Analysis of a Dynamic Voluntary Contribution Mechanism Public Good Game

TL;DR

This paper introduces a dynamic public good game where players invest in contribution productivity over time, analyzing equilibrium, worst-case, and optimal strategies through mathematical and simulation methods.

Contribution

It develops a novel dynamic model linking investment in contribution productivity with public good provision, providing insights into equilibrium and optimal strategies.

Findings

Multiple Nash equilibria exist with varied investment and contribution strategies.

The socially optimal strategy involves early investment followed by maximum contribution.

Mathematical analysis and simulations reveal the timing of optimal investment and contribution.

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.