= Constant-sum game
{title2=$u_1+u_2=K$}
In a two-player <constant-sum game>, the <sum> of the two <payoffs> is the same constant $K$ at every <strategy profile>. Replacing each player's <payoff> by $u_i-K/2$ gives a <zero-sum game> without changing <best responses> or <Nash equilibria>. If both players can guarantee $K/2$, then any <Nash equilibrium> gives each that value. An equilibrium in <pure strategies> must use <pure strategies> with that guarantee: otherwise the opponent could improve on $K/2$ by a <unilateral deviation>.
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