Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games

By Jong-Shi Pang, Masao Fukushima. Computational Management Science, 2009

468 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2746f1a4e286c26aae34e08b9cd380b1e33a3228

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Katsunori Kubota
2. Masao Fukushima

In Computational Theory and Mathematics

1. Katsunori Kubota
2. Masao Fukushima
3. Antonio J. Conejo
4. Jein-Shan Chen
5. Marc Christian Steinbach

Citations in the corpus

• On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling (2007, unknown): “Furthermore, EPEC models for electricity markets with generators and customers located on a network have been developed and analyzed in [11, 10, 22].”
• Gap Function Approach to the Generalized Nash Equilibrium Problem (2010, methodology): “many applications such as electric power models [14, 19 ] and river basin pollution games [12, 15, 16].”
• A class of gap functions for quasi-variational inequality problems (2007, unknown): “2000 Mathematics Subject Classification.65K10, 90C30”
• Generalized Nash equilibrium problems (2007, unknown): “These problems naturally arise when considering multi-leaderfollower games used in modeling complex competition situations, see, e.g., (Ehrenmann 2004; Fukushima and Pang 2005; Hu and Ralph 2006; Leyffer and Munson 2005; Zhou et al. 2005).”
• MULTI-LEADER-FOLLOWER GAMES: MODELS, METHODS AND APPLICATIONS (2015, background): “More recently, Nishimura, Hayashi and Fukushima [55] considered a more general NEP with uncertain data, where each player solves an optimization problem with a nonlinear objective function.”
• Equilibria in an Oligopolistic Electricity Pool With Stepwise Offer Curves (2012, background): “The EPEC approach, firstly introduced in [8], has been broadly used for modeling the strategic interaction between producers in network constrained electricity markets [9].”
• Solving strongly monotone variational and quasi-variational inequalities (2011, unknown): “Recently, Pang and Fukushima [ 18 ] applied this result in order to formulate the noncooperative multi-leader-follower game in terms of generalized Nash games, which in turn (under opportune assumptions), can be expressed as a quasi-variational inequality.”
• Finding Equilibria in the Pool-Based Electricity Market With Strategic Wind Power Producers and Network Constraints (2017, background): “To find the market equilibrium, an equilibrium problem with equilibrium constraints (EPEC) model was first introduced in [4].”