Generalized Nash Equilibrium Problems

Facchinei, Francisco; Kanzow, Christian

doi:10.1007/s10479-009-0653-x

Cited by 580 publications

(457 citation statements)

References 93 publications

Supporting

Mentioning

452

Contrasting

Unclassified

Order By: Relevance

“…Extensions of all the statements to the case of more than two players, and/or to the case when individual (not shared) constraints are present, are straightforward. GNEP setting goes back to [35]; for a modern survey, see [14]. Some other relevant references on theory and numerical methods for GNEP are [8, 11-13, 19-21, 26, 27, 32].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On error bounds and Newton-type methods for generalized Nash equilibrium problems

Izmailov

Solodov

2013

Comput Optim Appl

View full text Add to dashboard Cite

Error bounds (estimates for the distance to the solution set of a given problem) are key to analyzing convergence rates of computational methods for solving the problem in question, or sometimes even to justifying convergence itself. That said, for the generalized Nash equilibrium problems (GNEP), the theory of error bounds had not been developed in depth comparable to the fields of optimization and variational problems. In this paper, we provide a systematic approach which should be useful for verifying error bounds for both specific instances of GNEPs and for classes of GNEPs. These error bounds for GNEPs are based on more general results for constraints that involve complementarity relations and cover those (few) GNEP error bounds that existed previously, and go beyond. In addition, they readily imply a Lipschitzian stability result for solutions of GNEPs, a subject where again very little had been known. As a specific application of error bounds, we discuss Newtonian methods for solving GNEPs. While we do not propose any significantly new methods in this respect, some new insights into applicability to GNEPs of various approaches and into their convergence properties are presented.

show abstract

Section: Introductionmentioning

confidence: 99%

“…As commented in [12,Sects. 3.3,4.3] and [14,Sect. 5.6], error bounds for GNEP are not as well developed yet.…”

Section: Introductionmentioning

confidence: 99%

On error bounds and Newton-type methods for generalized Nash equilibrium problems

Izmailov

Solodov

2013

Comput Optim Appl

View full text Add to dashboard Cite

show abstract

“…In contrast, in a GNEP, the feasible strategies for player i, i ∈ Γ depend on the strategies of all other players [4,39,53,112]. We denote the feasible strategy space of each player by the point to set mapping: C i : X −i → X i , i ∈ Γ that emphasises the ability of other players to influence the strategies available to player i [39,51,112].…”

Section: The Generalised Nash Equilibrium Problemmentioning

confidence: 99%

“…We denote the feasible strategy space of each player by the point to set mapping: C i : X −i → X i , i ∈ Γ that emphasises the ability of other players to influence the strategies available to player i [39,51,112]. The distinction between a conventional Nash game and a GNEP can be viewed as analogous to the distinction between unconstrained and constrained optimisation.…”

Section: The Generalised Nash Equilibrium Problemmentioning

confidence: 99%

See 1 more Smart Citation

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

View full text Add to dashboard Cite

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader's decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal. We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity.

show abstract

Social Interaction‐Aware Dynamical Models and Decision‐Making for Autonomous Vehicles

Crosato,

Tian,

Shum

et al. 2023

Advanced Intelligent Systems

View full text Add to dashboard Cite

Interaction‐aware autonomous driving (IAAD) is a rapidly growing field of research that focuses on the development of autonomous vehicles (AVs) that are capable of interacting safely and efficiently with human road users. This is a challenging task, as it requires the AV to be able to understand and predict the behaviour of human road users. In this literature review, the current state of IAAD research is surveyed. Commencing with an examination of terminology, attention is drawn to challenges and existing models employed for modeling the behaviour of drivers and pedestrians. Next, a comprehensive review is conducted on various techniques proposed for interaction modeling, encompassing cognitive methods, machine‐learning approaches, and game‐theoretic methods. The conclusion is reached through a discussion of potential advantages and risks associated with IAAD, along with the illumination of pivotal research inquiries necessitating future exploration.

show abstract

Generalized Nash Equilibrium Problems

Cited by 580 publications

References 93 publications

On error bounds and Newton-type methods for generalized Nash equilibrium problems

On error bounds and Newton-type methods for generalized Nash equilibrium problems

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Social Interaction‐Aware Dynamical Models and Decision‐Making for Autonomous Vehicles

Contact Info

Product

Resources

About