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Abstract
In this paper, we study the problem of cost optimisation of individualbased institutional incentives (reward, punishment, and hybrid) for guaranteeing a certain minimal level of cooperative behaviour in a wellmixed, 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 1≤t≤N1, where N is the population size); and similarly, institutional punishment is carried out only when defection is too abundant. We study analytically the cases t=1 for the reward incentive under the small mutation limit assumption and two different initial states, showing that the cost function is always nondecreasing. 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.
Original language  English 

Article number  115 
Journal  Bulletin of Mathematical Biology 
Volume  86 
Issue number  9 
DOIs  
Publication status  Published  5 Aug 2024 
Bibliographical note
Publisher Copyright:© The Author(s) 2024.
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 2 Active

EPSRC standard grant "Evolutionary Game Theory Under Uncertainty"
Han, T. A. (PI)
1/02/24 → 28/02/26
Project: Research

Future of Life Institute grant "AI Governance Modelling Workshop"
Han, T. A. (PI)
1/12/23 → …
Project: Research