The Empirical Relationship between Fluctuation and Equilibrium in Public Goods Game

This is the first study on the relationship between fluctuation and equilibrium in repeated game experiment. We define fluctuation as the strategy movements. In public goods game, for example, fluctuation of an individual is the abstract value of the difference of contribution between one period and its previous period. Similarly, fluctuation of a population is the summary of the fluctuation over the whole subject population of an experimental session, and fluctuation of a group is the summary over a group, and so on. Therefore, it is natural to suppose that there must be a certain relationship between magnitude of fluctuation and deviation from equilibrium, namely, the more deviation from equilibrium, the more fluctuation; and vice versa. Employing data from two previous studies (Nikiforakis and Normann [Exp Econ, 2008] and Chen and Tang [JPE, 1998]), we examine whether there exists such a relationship from several perspectives. Our results show that, (1) at the experimental level, the average magnitude of fluctuation per round is positively related to the deviation from equilibrium; (2) both at the group level and at the individual level, the average magnitude of fluctuation is weakly positively related to deviation from equilibrium; (3) the relationship still holds when Nash Equilibrium moves to the interior of the set of feasible contributions. Briefly, we have identifies certain positive relation between fluctuation and deviation from equilibrium. This relationship might turn out to be a useful tool for examining equilibrium conditions in experiments.