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Free keywords:
replicator dynamics; adaptive dynamics
Abstract:
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-fortat,
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.
