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We investigate a multi-agent decision-making problem where a large populationof agents is responsible for carrying out a set of assigned tasks. The amountof 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 ormore tasks. Since each strategy allows an agent to perform multiple tasks at atime, possibly at distinct rates, the strategy selection of the agents needs tobe coordinated. We formulate the problem using the population game formalismand refer to it as the task allocation game. We discuss the design of adecision-making model that incentivizes the agents to coordinate in thestrategy selection process.  As key contributions, we propose a method to find a payoff-drivendecision-making model, and discuss how the model allows the strategy selectionof the agents to be responsive to the amount of remaining jobs in each taskwhile asymptotically attaining the optimal strategies. Leveraging analyticaltools from feedback control theory, we derive technical conditions that themodel needs to satisfy, which are used to construct a numerical approach tocompute the model. We validate our solution through simulations to highlighthow the proposed approach coordinates the agents in task allocation games.

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