Pure strategy ($s_i\in S_i$)

A pure strategy is a definite, complete plan for a player's choices. In a game with one simultaneous choice, it selects one available action with certainty: heads or tails in matching pennies, for example. In a sequential game it specifies an action at every situation where that player could be called upon to move, including situations never reached when the plan is followed. The plan can use only information available to the player: indistinguishable decision situations must prescribe the same action. An action at one such situation is only part of the plan.

If $S_i$ is player $i$'s set of pure strategies, the payoff $u_i(s_i,s_{-i})$ depends on the whole strategy profile. Thus the same pure strategy can be a best response against one opposing choice and perform poorly against another. A dominant strategy is the stronger case in which it is a best response against every opposing strategy profile.

A strategy is strictly dominated when another strategy gives a strictly larger payoff against every opposing strategy. A strictly dominated strategy cannot receive positive probability in a Nash equilibrium, because moving that probability to its dominator increases expected payoff.