Computing all solutions of linear generalized Nash equilibrium problems

Dreves, Axel

doi:10.1007/s00186-016-0562-0

Cited by 20 publications

(18 citation statements)

References 20 publications

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“…We observe that problems (9) and 11are MINLPs. The converse of Theorem 1, and of Theorem 2, is not necessarily true as it is witnessed by the following example.…”

Section: Methods Based On Potential Functionsmentioning

confidence: 84%

“…and at least one of these inequalities is strict. But this contradicts the fact that x is optimal for problem (9). Therefore, considering any generalized potential game with independent objective functions, by solving problem (9), we can compute only those equilibria that are also Pareto optima of problem (15).…”

Section: Methods Based On Potential Functionsmentioning

confidence: 96%

“…Theorem 3 Let x be a 0-approximate global solution of problem (9), then x is a Pareto optimum of problem (15).…”

Section: Methods Based On Potential Functionsmentioning

confidence: 99%

“…Linear GNEPs in a completely continuous setting have been widely studied in [8,9,15,35]. In our mixed-integer framework, the problem solved by any player ν is the following min…”

Section: Jointly Convex Linear Gneps With Mixed-integer Variablesmentioning

confidence: 99%

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Algorithms for generalized potential games with mixed-integer variables

Sagratella

2017

Comput Optim Appl

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We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixedinteger variables, i.e., games in which some variable are continuous while the others are discrete. We investigate which types of equilibria of the game can be computed by minimizing a potential function over the common feasible set. In particular, for a wide class of generalized potential games, we characterize those equilibria that can be computed by minimizing potential functions as Pareto solutions of a particular multi-objective problem, and we show how different potential functions can be used to select equilibria. We propose a new Gauss-Southwell algorithm to compute approximate equilibria of any generalized potential game with mixed-integer variables. We show that this method converges in a finite number of steps and we also give an upper bound on this number of steps. Moreover, we make a thorough analysis on the behaviour of approximate equilibria with respect to exact ones. Finally, we make many numerical experiments to show the viability of the proposed approaches. Keywords Generalized Nash equilibrium problem • Generalized potential game • Mixed-integer nonlinear problem • Parametric optimization The work of the author has been partially supported by Avvio alla Ricerca 2015 Sapienza University of Rome, under grant 488.

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“…We observe that problems (9) and 11are MINLPs. The converse of Theorem 1, and of Theorem 2, is not necessarily true as it is witnessed by the following example.…”

Section: Methods Based On Potential Functionsmentioning

confidence: 84%

Section: Methods Based On Potential Functionsmentioning

confidence: 96%

“…Theorem 3 Let x be a 0-approximate global solution of problem (9), then x is a Pareto optimum of problem (15).…”

Section: Methods Based On Potential Functionsmentioning

confidence: 99%

“…Linear GNEPs in a completely continuous setting have been widely studied in [8,9,15,35]. In our mixed-integer framework, the problem solved by any player ν is the following min…”

Section: Jointly Convex Linear Gneps With Mixed-integer Variablesmentioning

confidence: 99%

See 2 more Smart Citations

Algorithms for generalized potential games with mixed-integer variables

Sagratella

2017

Comput Optim Appl

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“…However, in many cases, there is no uniqueness of the equilibrium, and therefore it could be of great use to have a complete description of the equilibrium set. This was the motivation in [10,13,14,16,22,36,43]. In [43], the author studies a discrete strategy associated with a branch and bound method.…”

Section: Introductionmentioning

confidence: 99%

A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem

Migot

Cojocaru

2020

European Journal of Operational Research

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In this paper, we present a numerical method to describe the solution set of a generalized Nash equilibrium problem (GNEP). Previous approaches show how to reformulate the GNEP as a family of parametric variational inequalities in the special case where the game has shared constraints. We extend this result to generalized Nash problems by means of an umbrella shared constraint approximation of the game. We show the validity of our approach on numerical examples from the literature, and we provide new results that pinpoint the handling of the algorithm's parameters for its implementation. Last but not least, we extend, solve, and discuss an applied example of a generalized Nash equilibrium problem of environmental accords between countries.

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Nash and Stackelberg Equilibrium

Clempner,

Poznyak

2023

Studies in Systems, Decision and Control

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Computing all solutions of linear generalized Nash equilibrium problems

Cited by 20 publications

References 20 publications

Algorithms for generalized potential games with mixed-integer variables

Algorithms for generalized potential games with mixed-integer variables

A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem

Nash and Stackelberg Equilibrium

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