A Local Variation Method for Bilevel Nash Equilibrium Problems

Francesco Caruso (), Maria Carmela Ceparano and Jacqueline Morgan
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Francesco Caruso: Università di Napoli Federico II

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: We address the numerical approximation of bilevel problems consisting of one Nash equilibrium problem in the upper level and another Nash equilibrium problem in the lower level. These problems, widely employed in engineering and economic applications, are a generalization of the well-known Stackelberg (or bilevel optimization) problem. In this paper, we define a numerical method for bilevel Nash equilibrium problems where in the lower level there is a ratio-bounded game (introduced in Caruso, Ceparano, Morgan [CSEF Working Papers, 593 (2020)]) and in the upper level there is a potential game (introduced in Monderer, Shapley [Games Econ. Behav., 14 (1996)]). The method, relying on a derivative-free unconstrained optimization technique called local variation method, is shown to globally converge towards a solution of the problem and also allows to obtain error estimations.

Keywords: Bilevel Nash equilibrium problem; Stackelberg problem; multi-leader-follower game; ratio-bounded game; potential game; Nash equilibrium; existence and uniqueness; local variation method; global convergence; error estimation. (search for similar items in EconPapers)
Date: 2021-07-30
New Economics Papers: this item is included in nep-gth
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