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Indefinite Mean-Field Stochastic Cooperative Linear-Quadratic Dynamic Difference Game With Its Application to the
IEEE Transactions on Cybernetics
|May 25, 2021
Summary
This study introduces a new algorithm to find all Pareto optimal solutions for complex stochastic cooperative games. The mean-field Pareto optimality algorithm (MF-POA) addresses challenges in multi-objective decision-making for cooperative LQ games.
Area of Science:
- Control Theory
- Game Theory
- Optimization
Background:
- Stochastic cooperative linear-quadratic (LQ) difference games involve multiple players with potentially conflicting objectives over a finite time horizon.
- Finding Pareto optimal solutions in such games is challenging due to the complexity of coupled generalized difference Riccati equations (GDREs) and differing player cost functionals.
- Existing methods struggle to identify all Pareto optimal decision vectors when strategies depend on distinct weighting matrices.
Purpose of the Study:
- To develop a method for obtaining all Pareto optimal decision vectors and solutions for finite horizon indefinite mean-field stochastic cooperative LQ difference games.
- To establish the equivalence between solving N coupled GDREs and the multiobjective optimization problem.
- To present a novel algorithm for identifying Pareto optimal solutions in cooperative games.
Main Methods:
- Establishing the equivalence between the solvability of N coupled generalized difference Riccati equations (GDREs) and the multiobjective optimization problem.
- Developing a necessary and sufficient condition for cost convexity to ensure the weighting technique's effectiveness in finding Pareto optimal decision vectors.
- Presenting the mean-field Pareto optimality algorithm (MF-POA) utilizing weighted coupled GDREs and generalized difference Lyapunov equations (GDLEs).
Main Results:
- The equivalence between GDRE solvability and multiobjective optimization solvability is established.
- A condition for cost convexity is derived, making the weighting technique both sufficient and necessary for identifying Pareto optimal decision vectors.
- The MF-POA is presented and validated through a cooperative network security game, demonstrating its solvability, correctness, and efficiency.
Conclusions:
- The MF-POA effectively identifies all Pareto optimal decision vectors and solutions for the studied class of games.
- The developed condition for cost convexity is crucial for the successful application of weighting techniques in mean-field games.
- The algorithm provides a robust and efficient method for solving complex cooperative game theory problems with applications in network security.
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