Row Rank Equals Column Rank

Wardlaw, William P.

doi:10.2307/30044181

Cited by 2 publications

(2 citation statements)

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“…. , b qn ) (see also Wardlaw (2005)). Suppose (A, B) is of rank r, with A + B = ∑ r q=1 a q b q and therefore B…”

Section: Definitionmentioning

confidence: 93%

Fast Algorithms for Rank-1 Bimatrix Games

Adsul,

Garg,

Mehta

et al. 2018

Preprint

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The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices. For a game of rank r, the set of its Nash equilibria is the intersection of a generically one-dimensional set of equilibria of parameterized games of rank r − 1 with a hyperplane. We comprehensively analyze games of rank one. They are economically more interesting than zero-sum games (which have rank zero), but are nearly as easy to solve. One equilibrium of a rank-1 game can be found in polynomial time. All equilibria of a rank-1 game can be found by path-following, which finds only one equilibrium of a bimatrix game. The number of equilibria of a rank-1 game may be exponential. We also present a new rank-preserving homeomorphism between bimatrix games and their equilibrium correspondence.

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“…. , b qn ) (see also Wardlaw (2005)). Suppose (A, B) is of rank r, with A + B = ∑ r q=1 a q b q and therefore B…”

Section: Definitionmentioning

confidence: 93%

Fast Algorithms for Rank-1 Bimatrix Games

Adsul,

Garg,

Mehta

et al. 2018

Preprint

View full text Add to dashboard Cite

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“…Hence the solution υ υ υ will exist provided that W is of full column rank, that is, the columns of the explanatory variables are linearly independent, (Searle, 1971;Wardlaw, 2005;Basilevsky, 1983). This is a typical multiple regression problem and any statistical software package could be used to solve the system.…”

Section: Multiple Linear Regressionmentioning

confidence: 99%

Multiple linear regression with constrained coefficients: Application of the lagrange multiplier

Kikawa

Kloppers

2016

sasj

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In this paper, we present two unfamiliar novel estimation techniques (UNET) for the constrained regression coefficients in the frame-work of a standard multiple linear regression model. Estimation of a linear regression problem with constraints on the regression coefficients are firstly derived by minimising a formulated goal function that minimises the total sum of the squared errors, plus the sum of the linear constraints multiplied by a Lagrangian. We also show that the solution to the system of equations can be obtained without differentiating the goal function, rather expressed in terms of the known matrices. This is achieved by employing properties of a blocked linear system. The UNET is justified by a numerical simulated system of linear equations in 3-dimensions. The UNET yields estimates that are comparable to those generated by the Schur complement principle.

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Row Rank Equals Column Rank

Cited by 2 publications

References 0 publications

Fast Algorithms for Rank-1 Bimatrix Games

Fast Algorithms for Rank-1 Bimatrix Games

Multiple linear regression with constrained coefficients: Application of the lagrange multiplier

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