Evolutionary games are important tools for studying the emergence of cooperation in a competing population. They typically deal with a system of agents competing via pairwise two-person games, with every agent aiming at doing better by continually adapting the choice of actions to one’s competing environment. A class of evolutionary games using a self-questioning adaptive mechanism for strategy switching played in a population of connected agents is shown to be describable by an Ising model Hamiltonian of spins that are connected in the same way. The payoff parameters in the game combine to give the coupling between neighbouring spins and an external magnetic field. Depending on the payoff parameters, the mapping between the two problems covers the prisoner's dilemma, snowdrift games, and stag hunt games, played in spatial structures of a uniform degree. The equivalence is illustrated in a well-mixed system in which both problems allow exact solutions. For a chain of agents/spins, the known result of the Ising model leads to an exact closed-form solution to the games without any effort. The connection also allows the accuracy of standard dynamical approaches developed for the games, such as the site and link approximations, to be tested and quantified. The established equivalence connects two research areas, with each having much to offer to the other.
The Speaker: Pak Ming Hui received his PhD degree from the Ohio State University under the supervision of David Stroud in 1987. After postdoctoral work at Harvard University and an associate professorship at National Central University in Taiwan, he joined the Department of Physics of the Chinese University of Hong Kong in 1992. He has worked on various topics in inhomogeneous media, including random composites, semiconductor superlattices, photonic crystals, complex networks, and agent-based modelling of complex systems.
