機率研討會
主講者: Mr. Yu-Ting Chen (University of British Columbia, Canada)
講題: Sharp Benefit-to-Cost Rules for the Evolution of Cooperation on Regular Graphs
時間: 2012-05-18 (Fri.)  14:30 -
地點: 數學所 722 研討室 (台大院區)
Abstract: We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman, and Nowak [Nature, 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then we present a first-order approximation for fixation probabilities of general voter model perturbations on finite graphs subject to small perturbation in terms of the voter model fixation probabilities. In the context of regular graphs, we obtain algebraically explicit first-order approximations for the fixation probabilities of cooperators distributed as certain uniform distributions. These approximations lead to a rigorous proof that both of the rules of Ohtsuki et al. are valid and are sharp.
  || Close window ||