Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
Jong-Shi Pang,Masao Fukushima +1 more
TLDR
In Pang and Fukushima, a sequential penalty approach was presented for a quasi-variational inequality (QVI) with particular application to the generalized Nash game, but numerical results due to an inverted sign in the penalty term in the example and some missing terms in the derivatives of the firms’ Lagrangian functions are incorrect.Abstract:
In Pang and Fukushima (Comput Manage Sci 2:21–56, 2005), a sequential penalty approach was presented for a quasi-variational inequality (QVI) with particular application to the generalized Nash game. To test the computational performance of the penalty method, numerical results were reported with an example from a multi-leader-follower game in an electric power market. However, due to an inverted sign in the penalty term in the example and some missing terms in the derivatives of the firms’ Lagrangian functions, the reported numerical results in Pang and Fukushima (Comput Manage Sci 2:21–56, 2005) are incorrect. Since the numerical examples of this kind are scarce in the literature and this particular example may be useful in the future research, we report the corrected results.read more
Citations
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References
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Book
Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
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Mathematical Programs with Equilibrium Constraints
TL;DR: Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modelling of many practical problems.