Partners or rivals? Strategies for the iterated prisoner's dilemma

Within the class of memory-one strategies for the iterated Prisoner's Dilemma, we characterize partner strategies, competitive strategies and zero-determinant strategies. If a player uses a partner strategy, both players can fairly share the social optimum; but a co-player preferring an unfair solution will be penalized by obtaining a reduced payoff. A player using a competitive strategy never obtains less than the co-player. A player using a zero-determinant strategy unilaterally enforces a linear relation between the two players' payoffs. These properties hold for every strategy used by the co-player, whether memory-one or not.