  Decision-making individuals are typically either an imitator, who mimics the
action of the most successful individual(s), a conformist (or coordinating
individual), who chooses an action if enough others have done so, or a
nonconformist (or anticoordinating individual), who chooses an action if few
others have done so. Researchers have studied the asymptotic behavior of
populations comprising one or two of these types of decision-makers, but not
altogether, which we do for the first time. We consider a population of
heterogeneous individuals, each either cooperates or defects, and earns payoffs
according to their possibly unique payoff matrix and the total number of
cooperators in the population. Over a discrete sequence of time, the
individuals revise their choices asynchronously based on the best-response or
imitation update rule. Those who update based on the best-response are a
conformist (resp. nonconformist) if their payoff matrix is that of a
coordination (resp. anticoordination) game. We take the distribution of
cooperators over the three types of individuals with the same payoff matrix as
the state of the system. First, we provide our simulation results, showing that
a population may admit zero, one or more equilibria at the same time, and
several non-singleton minimal positively invariant sets. Second, we find the
necessary and sufficient condition for equilibrium existence. Third, we perform
stability analysis and find that only those equilibria where the imitators
either all cooperate or all defect are likely to be stable. Fourth, we proceed
to the challenging problem of characterizing the minimal positively invariant
sets and find conditions for the existence of such sets. Finally, we study the
stochastic stability of the states under the perturbed dynamics, where the
agents are allowed to make mistakes in their decisions with a certain small
probability.
