Existence theorems constitute a fundamental pillar in the study of game theory and exchange economies. These theorems rigorously establish the conditions under which equilibria or stable outcomes ...

Let $(w_1, w_2, w_3)$ be an ordered triple of real numbers such that $w_1 + w_2 + w_3 = 1$. Let $g$ be a real-valued function on the entire real axis which is of ...