Optimizing Resource Allocation in Multi-Robot Systems Through Game-Theoretic Strategies: A Two-Stage Model Approach

Abstract

In complex and dynamic environments, the decision-making sequence of individual robots significantly influences the effectiveness of collaboration and cooperation among multi-robot systems in completing tasks. This paper focuses on the division of labor in autonomous multi-robot systems, aiming to find optimal strategies for resource allocation among robots operating in complex scenarios. Each robot makes independent yet interacting decisions in relatively isolated dynamic environments. We propose a model that applies game theory from economics, classifying the robots into resource-providing robots and resource-consuming robots. Resource providers acquire resources and compete to determine the optimal strategy, while resource consumers purchase resources, making decisions based on the pricing set by providers. The problem is formulated as a two-stage game. In the first stage, resource providers engage in resource games, abstracted into Cournot or Stackelberg models, where optimal decisions are made based on available resources and estimated strategies of other participants. The second stage involves price games between providers and consumers, analogous to market supply and demand relationships. Price adjustments and demand changes lead to the discovery of Nash equilibria in the price game. Simulations were conducted to compare the system-wide benefits when providers adopt different strategies in the first stage. Results indicate that using the Stackelberg model yields higher overall benefits, further demonstrating the practicality and effectiveness of the proposed strategies. This highlights the importance of strategic model selection in optimizing the performance and resource efficiency of multi-robot systems operating in dynamic environments.