Evolution of creation-annihilation cyclic games in regular networks

We introduce a model of a cyclic game. Designed to take advantage of the recurring nature of certain economic and social situations, a cyclic game differs from an extensive form game in that a cyclic game does not necessarily have an end. The same situations, although with different players, may be repeated infinitely often. In this paper, the domain evolution process in a novel kind of cyclic game in regular networks is investigated by simulation method. Different with the classical cyclic games, this process is called “creation-annihilation process”, which likes the autocatalysis reactions. We consider the regular networks with the situations of full occupied, partial occupied and gradient occupied. The results of numerical simulations show that the evolutions of such “creation-annihilation” cyclic games in regular networks with three, four or five states have some special feature: the evolution of three states can spread throughout the whole networks; however, the cases of four or five states usually has a stable boundary, and the growth is driven by the internal-evolution of the domain. Considering with the widespread of the cyclic autocatalysis in organism activities, such internal-evolution driven growth could be universal in many organism systems.