Reference · Cheat Sheet 05
Coordination & Focal Points
Core idea: when a game has several Nash equilibria, rationality alone doesn't select among them. The question shifts from what's optimal? to how do we converge? Focal points, communication, first-mover commitment, and conventions are the selection tools.
Two types of coordination game
Pure coordination
Players want to match; roughly indifferent which equilibrium. Any salient signal solves it. Focal points and conventions work well.
Battle of the sexes
Players must match but prefer different equilibria — distributional tension overlays coordination. First-mover commitment and default-setting tend to determine who wins.
The selection toolkit
- Focal point (Schelling point). The option each player expects the other to expect — selected by salience, culture, history, or simplicity. Not necessarily the best option; just the most obviously shared one. Origin: Thomas Schelling, The Strategy of Conflict (1960).
- Communication / cheap talk. Credible and effective when interests align (both just want to pick the same thing). Loses coordination power when interests conflict — both sides claim the equilibrium they prefer, and everyone knows it.
- First-mover commitment. Publicly committing to one equilibrium forces the other side's best response — especially powerful in battle-of-the-sexes games. Announcement + credibility = the default becomes the focal point.
- Conventions and standards. Equilibria sustained by network effects and history. Disrupting them requires a coordination mechanism (critical mass, regulatory mandate, clear migration path), not just a better product.
Battle-of-the-sexes worked matrix
Referral platform choice: payoffs (You, Partner). Higher is better for each player.
|
Partner adopts A |
Partner adopts B |
| You adopt A |
(2, 1) ✓ eq |
(0, 0) |
| You adopt B |
(0, 0) |
(1, 2) ✓ eq |
- (A,A) = (2,1) — Nash equilibrium. You get the higher share. Neither player wants to switch alone: switching drops them to 0.
- (B,B) = (1,2) — Nash equilibrium. Partner gets the higher share. Same logic.
- Mismatched cells (A,B) and (B,A) are not equilibria — both players want to switch away.
- The fight is entirely distributional: whoever sets the default or commits first tends to capture their preferred equilibrium.
Cheap talk — the one-liner
Cheap talk coordinates when interests align. When interests conflict (battle of the sexes), each side claims the equilibrium it prefers — so the message carries no new information and ceases to coordinate.
Quick diagnostic
- Multiple equilibria present? → You have a coordination problem, not just a competition.
- Both prefer the same equilibrium? → Pure coordination. Find the focal point or send any credible signal.
- Each prefers a different equilibrium? → Battle of the sexes. Can you commit publicly or set the default first?
- Repeated interaction? → Convention can lock in over time — or be locked in against you if you don't move early.