Partial randomization can turn a conflict-addled game into a profitable equilibrium

Evidence

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

Categorization

• ADDENDUM: The fruit-tree and randomization mechanics of splitting a shared resource/coordination problem echo how a private enforcer’s intervention could impose a pareto-improving ‘split’ where parties cannot credibly commit among themselves — directly relevant to a third-party enforcement argument.
• XREF: connects to: Lotteries make indivisible objects and obligations divisible and fair — Thomas C. Schelling, The Strategy of Conflict, 387; Game theory succeeds on pure conflict but fails on mixed conflict-cooperation — Thomas C. Schelling, The Strategy of Conflict, 202; Most conflicts are variable-sum games with common interests — Thomas C. Schelling, The Strategy of Conflict, 20 (+3 more)

Related

• Game theory succeeds on pure conflict but fails on mixed conflict-cooperation (similarity 0.80)
• Among plausible coordination rules, choosing the greater payoff is the more natural (similarity 0.79)
• A mixed-strategy equilibrium can be jointly dominated by a pure coordinating point. (similarity 0.79)
• Most conflicts are variable-sum games with common interests (similarity 0.78)

Broader Connections

• Game theory succeeds on pure conflict but fails on mixed conflict-cooperation #qualifies (0.82) — Thomas C. Schelling, The Strategy of Conflict, 202
• Most conflicts are variable-sum games with common interests #corroborates (0.75) — Thomas C. Schelling, The Strategy of Conflict, 20
• Mixed-motive games require tacit social coordination absent from zero-sum games #qualifies (0.75) — Thomas C. Schelling, The Strategy of Conflict, 367