Feng Xue, Zhang Yanling, Wang Long
Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.
J Theor Biol. 2017 May 21;421:71-80. doi: 10.1016/j.jtbi.2017.03.022. Epub 2017 Mar 29.
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.
在重复连续博弈中，给定轮次的合作投资由初始投资和互惠率决定，初始投资和互惠率分别描述第一轮的投资以及当前投资对伙伴上一步行动的依赖性。这两个特征在进化过程中通常相互交织。然而，它们的共同进化尚未得到充分研究。因此，在本文中，我们研究它们在重复连续公共品博弈中的共同进化。我们发现，在有限和无限种群的共同进化过程中，互惠率起着主导作用。如果它超过一个阈值，个体投资不超过其伙伴上一轮投资的吝啬种群会进化为完全合作，而个体投资超过其伙伴上一轮投资的慷慨种群会减少到适度合作状态，在第一轮投资一部分，然后在接下来的轮次中增加投资。否则，吝啬种群会进化为完全背叛，而慷慨种群会上升到另一种适度合作状态。
