In any finite two-person zero-sum game there is a strategy pair from which neither side can profitably deviate.
Von Neumann's 1928 proof, which founded game theory. Its guarantee holds only for zero-sum games, and finding a value at all required allowing mixed strategies.
In practice
- A goalkeeper who always dives right is beaten; the strategy is to be genuinely unpredictable.
- A negotiator with a predictable concession pattern is read after two rounds, and randomising the pace is worth more than any argument.
- Further reading
- Wikipedia
- Subject
- Games & Strategic Interaction
- Essay
- What is provable, and what people actually do