contribution productivity. Therefore, there are infinitely many Nash Equilibria strategies. Finally, the socially optimal result occurs when players invest everything in early periods, then at some point switch to contributing everything. My goal is to discover and explain this point. I use mathematical analysis and computer simulation to derive the results.

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  • Dmytro Bogatov, 2018. "Analysis of a Dynamic Voluntary Contribution Mechanism Public Good Game," Papers 1807.04621, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:1807.04621
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    1. Robert Gibbons, 1997. "An Introduction to Applicable Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 127-149, Winter.
    2. R. Mark Isaac & James M. Walker, 1988. "Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 179-199.
    3. Ananish Chaudhuri, 2011. "Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature," Experimental Economics, Springer;Economic Science Association, vol. 14(1), pages 47-83, March.
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