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 are 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.
