(A) If Row is committed to row i, with a penalty of 5 for breaking his commitment, Column can see that row i will be chosen, no matter which column he chooses; Column chooses his preferred cell in the upper row, which is the upper left cell, i,I. And Row knows that, if he commits himself to row i, he gets the payoff in that upper-left cell, which is 2. (B) If, instead, Row commits himself to row ii (subtracts 5 from his payoff in row i), Column chooses II in preference to I; and Row knows he will get 5. Finally, (C) if Row remains uncommitted, Column knows that Row will pick the highest row payoff in the column chosen; thus if Column chooses I, Row takes i, and Column gets 5; if Column takes II, Row takes ii, and Column gets 2. Column prefers I; this leaves Row a payoff of 2; and Row can anticipate it. So Row’s best outcome is to commit himself to row ii. This is the evident “solution”; it has a payoff of [5 2], and it corresponds to the strategy 2; I-ii, II-ii for Row, and to all four strategies containing 2-II for Column. (What Column would have done in contingencies 0 and 1 is of no material consequence, once Row has made his first move.)

DEFINE: Illustrates the concept of commitment as a strategic device that changes opponents' expectations and thus outcomes. Pays off: "Commitment transforms indeterminate bargaining into a determinate game."

Thomas C. Schelling, The Strategy of Conflict, loc. 353