A partial randomized strategy may also be used to reduce an area of conflict. Suppose two people, seated at North and East sides of a card table, are to move to another card table adjacent that is identically oriented, must choose without communication what seats they will take at the other table, and will win prizes of $1 apiece if they pick adjacent seats. This is an easy coordination problem; but let us subvert the incentives, by giving an additional $2 premium to the player who is on the other's right in the event they succeed in sitting next to each other. This game has no equilibrium point; interests do not converge; there is no seating arrangement that would not give one an incentive to move. (Each may wish that he could promise to sit on the other's left, but cannot.) A random strategy yields each player a minimax value of $1. But, if each decides where he would sit in the pure common-interest game, then flips a coin to see whether he does sit there or sits opposite, the players guarantee that they neither choose the same seat nor sit opposite each other and share equal chances of winning the premium. This is an equilibrium pair of (mixed) strategies, worth an expected value of $2 apiece.

XREF: Connects to game theory concepts like Schelling points, mixed strategies, and coordination games — echoes common-interest vs. mixed-interest coordination problems.

Thomas C. Schelling, The Strategy of Conflict, loc. 747