<P> In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero - determinant" (ZD) strategies . The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: s x = D (P, Q, S x) (\ displaystyle s_ (x) = D (P, Q, S_ (x))) and s y = D (P, Q, S y) (\ displaystyle s_ (y) = D (P, Q, S_ (y))), which do not involve the stationary vector v. Since the determinant function s y = D (P, Q, f) (\ displaystyle s_ (y) = D (P, Q, f)) is linear in f, it follows that α s x + β s y + γ = D (P, Q, α S x + β S y + γ U) (\ displaystyle \ alpha s_ (x) + \ beta s_ (y) + \ gamma = D (P, Q, \ alpha S_ (x) + \ beta S_ (y) + \ gamma U)) (where U = (1, 1, 1, 1)). Any strategies for which D (P, Q, α S x + β S y + γ U) = 0 (\ displaystyle D (P, Q, \ alpha S_ (x) + \ beta S_ (y) + \ gamma U) = 0) is by definition a ZD strategy, and the long term payoffs obey the relation α s x + β s y + γ = 0 (\ displaystyle \ alpha s_ (x) + \ beta s_ (y) + \ gamma = 0). </P> <P> Tit - for - tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player . However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own . The extorted player could defect but would thereby hurt himself by getting lower payoff . Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game . Specifically, X is able to choose a strategy for which D (P, Q, β S y + γ U) = 0 (\ displaystyle D (P, Q, \ beta S_ (y) + \ gamma U) = 0), unilaterally setting s y (\ displaystyle s_ (y)) to a specific value within a particular range of values, independent of Y' s strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set s x (\ displaystyle s_ (x)) to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection .) </P> <P> An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing . This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones . It has been shown that unfair ZD strategies are not evolutionarily stable . The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus). </P> <P> Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is bigger . In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face - off between uniform defectors and win--stay, lose--switch agents . </P>

The prisoner's dilemma has all of the following characteristics except