Does a tag system effectively support emerging cooperation?

This paper investigates whether the so-called Tag Systems support emerging cooperation with respect to 2x2 games. The Tag System, initially proposed by Riolo et al. [2001. Evolution of cooperation without reciprocity. Nature 414, 441-443], gives each agent both a Tag and Tol defined by [0,1] real numbers. Tol is a tolerance for recognizing an opponent as a company. Both Tag and Tol are assumed to be evolving. Results show that the tag's effectiveness depends on whether the AllD strategy is allowed in the system. Allowing AllD implies that green beard effect does not work in the system. Thus, (1) the tag's effectiveness is more meager than that reported by Riolo et al., (2) the Tag System can use alternating reciprocity more effectively than the analytic solution in a Hero game; (3) a system using a 2D tag space supports cooperation more effectively than the usual Tag System.