Market equilibria with hybrid linear-Leontief utilities

Chen, Xi; Huang, Lijie; Teng, Shang‐Hua

doi:10.1016/j.tcs.2008.12.030

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…Using the connection between Nash equilibria and Arrow-Debreu equilibria, our complexity result on sparse games can be extended to market equilibria in economies with sparse exchange structures [Chen et al 2006b]. …”

Section: Theorem 14 Bimatrix Is Not In Smoothed Polynomial Time Unlmentioning

confidence: 99%

Settling the complexity of computing two-player Nash equilibria

Chen

Deng

Teng

2009

J. ACM

Self Cite

498

610

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We prove that BIMATRIX, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991.Our result, building upon the work of Daskalakis et al. [2006a] on the complexity of four-player Nash equilibria, settles a long standing open problem in algorithmic game theory. It also serves as a starting point for a series of results concerning the complexity of two-player Nash equilibria. In particular, we prove the following theorems:-BIMATRIX does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. -The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for BIMATRIX is not polynomial unless every problem in PPAD is solvable in randomized polynomial time.Our results also have a complexity implication in mathematical economics:-Arrow-Debreu market equilibria are PPAD-hard to compute.

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Section: Theorem 14 Bimatrix Is Not In Smoothed Polynomial Time Unlmentioning

confidence: 99%

Settling the complexity of computing two-player Nash equilibria

Chen

Deng

Teng

2009

J. ACM

Self Cite

498

610

View full text Add to dashboard Cite

show abstract

“…We anticipate that our reduction techniques will help to resolve more complexity-theoretic questions concerning other families of exchange markets such as the general CES markets and the hybrid linear-Leontief markets [7].…”

Section: Our Contributionmentioning

confidence: 99%

“…Now we let x ′ and y ′ denote the two vectors obtained in (7). By Lemma 1 we have x ′ k , y ′ k ∈ [0, 1] for all k ∈ [n].…”

Section: Proof Of Theoremmentioning

confidence: 99%