Siegfried, Tom. "8 Bacon’s Links--Networks, society, and games." A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature. Washington, DC: The National Academies Press, 2006.
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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
However, as physicists Francisco Santos and Jorge Pacheco have pointed out, the “spatial constraint” of agents interacting only with their neighbors is not realistic, either. A more realistic spatial description of the agents, or players, is likely to be a scale-free network of the agent’s relationships, simulating actual social connections. Merging the math of scale-free networks with game theory, the physicists found that cooperation ought to emerge with either the Prisoner’s Dilemma or snowdrift games. “Contrary to previous results, cooperation becomes the dominating trait on both the Prisoner’s Dilemma and the snowdrift game, for all values of the relevant parameters of both games, whenever the network of connections correspond to scale-free graphs generated via the mechanisms of growth and preferential attachment,” the physicists reported in 2005 in Physical Review Letters.13
Numerous other papers have explored links between game theory and network math. It strikes me as a sensible trend that is bound to bear ever more mathematical fruit. Networks are, after all, complex systems that have grown and evolved over time. And game theory, as evolutionary biologists have discovered, is a powerful tool for describing the evolution of such complexity. (One paper specifically models a version of the Prisoner’s Dilemma game showing how repeated play can lead to a complex network in a state that the authors refer to as a “network Nash equilibrium.”)14 Game theory’s importance to society thus cannot help but expand dramatically as the critical nature of social networks becomes ever more clear.
In fact, physicists building their version of a Code of Nature with the tools of statistical mechanics (as did Asimov’s Hari Seldon) have turned increasingly to using those tools on a network-based foundation. This alliance of statistical physics and network math, coupled with game theory’s intimate links to networks, argues that game theory and statistical physics may together nourish the new science of collective human behavior that physicists have already begun to call sociophysics.