On regulation with zero–determinant strategies

The regulation of two players is modeled as an iterated game with no discounting where first two players (two countries providing carbon emissions) also interact with a regulator (an independent regulator responsible for controlling the carbon emission levels by imposing punishments). In our setting, employing a zero-determinant (ZD) strategy, the regulator gains a unilateral advantage to enforce a linear relation between the expected payoffs of players. We identify two conditions and prove that the first guarantees the existence of a ZD strategy while the second ensures the existence of an optimal one. Furthermore, we propose an intuitive and simple cost structure in order to enable the regulator to employ an uncomplicated ZD strategy and attain a maximal ZD payoff.