title: Emergence of scale-free characteristics in socio-ecological systems with bounded rationality.
abstract: Socio-ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback--Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where multiple equilibria are possible, the correlation between the scale-freeness of the system and the fraction of links with multiple equilibria goes through a rapid transition when the average system rationality increases. Our results explain the influence of the topological structure of socio-ecological systems in shaping their collective cognitive behaviour, and provide an explanation for the prevalence of scale-free and small-world characteristics in such systems.
authors.affiliation: Centre for Complex Systems Research, Faculty of Engineering and IT, The University of Sydney, NSW 2006, Australia.
authors.forename: Dharshana
authors.initials: D
authors.lastname: Kasthurirathna
authors.affiliation: Centre for Complex Systems Research, Faculty of Engineering and IT, The University of Sydney, NSW 2006, Australia.
authors.forename: Mahendra
authors.initials: M
authors.lastname: Piraveenan
mesh_terms: D003071:Cognition; D006801:Humans; D008962:Models, Theoretical; D011908:Rationalization; D012919:Social Behavior; D012944:Social Support