Multiple Equilibrium Points all have Equal Payoffs

Theorem

Let $G$ be a two-person zero-sum game.

Let $G$ have more than one equilibrium point.

Then every equilibrium point of $G$ has the same payoff.

Proof

This theorem requires a proof. In particular: Stated without proof, or even an explanatory comment on its scope of applicability, in Davis. This work is too vague to be useful. I am going to have to use a different work. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1983: Morton D. Davis: Game Theory (revised ed.) ... (previous) ... (next): $\S 2$: The Two-Person, Zero-Sum Game with Equilibrium Points