 EXTORT-2 is an example of an “extortionary” ZD strategy. If Player One adopts EXTORT-2, then his payoff \(V(\bone,\btwo)\) will always be \(2V(\btwo,\bone)-1\) (where \(V(\btwo,\bone)\) is the payoff to Player Two). Player Two can, of course, guarantee herself a return of at least one by constant defection. If she does, Player One will defect with increasing frequency and their average payoffs will both approach the punishment value. Because of the linear relation that links their payoffs, however, if she does better than this, she will necessarily lose to Player One. Indeed, any increment above punishment to her own score will be only half the same increment to her opponent's. Against a naïve, utility-maximizing opponent, EXTORT-2 is even more effective than SET-2. No tricks are needed. Whenever the naïve opponent scores more than the punishment payoff she loses to the extortionist. Whatever she does to increase her own payoff, will, of necessity, increase the extortionist's by double the amount. The best that she can do against EXTORT-2 is to cooperate unconditionally. This will result in the pair realizing the outcomes \(\bC\bC\) and \(\bD\bC\) in a ratio of three to one, giving the her an average payoff of 2.25, while the extortionist nets 3.5. Her only hope of escape is to abandon utility-maximization and acquire what Press and Dyson call a “theory of mind.” If she realizes that her actions might cause the extortionist to abandon his strategy, she might herself adopt an extortionary strategy. This would lower both of their payoffs in the short term, but she might hope for better results in the long term. The upshot, according to Press and Dyson, is that while an extortionist strategy will always defeat a naïve utility-maximizer, the 2IPD between an extortionist and a more sophisticated agent becomes an ultimatum game. The extortionist proposes an unfair division of the joint payoffs, leaving his opponent with the unhappy choice of accepting it or making both players worse off. (It is perhaps worth noting that this analysis omits the possibility that the extorted party is aware of the payoffs to her opponent as well as herself, and, realizing that the IPD is being played between just two agents, seeks to minimize the difference between her opponent's payoff and her own. Adopting such an attitude would presumably lead her to a strategy of unconditional defection. The payoffs of both players would then approach the punishment value, the extortionist's from below and the extorted's from above.)