Mixed-equilibrium calculation
To find an interior mixed equilibrium, choose each player’s mixing probability to make the other player indifferent between actions in their support.
Definition
To find an interior mixed equilibrium, choose each player’s mixing probability to make the other player indifferent between actions in their support.
Intuition
Your opponent’s mix determines your indifference, and your mix determines theirs. Reversing this is a common calculation error.
Worked example
In matching pennies with payoffs +1 for a match and −1 otherwise to player 1, if player 2 chooses heads with probability q, the two expected payoffs are 2q−1 and 1−2q. Equality gives q=1/2.
The math
Solve the indifference equations, check all probabilities lie in [0,1], and verify excluded actions do not offer a profitable deviation.
Where it is used
Use support enumeration when there are more than two actions. Not every equilibrium uses every available action.
Sources
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