Evolution of extortion in Iterated Prisoner’s Dilemma games
Edited by Kenneth Wachter, University of California, Berkeley, CA, and approved March 15, 2013 (received for review August 29, 2012)
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-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.
Acknowledgments
We thank M. Abou Chakra, A. Traulsen, J.A. Damore and R. Trivers for useful discussions. K.S. acknowledges support from the Foundational Questions in Evolutionary Biology Fund (Grant RFP-12-21).
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Cover image: Pictured is a late-stage pluteus larva of the purple sea urchin, Strongylocentrotus purpuratus. The larvae disperse in ocean currents before returning to rocky shores, where they settle and complete metamorphosis into their adult form. Brian Gaylord et al. found that intense water turbulence—a potential environmental signpost for the wave-swept coasts where adults live—triggers an unusual and abrupt acceleration in larval development that primes individuals for entry into a suitable habitat. The findings reveal a previously unrecognized response of larval invertebrates to fluid dynamics that could help the organisms complete their life cycle in advantageous locations. See the article by Gaylord et al. on pages 6901–6906. Image courtesy of Jason Hodin.
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Published online: April 9, 2013
Published in issue: April 23, 2013
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Acknowledgments
We thank M. Abou Chakra, A. Traulsen, J.A. Damore and R. Trivers for useful discussions. K.S. acknowledges support from the Foundational Questions in Evolutionary Biology Fund (Grant RFP-12-21).
Notes
This article is a PNAS Direct Submission.
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The authors declare no conflict of interest.
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