## Optimization Seminar

Thursday, April 12, 2018 · 10:30 AM - Noon

**Title:**

*When is a skew-symmetric matrix game completely-mixed?*

**Speaker:**Michael Orlitzky

**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.**

Abstract:

Abstract:

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.