Cooperation, Competition, and Common Pool Resources in Mean Field Games

The tragedy of the commons (TOTC) states that the individual incentives will result in overusing common pool resources (CPRs) which in turn may have detrimental future consequences that affect everyone involved negatively. However, in many real-life situations this does not occur and researchers such as Nobel laureate Elinor Ostrom suggested that mutual restraint by individuals can be the preventing factor. In mean field games (MFGs), since individuals are insignificant and fully non-cooperative, the TOTC is inevitable. This suggests that MFG models involving CPRs must incorporate mixtures of selfishness and altruism to better capture real-world behavior. Motivated by this, we discuss equilibrium notions that blend cooperative and non-cooperative actions. We first introduce mixed individual MFGs and mixed population MFGs, along with modeling aspects of CPRs. The former captures altruistic tendencies at the individual level and the latter represents a population composed of fully cooperative and non-cooperative individuals. For both, we briefly outline equilibrium definitions and their characterization via forward–backward stochastic differential equations. We then present a fisheries-inspired example where the fish stock is the CPR, discussing existence, uniqueness, and experimental results. Finally, we discuss the challenge of learning the altruism levels from observed data.