title: Evolution of stinginess and generosity in finite populations.
abstract: In iterated continuous games, the cooperative investment in a given round is determined by the initial investment and the reciprocation rate, which describe the investment in the first round and the dependence of current investment on the partner's last move, respectively. These two traits usually intertwine during evolution. However, their coevolution is not fully explored. In this paper, we thereby study their coevolution in the iterated continuous public goods games. We find that the reciprocation rate plays a dominant role during the coevolution in both finite and infinite populations. If it exceeds a threshold, a stingy population where individuals invest no more than their partner's last investment evolves to full cooperation, and a generous population where individuals invest more than their partner's last investment decreases to a moderate cooperative state, investing a portion in the first round and then escalating investment in the following rounds. Otherwise, the stingy population evolves to full defection, and the generous one rises to another moderate cooperative state.
authors.affiliation: Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China. Electronic address: xuexiaoyu@pku.edu.cn.
authors.forename: Xue
authors.initials: X
authors.lastname: Feng
authors.affiliation: School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.
authors.forename: Yanling
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China. Electronic address: longwang@pku.edu.cn.
authors.forename: Long
authors.initials: L
authors.lastname: Wang
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D007398:Interpersonal Relations; D008960:Models, Psychological; D011157:Population Dynamics; D012919:Social Behavior
keywords: Adaptive dynamics; Coevolution; Cooperation; Direct reciprocity; Iterated continuous game