School of Mathematics, University of Birmingham, Birmingham, UK.
School of Computing, Engineering and Digital Technologies, Teesside University, Middlesbrough, UK.
Bull Math Biol. 2024 Aug 5;86(9):115. doi: 10.1007/s11538-024-01344-7.
In this paper, we study the problem of cost optimisation of individual-based institutional incentives (reward, punishment, and hybrid) for guaranteeing a certain minimal level of cooperative behaviour in a well-mixed, finite population. In this scheme, the individuals in the population interact via cooperation dilemmas (Donation Game or Public Goods Game) in which institutional reward is carried out only if cooperation is not abundant enough (i.e., the number of cooperators is below a threshold , where N is the population size); and similarly, institutional punishment is carried out only when defection is too abundant. We study analytically the cases for the reward incentive under the small mutation limit assumption and two different initial states, showing that the cost function is always non-decreasing. We derive the neutral drift and strong selection limits when the intensity of selection tends to zero and infinity, respectively. We numerically investigate the problem for other values of t and for population dynamics with arbitrary mutation rates.
在本文中，我们研究了个体本位制度激励（奖励、惩罚和混合）成本优化的问题，以保证在均匀混合的有限群体中达到一定的合作行为最小水平。在这个方案中，群体中的个体通过合作困境（捐赠博弈或公共物品博弈）进行互动，只有当合作不够丰富时（即合作人数低于一个阈值 ，其中 N 是群体规模）才会实施制度奖励；同样，只有当背叛过于丰富时才会实施制度惩罚。我们在小突变极限假设和两种不同初始状态下对奖励激励的情况进行了分析，表明成本函数总是单调递增的。当选择强度分别趋于零时和无穷大时，我们推导出中性漂移和强选择极限。我们还针对其他 t 值和具有任意突变率的群体动态数值研究了这个问题。
