Computation, Multiplicity, and Comparative Statics of Cournot Equilibria in Integers

Todd, Michael J.

doi:10.1287/moor.2015.0771

Cited by 6 publications

(12 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As a consequence, we can apply the isomorphism and the polynomial time algorithm for atomic splittable congestion games to efficiently compute Cournot equilibria for models with firm-specific affine price functions and quadratic production costs. In addition, our analysis for integrally-splittable games also implies new bounds on the difference between real and integral Cournot equilibria complementing and extending recent results of Todd [69] obtained for a single market.…”

supporting

confidence: 73%

“…Lastly, we extend a very recent result by Todd [69], where the total and individual production in one market in an integer equilibrium and a real equilibrium are compared. Theorem 3.7.7.…”

Section: Multimarket Cournot Oligopolymentioning

confidence: 53%

“…Finally, our analysis for integral 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 [69] towards multimarkets.…”

Section: Equilibrium Computation For Games With Affine Costsmentioning

confidence: 84%

“…Using supermodularity, one can obtain existence results without assuming that the utility functions are quasi-convex. Very recently, Todd [69] considered Cournot competition on a single market, where the price functions are linear and cost functions are quadratic. For such games, he proved that equilibria exist and can be computed in time Opn logpnqq, where n denotes the number of firms.…”

Section: Related Workmentioning

confidence: 99%

“…Todd [69] showed that the total production in a 1-splittable equilibrium is in the worst-case at most n{2 away from that in the real equilibrium, and the individual firm's choice can be more that pn´1q{4 away from her choice in the real equilibrium. Our bounds a larger than Todd's, yet, they hold for a more general model -multiple markets and firm-specific price functions.…”

Section: Multimarket Cournot Oligopolymentioning

confidence: 99%

See 4 more Smart Citations

Uniqueness and computation of equilibria in resource allocation games

Timmermans¹

View full text Add to dashboard Cite

People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

show abstract

supporting

confidence: 73%

“…Lastly, we extend a very recent result by Todd [69], where the total and individual production in one market in an integer equilibrium and a real equilibrium are compared. Theorem 3.7.7.…”

Section: Multimarket Cournot Oligopolymentioning

confidence: 53%

Section: Equilibrium Computation For Games With Affine Costsmentioning

confidence: 84%

Section: Related Workmentioning

confidence: 99%

Section: Multimarket Cournot Oligopolymentioning

confidence: 99%

See 3 more Smart Citations

Uniqueness and computation of equilibria in resource allocation games

Timmermans¹

View full text Add to dashboard Cite

show abstract

Potential games, path independence and Poisson’s binomial distribution

Sen

2018

Math Meth Oper Res

View full text Add to dashboard Cite

This paper provides a simple characterization of potential games in terms of path independence. Using this characterization we propose an algorithm to determine if a finite game is potential or not. We define the storage requirement for our algorithm and provide its upper bound. The number of equations required in this algorithm is lower or equal to the number obtained in the algorithms proposed in the recent literature. We also show that for games with same numbers of players and strategy profiles, the number of equations for our algorithm is maximum when all players have the same number of strategies. To obtain our results, the key technique of this paper is to identify an associated Poisson's binomial distribution. This distribution enables us to derive explicit forms of the number of equations, storage requirement and related aspects.

show abstract

Equilibrium computation in resource allocation games

Harks

Timmermans

2021

Math. Program.

View full text Add to dashboard Cite

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).

show abstract

Computation, Multiplicity, and Comparative Statics of Cournot Equilibria in Integers

Cited by 6 publications

References 11 publications

Uniqueness and computation of equilibria in resource allocation games

Uniqueness and computation of equilibria in resource allocation games

Potential games, path independence and Poisson’s binomial distribution

Equilibrium computation in resource allocation games

Contact Info

Product

Resources

About