However, the incentive to cheat does not end with this threat of punishment. The player considering cheating would only cooperate if the payoffs from cheating, once added to the payoffs of forever playing low, are less than or equal to the payoffs from cooperating forever. This idea is shown mathematically by the following. The interest rate is represented by i, and it is used to discount the inflation on the future value of the payoffs. A collusive agreement such as this one only works when players have a sufficient incentive and take into account that their current actions affect future periods.
Similar problems occur when resources are commonly owned, such as a fishing lake.
This action is observed because the individual will only bare part of the costs of this overuse, yet receive all the benefits. Similarly, if the individual fisherman tried to conserve fish, he would assume extra costs because what he did not take for himself, another fisherman would take. However, if the resource is private, the owner assumes responsibility for all the benefits and costs of the lake. This fisherman would take out fewer fish, leaving enough for the resource to regenerate. While privatization solves the commons problem, many resources cannot be privatized for either technical or political reasons.