A Lemke-Like Algorithm for the Multiclass Network Equilibrium Problem

Meunier, Frédéric; Pradeau, Thomas

doi:10.1007/978-3-642-45046-4_30

Cited by 4 publications

(2 citation statements)

References 28 publications

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“…For the computation of equilibria, Marcotte [31] proposed four numerical algorithms and showed local convergence results. Meunier and Pradeau [32] developed a pivoting-algorithm (similar to Lemkes algorithm) for nonatomic network congestion games with affine playerspecific cost functions. Polynomial running time was, however, not shown and seems unlikely to hold.…”

Section: Related Workmentioning

confidence: 99%

Equilibrium computation in resource allocation games

Harks

Timmermans

2021

Math. Program.

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We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and player-specific affine cost functions, we devise the first polynomial time algorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute an equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in integral multiples of a common packet size. While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm. We then develop a polynomial time computable transformation mapping a multimarket Cournot competition game with firm-specific affine price functions and quadratic costs to an associated atomic splittable congestion game as described above. The transformation preserves equilibria in either game and, thus, leads – via our first algorithm – to a polynomial time algorithm computing Cournot equilibria. Finally, our analysis for integrally-splittable games implies new bounds on the difference between real and integral Cournot equilibria. The bounds can be seen as a generalization of the recent bounds for single market oligopolies obtained by Todd (Math Op Res 41(3):1125–1134 2016, 10.1287/moor.2015.0771).

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Section: Related Workmentioning

confidence: 99%

Equilibrium computation in resource allocation games

Harks

Timmermans

2021

Math. Program.

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“…For the computation of equilibria, Marcotte [46] proposed four numerical algorithms and showed local convergence results. Meunier and Pradeau [48] developed a pivoting-algorithm (similar to Lemkes algorithm) for nonatomic network congestion games with affine player-specific cost functions. Poly-nomial running time was, however, not shown and seems unlikely to hold.…”

Section: Related Workmentioning

confidence: 99%

Uniqueness and computation of equilibria in resource allocation games

Timmermans¹

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Equilibrium Computation in Atomic Splittable Singleton Congestion Games

Harks

Timmermans

2017

Integer Programming and Combinatorial Optimization

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A Lemke-Like Algorithm for the Multiclass Network Equilibrium Problem

Cited by 4 publications

References 28 publications

Equilibrium computation in resource allocation games

Equilibrium computation in resource allocation games

Uniqueness and computation of equilibria in resource allocation games

Equilibrium Computation in Atomic Splittable Singleton Congestion Games

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