cousin_it’s example seemed to be a special case of a more general type of theorem. That theorem (in various forms) is that there exists nash equilibriums for repeated games for every situation where everyone gets more than their absolute guaranteed minimum. The equilibrium goes like “everyone commits to this strategy, and if anyone disobeys, we punish them by acting so as to keep their gains to the strict minimum”. Then nobody has any incentive to deviate from that.
cousin_it’s example seemed to be a special case of a more general type of theorem. That theorem (in various forms) is that there exists nash equilibriums for repeated games for every situation where everyone gets more than their absolute guaranteed minimum. The equilibrium goes like “everyone commits to this strategy, and if anyone disobeys, we punish them by acting so as to keep their gains to the strict minimum”. Then nobody has any incentive to deviate from that.