Payoff Mechanism Design for Coordination in Multi-Agent Task Allocation Games

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.