2.5a Mixed Strategies

Mixed Strategy

In a strategic form game, the mixed strategy ${\sigma }_i$ of player $i\in N$ represents the probability distribution of $i$ playing each of their possible pure strategies $s_i^k\in S_i$, such that
\begin{alignat}{0}\sum^{|S_i|}_{k=1}\sigma_i(s_i^k)=1\end{alignat}
where ${\sigma }_i(s_i^k)\ge 0$ for all $s_i^k$.

Properties

(Degenerate Case) A pure strategy $s_i^{\prime }$ may be represented as a mixed strategy such that ${\sigma }_i(s_i^{\prime })=1$ and ${\sigma }_i(s_i)=0$ for $s_i\ne s_i^{\prime }$.