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A sequential model in game theory in which a leader commits to an action before a follower observes it and chooses a best response. The leader anticipates the follower's response when optimizing. With private follower information, the leader maximizes its expected payoff over follower types. The resulting solution is a Stackelberg equilibrium.

A solution of Stackelberg competition in which the follower chooses a best response after each observed leader action and the leader optimizes given those responses. Indifference may require a specified response or leader-selection convention; it cannot be silently treated as a strict inequality. In a sequential private-value all-pay contest, the leader's objective is $vF(b)-b$.

The support of a finite mixed strategy consists of the pure strategies assigned positive probability. At a Nash equilibrium, every action in the support is a best response. In a game satisfying nondegeneracy of a bimatrix game, the two equilibrium supports have equal size.

The support of a mixed strategy consists of the pure strategies used with positive probability. At a Nash equilibrium, every supported pure strategy is a best response, while unused strategies may give no higher payoff.

// Target: computer-science.bigb

The continuous gain map takes a probability simplex to itself. The Brouwer fixed-point theorem supplies a fixed point, whose positive gains would contradict the zero strategy-weighted average payoff excess. Thus all gains vanish, giving a strategy that is a best response to itself. In a symmetric bimatrix game, this produces a symmetric equilibrium.

A strategy is weakly dominated if another gives at least as much payoff against every opponent strategy and strictly more against at least one. Unlike a strictly dominated strategy, it may remain a best response to opponents who never choose a strategy where the comparison is strict. Thus weak domination does not exclude equilibrium strategies.