Achieving the Social Optimum in a Nonconvex Cooperative Aggregative Game: A Distributed Stochastic Annealing Approach

Area of Science:

• Optimization algorithms
• Game theory
• Distributed systems

Background:

• Cooperative aggregative games involve players whose costs depend on individual and collective decisions.
• Finding the social optimum in such games is challenging, especially with non-convex cost functions and dynamic communication networks.
• Existing methods may struggle with the complexities of non-convexity and time-varying topologies.

Purpose of the Study:

• To design a novel distributed stochastic annealing algorithm for non-convex cooperative aggregative games.
• To address scenarios with time-varying communication topologies between players.
• To analyze the algorithm's convergence towards the social optimum.

Main Methods:

• Development of a distributed stochastic annealing algorithm tailored for cooperative aggregative games.
• Mathematical analysis to prove the weak convergence of the proposed algorithm to the social optimum.
• Simulation using a numerical example to demonstrate the algorithm's practical effectiveness.

Main Results:

• The proposed distributed stochastic annealing algorithm is effective in finding the social optimum.
• The algorithm demonstrates convergence properties even under non-convex local cost functions.
• The approach is validated through a numerical example, showing its practical applicability.

Conclusions:

• The developed distributed stochastic annealing algorithm offers a viable solution for optimizing non-convex cooperative aggregative games.
• The algorithm's ability to handle time-varying communication structures enhances its applicability in real-world distributed systems.
• Future work could explore extensions to different game structures or convergence criteria.