Mixed Strategies

Mixed Strategies involve players randomizing over their possible actions with specific probabilities to optimize outcomes.

Definition

A mixed strategy for player \(i\) is a probability distribution \(p_i\) over their strategy set \(S_i\).

Examples

In Rock-Paper-Scissors, playing each option with \(p = \frac{1}{3}\) is a mixed strategy equilibrium.

Calculation

Expected payoff: \(E[u] = \sum_{s_1, s_2} p_1(s_1) p_2(s_2) u(s_1, s_2)\).