Editing Minimax (section)

=== In zero-sum games ===
<span id='Minimax theorem'></span><!-- added label in order not to break incoming links -->
In two-player [[zero-sum game]]s, the minimax solution is the same as the [[Nash equilibrium]].

In the context of zero-sum games, the [[minimax theorem]] is equivalent to:<ref name=Osborne>{{cite book |author1=Osborne, Martin J. |author2=Rubinstein, A. |author2-link=Ariel Rubinstein |year=1994 |title=A Course in Game Theory |place=Cambridge, MA |publisher=MIT Press |edition=print |isbn=9780262150415}}</ref>{{Failed verification|date=February 2015}}

<blockquote>For every two-person [[zero-sum]] game with finitely many strategies, there exists a value {{mvar|V}} and a mixed strategy for each player, such that
:(a) Given Player&nbsp;2's strategy, the best payoff possible for Player&nbsp;1 is {{mvar|V}}, and
:(b) Given Player&nbsp;1's strategy, the best payoff possible for Player 2 is −{{mvar|V}}.
</blockquote>
Equivalently, Player&nbsp;1's strategy guarantees them a payoff of {{mvar|V}} regardless of Player&nbsp;2's strategy, and similarly Player&nbsp;2 can guarantee themselves a payoff of −{{mvar|V}}. The name ''minimax'' arises because each player minimizes the maximum payoff possible for the other – since the game is zero-sum, they also minimize their own maximum loss (i.e., maximize their minimum payoff).
See also [[example of a game without a value]].