Prevalence of cooperation within groups of selfish individuals is puzzling inthat it contradicts with the basic premise of natural selection. Favoringplayers with higher fitness, the latter is key for understanding the challengesfaced by cooperators when competing with defectors. Evolutionary game theoryprovides a competent theoretical framework for addressing the subtleties ofcooperation in such situations, which are known as social dilemmas. Recentadvances point towards the fact that the evolution of strategies alone may beinsufficient to fully exploit the benefits offered by cooperative behavior.Indeed, while spatial structure and heterogeneity, for example, have beenrecognized as potent promoters of cooperation, coevolutionary rules can extendthe potentials of such entities further, and even more importantly, lead to theunderstanding of their emergence. The introduction of coevolutionary rules toevolutionary games implies, that besides the evolution of strategies, anotherproperty may simultaneously be subject to evolution as well. Coevolutionaryrules may affect the interaction network, the reproduction capability ofplayers, their reputation, mobility or age. Here we review recent works onevolutionary games incorporating coevolutionary rules, as well as give adidactic description of potential pitfalls and misconceptions associated withthe subject. In addition, we briefly outline directions for future researchthat we feel are promising, thereby particularly focusing on dynamical effectsof coevolutionary rules on the evolution of cooperation, which are still widelyopen to research and thus hold promise of exciting new discoveries.
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