# Multiple Equilibrium Points all have Equal Payoffs

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## 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