= Boolean game
A finite game represented succinctly by <propositional logic>. Each player controls a disjoint collection of <Boolean variables> and chooses their truth values. Together those choices determine a <Boolean valuation>. A player's goal is a <propositional formula>, with <payoff> one if satisfied and zero otherwise. The control sets normally form a <set partition> of all variables.
A <pure strategy> <strategy profile> is a <Nash equilibrium> if every unsatisfied player remains unsatisfied after every change to that player's controlled variables. Checking a candidate can therefore require solving a <Boolean satisfiability problem>, even though evaluating its current <payoffs> is easy.
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