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Abstract
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 1≤t≤N−1, 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 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.
Original language | English |
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Article number | 115 |
Number of pages | 43 |
Journal | Bulletin of Mathematical Biology |
Volume | 86 |
DOIs | |
Publication status | Published - 5 Aug 2024 |
Keywords
- Evolutionary game theory
- Population dynamics
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Evolutionary Game Theory Under Uncertainty
Duong, H. (Principal Investigator)
Engineering & Physical Science Research Council
1/05/24 → 31/01/26
Project: Research Councils
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Model reduction in evolutionary game dynamics in finite populations
Duong, H. (Principal Investigator)
31/03/23 → 30/03/25
Project: Research Councils
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Variational structures, convergence to equilibrium and multiscale analysis for non-Markovian systems
Duong, H. (Principal Investigator)
Engineering & Physical Science Research Council
1/02/22 → 30/06/24
Project: Research Councils