The Emergence of Cooperation in Evolutionary Game Theory

Cooperation is a fundamental aspect of biological systems. The evolution of complex organism, intelligence and complex societies all depend on cooperative behavior. Yet it is not clear how cooperation can evolve through natural selection. This essay will review game theoretical models of cooperation following a chronological approach with the final aim to explore their connection to physics. Motivation and Historical Background: Cooperation is a fundamental aspect of biological systems. The emergence of mutli-cellular organisms from uni-cellular ones, collective behavior in groups of animals, human societies are just a few of the countless examples of complex biological systems that depend on cooperative interactions. Yet it is not clear how cooperation can emerge in the face of exploitation. Cooperators make an investment for the common good while exploiters reap of the benefit avoiding costs, thus based on the evolutionary principle that the fittest survives or simply on rational behavior to generate the highest payoff one would expect exploitation to be dominant and cooperation to be rare in nature. Therefore the problem of finding mechanisms the can lead to the evolution of cooperation through natural selection has remained a core problem of biology since Darwin. Darwin’s theory provides a mechanism for evolution (natural selection) but also is explicitly competitive (the survival of the fittest) and based on the struggle for existence. One of the first to criticize the prevailing blindly competitive interpretation of evolution and draw attention to cooperation in evolution was P. Kropotkin in his classic “Mutual AidA Factor of Evolution” first published in 1890[1]. Still, until the 1960’s collective phenomena drew little attention. Selection was mainly thought of as happening at the level of populations or even species. Cooperation was regarded as being adaptive. One of the first extensions of evolutionary theory accounting for cooperation and altruism was Hamilton’s kinship theory [2] which took the gene-eye’s view of evolution. This theory regarded the gene to be the fundamental unit of evolution that looks beyond its mortal bearer and seeks a potentially immortal set of its replicas to exist in a population related to it and explained altruism and cooperation as a mechanism for a gene to increase its frequency [3]. But still there are a lot of examples of cooperation, though rarely at the level of self sacrifice, between unrelated individuals and even different species in nature that this argument fails to explain. Following the pioneering paper by Trivers, Axelrod used game theory to explain the emergence of cooperation based on a well studied game the Prisoners Dilemma. Since then game theoretical approaches in evolution have attracted huge interests and have been widely used to explain mechanisms through which cooperation can emerge and be maintained in different settings. The game theoretical approach is based on the theory first formulated by Morgenstern and Von Neumann [4] in the 1940’s and applies methods previously developed in economics to evolutionary settings. Game theory offers a mathematical framework for addressing these questions. In this paper we are going to review the most promising results of this approach and try to establish a link to physics.