Optimization Seminar
Location
Sherman Hall : 148C
Date & Time
April 12, 2018, 10:30 am – 12:00 pm
Description
Title: When is a skew-symmetric matrix game completely-mixed?
Speaker: Michael Orlitzky
Abstract:
In 1945, Irving Kaplansky proved that a two-person zero-sum matrix game whose value is zero is completely-mixed if and only if the associated real n-by-n matrix has rank (n-1) and if all of its cofactors are nonzero and of the same sign.
Fifty years later, in 1995, Kaplansky published another result giving more-specific conditions for skew-symmetric matrices. However, that result turns out to be false due to a small mistake.
In a recent manuscript, T. Parthasarathy corrects the necessary and sufficient conditions for a skew-symmetric matrix game to be completely-mixed. This talk provides the background for and proof of his theorem.
Speaker: Michael Orlitzky
Abstract:
In 1945, Irving Kaplansky proved that a two-person zero-sum matrix game whose value is zero is completely-mixed if and only if the associated real n-by-n matrix has rank (n-1) and if all of its cofactors are nonzero and of the same sign.
Fifty years later, in 1995, Kaplansky published another result giving more-specific conditions for skew-symmetric matrices. However, that result turns out to be false due to a small mistake.
In a recent manuscript, T. Parthasarathy corrects the necessary and sufficient conditions for a skew-symmetric matrix game to be completely-mixed. This talk provides the background for and proof of his theorem.
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