Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the ability to use conditional strategies that depend on the outcome of previous interactions, thus allowing for reciprocation. Recently, a new class of strategies has been proposed, so-called “zero-determinant” strategies. These strategies enforce a fixed linear relationship between one’s own payoff and that of the other player. A subset of those strategies allows “extortioners” to ensure that any increase in one player’s own payoff exceeds that of the other player by a fixed percentage. Here, we analyze the evolutionary performance of this new class of strategies. We show that in reasonably large populations, they can act as catalysts for the evolution of cooperation, similar to tit-for-tat, but that they are not the stable outcome of natural selection. In very small populations, however, extortioners hold their ground. Extortion strategies do particularly well in coevolutionary arms races between two distinct populations. Significantly, they benefit the population that evolves at the slower rate, an example of the so-called “Red King” effect. This may affect the evolution of interactions between host species and their endosymbionts.

Significance: Many of the world’s most pressing problems, like the prevention of climate change, have the form of a large-scale social dilemma with numerous involved players. Previous results in evolutionary game theory suggest that multiplayer dilemmas make it particularly difficult to achieve mutual cooperation because of the lack of individual control in large groups. Herein, we extend the theory of zero-determinant strategies to multiplayer games to describe which strategies maintain cooperation. Moreover, we propose two simple models of alliances in multiplayer dilemmas. The effect of these alliances is determined by their size, the strategy of the allies, and the properties of the social dilemma. When a single individual’s strategic options are limited, forming an alliance can result in a drastic leverage.

Cooperation in public good games is greatly promoted by positive and negative incentives. In this paper, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trust (the propensity to cooperate in the absence of information on the co-players). If both positive and negative incentives are available, evolution leads to a population where defectors are punished and players cooperate, except when they can get away with defection. Rewarding behaviour does not become fixed, but can play an essential role in catalysing the emergence of cooperation, especially if the information level is low.

Significance: Direct reciprocity is one of the fundamental mechanisms for cooperation. It is based on the idea that individuals are more likely to cooperate if they can expect their beneficiaries to remember and to return their cooperative acts in future. Previous computational models, however, often had to restrict the number of past rounds subjects can memorize. Herein we suggest an alternative approach. We propose general properties that robust cooperative strategies ought to have. Then we characterize all memory- n strategies that meet these properties, and we show that such strategies naturally emerge across different evolutionary scenarios. Our results are applicable to general social dilemmas of arbitrary size. For some dilemmas, longer memory is all it takes for cooperation to evolve.