Strategic interaction and externalities: FD-games and pollution

To analyze strategic interaction which may induce externalities, we designed Bathroom Games with frequency-dependent stage payoffs. Two people regularly use a bathroom, before leaving they can either clean up the mess made, or not. Cleaning up involves an effort, so this option always gives a lower immediate utility than not cleaning up. The immediate utility of using the bathroom depends on its condition: the cleaner it is, the higher the utility. The pollution at a certain point in time depends on how often the players did not clean up in the past. Furthermore, as the bathroom's condition deteriorates, cleaning up becomes more burdensome, leading to increasing disutilities. We follow the analysis of repeated games and find that if the agents are sufficiently patient, individually-rational rewards can be supported by (subgame perfect) equilibria involving threats. In almost every such equilibrium, the bathroom is cleaned up regularly.