  Whether a population of decision-making individuals will reach a state of
satisfactory decisions is a fundamental problem in studying collective
behaviors. In the framework of evolutionary game theory and by means of
potential functions, researchers have established equilibrium convergence under
different update rules, including best-response and imitation, by imposing
certain conditions on agents' utility functions. Then by using the proposed
potential functions, they have been able to control these populations towards
some desired equilibrium. Nevertheless, finding a potential function is often
daunting, if not near impossible. We introduce the so-called coordinating agent
who tends to switch to a decision only if at least another agent has done so.
We prove that any population of coordinating agents, a coordinating population,
almost surely equilibrates. Apparently, some binary network games that were
proven to equilibrate using potential functions are coordinating, and some
coloring problems can be solved using this notion. We additionally show that
any mixed network of agents following best-response, imitation, or rational
imitation, and associated with coordination payoff matrices is coordinating,
and hence, equilibrates. As a second contribution, we provide an
incentive-based control algorithm that leads coordinating populations to a
desired equilibrium. The algorithm iteratively maximizes the ratio of the
number of agents choosing the desired decision to the provided incentive. It
performs near optimal and as well as specialized algorithms proposed for
best-response and imitation; however, it does not require a potential function.
Therefore, this control algorithm can be readily applied in general situations
where no potential function is yet found for a given decision-making
population.
