Chicken
Chicken is a two-player game in which each player prefers to hold firm while the other backs down, but if both hold firm the result is the worst outcome for both. It has two pure Nash equilibria, in each of which one player yields, and a mixed equilibrium in which both sometimes risk the crash.
Payoff matrix
| Row player (rows) / Column player (columns) | Back down | Hold firm |
|---|---|---|
| Back down | (3, 3) | (1, 5) Nash equilibrium |
| Hold firm | (5, 1) Nash equilibrium | (0, 0) |
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 Back down, Column player plays Hold firm. Payoffs (1, 5).
- Pure: Row player plays Hold firm, Column player plays Back down. Payoffs (5, 1).
- Mixed: Row player plays Back down 33.3%, Hold firm 66.7%; Column player plays Back down 33.3%, Hold firm 66.7%. Expected payoffs (1.67, 1.67).
Computed by the DecisionPlay solver from the matrix above. [MODELED]
Where it shows up
Illustrative
- Two drivers on a collision course. The textbook origin: each driver prefers that the other swerve, but if neither swerves both crash.
- A market that fits one entrant. Two firms can each enter a market that is profitable for only one. If one stays out the other profits; if both enter, both lose money.
Common misreadings
- Both players should hold firm. Mutual holding firm is the worst outcome for both players and is not an equilibrium. In each pure equilibrium exactly one player yields.
- Whoever is more stubborn always wins. Commitment helps only when the other player believes it and can observe it. A commitment the other side does not believe or cannot see changes nothing.
- Chicken is the same as a Prisoner's Dilemma. Neither player has a strategy that is best whatever the other does, and there are two pure equilibria instead of one.
Try it
Map your own scenario or edit a payoff matrix in the solver.