Max-dominated strategy

In game theory a max-dominated strategy is a strategy which is not a best response to any strategy profile of the other players. This is an extension to the notion of strictly dominated strategies, which are obviously max-dominated as well.

A strategy ${\displaystyle s_{i}\in S_{i}}$ of player ${\displaystyle i}$ is max-dominated if for every strategy profile of the other players ${\displaystyle s_{-i}\in S_{-i}}$ there is a strategy ${\displaystyle s_{i}^{\prime }\in S_{i}}$ such that ${\displaystyle u_{i}(s_{i}^{\prime },s_{-i})>u_{i}(s_{i},s_{-i})}$. This definition means that ${\displaystyle s_{i}}$ is not a best response to any strategy profile ${\displaystyle s_{-i}}$, since for every such strategy profile there is another strategy ${\displaystyle s_{i}^{\prime }}$ which gives higher utility than ${\displaystyle s_{i}}$ for player ${\displaystyle i}$.

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