Dominance of Strategies
July 12, 2023
Strategy $x'$ of player 1 dominates the strategy $x''$ if the following inequalities hold
$$ x' a_j \geq x'' a_j ~~\forall j \in \{1,\dots, n\} $$Similarly, strategy $y'$ of player 2 dominates the strategy $y''$ if the following inequalities hold
$$y' a_i \leq y'' a_i ~~\forall i \in \{1,\dots, m\}$$Using the concept of dominance of strategies, we could reduce a game $\Gamma$ to $\Gamma'$ by the elimination of dominated strategies, and the value of the game $v$ will be equal to $v'$.