MEAN FIELD APPROXIMATION FOR A STOCHASTIC PUBLIC GOODS GAME

We consider a cellular automaton in the context of mean field approximation to model an interacting public goods game. In this game, players are offered to invest their money in a common pool and the profits are equally distributed among all participants irrespective of their contribution. In our version, players have a motivational level that controls the investment which is updated according to the profit obtained by each player due to two sources: a deterministic (risk free parameter) and a stochastic one (external noise). Analytical results are obtained to describe the stationary state of the average motivation level of the population for different initial conditions and Monte Carlo simulations are used to corroborate the theoretical results.