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Yes, I was thinking about adding the property concerning column order to the list. Maybe I should have. The "meta" question: The value of a matrix game can be defined as the maximum constant $v$ for which there is a probability vector $\mathbf{x}$ such that $\mathbf{x}^T A \geq v \mathbf{1}^T$. So the definition of value is connected to the definition of an optimal row or column strategy. However, I am looking for an alternative definition of the value of a matrix game which does not use mixed strategies. Can this be done with a sequence of axioms like those described above?
