We study participation games with negative feedback, i.e. games where players choose either to participate in a certain project or not and where the payoff for participating decreases in the number of participating players. We use the replicator dynamics to model the competition between different behavioral rules that specify how to play the game in a repeated setting. This results in an analytically tractable model which is able to describe the type of behavior found in the experimental and computational literature. We find that an increase in the number of players destabilizes the unique symmetric mixed strategy Nash equilibrium. The time series of perpetually fluctuating participation rates typically exhibits linear autocorrelation structure and underparticipation. We investigate whether this time series structure can be exploited, and we relate underparticipation to the payoff structure of the participation game.
participation games evolutionary game theory nonlinear dynamics