Committing to a strategy can yield a better outcome than remaining uncommitted

Evidence

(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.) — Thomas C. Schelling, The Strategy of Conflict, 353

Categorization

• XREF: The worked example proves commitment beats non-commitment (5 vs 2) — the exact logic of why Corleone’s public, irreversible promise changes the game rather than merely informing. — connects to: Leaving a final standing offer is a winning commitment tactic. — Thomas C. Schelling, The Strategy of Conflict, 636; Among plausible coordination rules, choosing the greater payoff is the more natural — Thomas C. Schelling, The Strategy of Conflict, 676; Commitment buys first move while threat commits to a second-move response strategy — Thomas C. Schelling, The Strategy of Conflict, 294 (+4 more)

Related

• Leaving a final standing offer is a winning commitment tactic. (similarity 0.86)
• Among plausible coordination rules, choosing the greater payoff is the more natural (similarity 0.83)
• Commitment buys first move while threat commits to a second-move response strategy (similarity 0.82)
• Commitment converts an indeterminate bargaining situation into a determinate two-move game (similarity 0.81)
• Threats, promises, and commitments unify as payoff-restricting reaction functions (similarity 0.81)
• One player’s promise can worsen the other player’s position (similarity 0.81)
• Commitments, promises, and threats all reduce a player’s own payoffs visibly and irreversibly (similarity 0.80)
• A credible conditional commitment must combine both a promise and a threat. (similarity 0.79)

Broader Connections

• Commitment converts an indeterminate bargaining situation into a determinate two-move game #expands (0.90) — Thomas C. Schelling, The Strategy of Conflict, 289
• First-mover advantage decides bargaining when commitments are costless and binding #corroborates (0.85) — Thomas C. Schelling, The Strategy of Conflict, 69
• Worsening one’s own outcomes can be strategically advantageous in mixed-motive games. #exemplifies (0.80) — Thomas C. Schelling, The Strategy of Conflict, 358
• Trust reduces future complexity by committing to a determinate future #expands (0.75) — Niklas Luhmann, Trust and Power, 138