Coordination Game
A coordination game is a two-player game in which both players earn more when they choose the same option than when they choose different ones. It has at least two pure Nash equilibria, one for each shared choice, so the difficulty is agreeing on which option to pick, not whether to cooperate.
Payoff matrix
| Row player (rows) / Column player (columns) | Option A | Option B |
|---|---|---|
| Option A | (5, 5) Nash equilibrium | (0, 0) |
| Option B | (0, 0) | (4, 4) Nash equilibrium |
Payoffs are ordinal scores from the DecisionPlay engine's template for this game, 0 to 5, higher is better. They rank outcomes and are not dollar values. [MODELED]
Nash equilibria
- Pure: Row player plays Option A, Column player plays Option A. Payoffs (5, 5).
- Pure: Row player plays Option B, Column player plays Option B. Payoffs (4, 4).
- Mixed: Row player plays Option A 44.4%, Option B 55.6%; Column player plays Option A 44.4%, Option B 55.6%. Expected payoffs (2.22, 2.22).
Computed by the DecisionPlay solver from the matrix above. [MODELED]
Where it shows up
Illustrative
- Which side of the road to drive on. Each driver does best by matching the other, and either convention works as long as everyone follows the same one.
- Adopting a common standard. Two firms whose products must work together each gain when both adopt the same technical standard, whichever of the compatible standards it is.
Common misreadings
- All equilibria are equally good. Equilibria can differ in payoffs. A less efficient equilibrium can persist because no player gains by switching alone.
- Rational players will automatically pick the best equilibrium. Rationality alone does not select among equilibria. Communication, convention, or a focal point is what usually settles the choice.
Try it
Map your own scenario or edit a payoff matrix in the solver.