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Extraproximal method application for a Stackelberg-Nash equilibrium calculation in static hierarchical games
Samuel Moya1, Alexander S Poznyak
1Department of Automatic Control, Center for Advanced Study and Research of the National Polytechnic Institute (CINVESTAV-IPN), 07360 México, México. smoya@ctrl.cinvestav.mx
Summary
A new regularized extraproximal method finds Stackelberg-Nash equilibrium in hierarchical games. This approach analyzes convergence and demonstrates feasibility through simulations for leader-follower decision-making.
Area of Science:
- Game Theory
- Optimization
- Computational Economics
Background:
- Multiparticipant static games involve hierarchical decision-making structures.
- Finding Stackelberg-Nash equilibrium is crucial for understanding leader-follower dynamics.
- Existing methods may face challenges in convergence and efficiency for complex games.
Purpose of the Study:
- To propose a regularized extraproximal method for solving Stackelberg-Nash equilibrium problems.
- To analyze the convergence properties of the suggested algorithm.
- To demonstrate the method's practical applicability through simulations.
Main Methods:
- A regularized extraproximal algorithm is developed.
- The method incorporates hierarchical decision-making with a leader and N-1 followers.
- Convergence analysis of the proposed procedure is performed.
Main Results:
- The regularized extraproximal method successfully attains the Stackelberg-Nash equilibrium.
- The convergence of the suggested procedure is theoretically analyzed.
- Simulation results confirm the method's feasibility and effectiveness.
Conclusions:
- The proposed regularized extraproximal method offers an effective approach to finding Stackelberg-Nash equilibrium in hierarchical games.
- The method's convergence properties are established.
- Simulations validate its practical utility.
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