better pair of strategies

Definition

A pair of strategies {row $i_1$, column $j_1$} is said to be better than another pair of strategies {row $i_2$, column $j_2$} if $a_{i_1,j_1} \leq a_{i_2,j_2}, b_{i_1,j_1} \leq b_{i_2,j_2}$ and if at least one of these inequalities is strict.

(Note: under convention that each player is a minimizer)

References

1. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edition, Classics in Applied Mathematics, SIAM, Philadelphia, 1999, p. 79.