Mixed strategy

When no fixed choice is optimal, it is worth randomising: playing one’s own actions with set probabilities. This is where game theory meets expected value.

Definition — Mixed strategy

A player adopts a mixed strategy when they choose their actions with a fixed probability distribution $(p_1,\ldots,p_n)$. The expected winnings become the weighted average of the payoffs over the actions, and it is linear in the probabilities. Optimising means choosing $(p_i)$ so as to maximise one’s own expected winnings given the (possibly mixed) behaviour of the opponent.

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Topics: Probabilita
Concepts: Equilibrio di nash · Strategia mista · Valore atteso
Methods: Strategia mista
Skills: Calcolo probabilita · Modellizzare