Example [efr-5E1V]

Consider the selection relation \mathrm {argmax}_X \boxtimes \mathrm {argmax}_Y on {\mathbb {R} \times \mathbb {R} \choose X \times Y}. A point (x,y) is an equilibrium for a function k: X \times Y \to \mathbb {R}^2 if and only if x maximizes k_1(-,y) and y maximizes k_2(x,-). In other words, if x,y is a Nash equilibrium (Reference [nash-noncoop-games]) in the usual sense for the game with payoff matrix k.