Chicken (game)
A game where each prefers the other to give way, but mutual refusal is the worst outcome, so the equilibria have one player yielding. Also called Hawk–Dove or snowdrift.
Chicken (game)
Two drivers head for each other. Each can swerve (C) or keep going (D). Payoffs are ordinal, 4 best to 1 worst, (row, column).
| Column swerve | Column straight | |
|---|---|---|
| Row swerve | 3, 3 | 2, 4 |
| Row straight | 4, 2 | 1, 1 |
Temptation > reward > sucker > punishment (T > R > S > P). The top row is the same as the Prisoner's Dilemma: if you swerve, I'd rather not. The bottom is swapped: the crash is the worst outcome, worse than swerving alone. In terms of Greed and fear, greed but no fear.
Equilibria
- No dominant strategy. If I'm sure you'll go straight, I swerve.
- Two pure equilibria, each with one player giving way.
- One mixed equilibrium: with these numbers each swerves with probability 1/2, and the crash happens a quarter of the time.
two different conventions about the player who yields.
— Martin J. Osborne and Ariel Rubinstein, A Course in Game Theory (1994), p. 17, on Hawk–Dove
Names
Hawk–Dove (biology), snowdrift (who clears the drift; Doebeli and Hauert, Ecology Letters, 2005), brinkmanship. Osborne and Rubinstein (p. 30) note that Hawk–Dove is also known as Chicken. Heckathorn gets it from the prisoner's dilemma by reversing the two bottom payoffs ("The Dynamics and Dilemmas of Collective Action", 1996, pp. 258–259). Sandler gets it from a summation public good when doing nothing has dire consequences (Global Collective Action, 2004, p. 62). The n-person form is the Volunteer's dilemma. The course groups both, with battle of the sexes and hold-outs, as the chicken pattern (formally, the volunteer's dilemma). More aliases: Names of collective action problems.
The dynamic version is the war of attrition: each chooses when to concede (Osborne and Rubinstein p. 18, Example 18.4).
Typical failure and fix
- Failure: the good usually gets provided, but the wrong person pays: the most committed, or whoever can't credibly refuse. Waiting games, brinkmanship, the occasional crash. Committing to refuse is a weapon; Taylor (The Possibility of Cooperation, 1987, p. 43) notes that in the n-person game the rush to commit can overshoot so that nobody provides.
- Fix: where one person giving way is enough, allocate the job. Name who gives way, rotate, take turns, draw lots, or share the cost. A public random signal lets players alternate between the two equilibria (Osborne and Rubinstein p. 44, on battle of the sexes). Assurance backfires: if I know you'll swerve, I go straight.
- Where everyone acting is best for the group, chicken is fixed much like a prisoner's dilemma; for the case where some can shirk, Dixit, Skeath and Reiley suggest rotation (Games of Strategy, 4th ed., 2015, p. 449):
The roles of participants and shirkers can be rotated to equalize payoffs over time.
— Avinash Dixit, Susan Skeath and David Reiley, Games of Strategy (4th ed., 2015), p. 449
Heckathorn (p. 258) calls bargaining the essential problem in two-player chicken. That makes it feel less like collective action than the n-person volunteer's dilemma.
Cases
- Standoffs and brinkmanship; the commitment device in Dr. Strangelove.
- Taylor's two factories polluting a small lake (p. 37), and his fishery that tolerates two boats but collapses with three (pp. 43–44): chicken on the taking side.
Related
- Chicken vs prisoner's dilemma
- Stag hunt vs chicken
- Coordination game (battle of the sexes)
- Patterns of collective action
