Can you stay unpredictable?
Mixed strategies randomize over actions. Matching pennies has no pure Nash equilibrium: after any fixed pair of choices, one player wants to change.
Inside this model
Matching choices pay A +s and B −s; different choices reverse the payoffs. A's expected heads payoff is s(2p−1), and tails is its negative. At a 50/50 opponent, both pay zero in expectation. In equilibrium both randomize equally.
Out in the world
A practical use
A predictable inspection schedule can be exploited. Randomization can make a pattern harder to anticipate.
A useful lens. Not a universal law.
- This is a zero-sum game with a fixed opponent policy. It does not imply that random behavior is best in general.
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.
PNAS — The Nash equilibrium: a perspective ↗