Evolutionary Aspects of Belief Strategy

Dempster-Shafer evidence theory is one of many scientific fields where the evolutionary game theory finds applications. An extension of the mixed strategy of population games—belief strategy—is based on the idea of belief function or mass function in the evidence theory. Additionally, the non-empty subsets of the population game’s strategy set are designated as propositions or strategies of the associated Jaccard matrix game (JMG), and their evolutionary aspects are described using replicator dynamics. In this article, we establish, particularly in the case of two strategies, that if for some uncertainty parameter, there is full belief in some proposition, then the corresponding mass function is an ESS of the JMG. The idea of the best-supported evidence, or best-supported belief-based ESS, based on the convergence time of solution trajectories of the replicator system associated with JMG, is investigated. The belief or mass function corresponding to several values of uncertainty parameter/parameters are taken as initial evidence. We have demonstrated numerically, using examples, that each solution trajectory of this replicator system converges to ESS of JMG, if we can not believe a proposition fully under a given uncertain environment.