  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 $1\leq t\leq N-1$, 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.
