Mixed Strategy Equilibria in the Threshold Public Goods Game
Threshold contribution games are common when modeling private contributions to publicly beneficial projects such as the construction of a new library, or charity initiatives. However, when analyzing data from past experimental studies on these games, it becomes clear that there is a tendency for contribution amounts to exhibit a significant amount of small but persistent variation from trial to trial. My research focused on providing a mathematical and strategical justification for this behavior, drawing on the intuition of the Free Rider Problem. I considered the effects of various different modifications to the game such as the presence of a “money back guarantee” should the project fall through, and the ability to make more than one contribution after observing the other player’s actions. Special attention was given to determining the uniqueness and stability of the resulting equilibria. My main result was to confirm the existence of a family of mixed trembling hand perfect equilibria in the two person threshold public goods game in which players make use of strategic randomness when determining their contributions. This randomness could provide a potential explanation for the persistent variation we see in the experimental data.