Task Allocation Game with the Loss Function

Task allocation problem has drawn a wide attention in the field of artificial intelligence, and we introduce the loss function into task allocation game model to simulate the issue of maintaining a balance between economic development and environmental protection. The article establishes a mathematical model of the game, studies how the task payoff difference varies when changing parameters of the model, and uses the fixation probability to analyze the impact of the loss function on self-organized evolution of task allocation in the group. We draw three main conclusions, firstly synergistic benefit facilitates the formation of division of labor, secondly the loss function has both positive and negative effects on cooperation in the group, and finally the loss function significantly reduces the willingness of individuals to perform task. The paper presents a new application scenario of task allocation game, and provides a novel idea for controlling environmental pollution.