  We investigate a multi-agent decision-making problem where a large population
of agents is responsible for carrying out a set of assigned tasks. The amount
of jobs in each task varies over time governed by a dynamical system model.
Each agent needs to select one of the available strategies to take on one or
more tasks. Since each strategy allows an agent to perform multiple tasks at a
time, possibly at distinct rates, the strategy selection of the agents needs to
be coordinated. We formulate the problem using the population game formalism
and refer to it as the task allocation game. We discuss the design of a
decision-making model that incentivizes the agents to coordinate in the
strategy selection process.
  As key contributions, we propose a method to find a payoff-driven
decision-making model, and discuss how the model allows the strategy selection
of the agents to be responsive to the amount of remaining jobs in each task
while asymptotically attaining the optimal strategies. Leveraging analytical
tools from feedback control theory, we derive technical conditions that the
model needs to satisfy, which are used to construct a numerical approach to
compute the model. We validate our solution through simulations to highlight
how the proposed approach coordinates the agents in task allocation games.
