Abstract
This paper presents a Stackelberg–Nash game for modeling multiple leaders and followers. The model involves two Nash games restricted by a Stackelberg game. We propose a computational approach to find the equilibrium point based on the extraproximal method for ergodic controlled finite Markov chains. The extraproximal method consists of a two-step iterated procedure: the first step is a prediction and the second is a basic adjustment of the previous step. We formulate the game as coupled nonlinear programming problems using the Lagrange principle. The Tikhonov’s regularization method is used to guarantee the convergence to a unique equilibrium point. Validity of the method is demonstrated applying this framework to model an oligopoly competition.
Original language | English |
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Pages (from-to) | 650-673 |
Number of pages | 24 |
Journal | Cybernetics and Systems |
Volume | 47 |
Issue number | 8 |
DOIs | |
State | Published - 16 Nov 2016 |
Keywords
- Extraproximal method
- Markov chains
- Nash
- Stackelberg games
- multiple leader–follower