Stag hunt vs chicken
The two "half" dilemmas. The stag hunt has fear without greed and needs assurance; chicken has greed without fear and needs allocation. The same fix works on one and backfires on the other.
Stag hunt vs chicken
Payoffs ordinal, 4 best to 1 worst, (row, column).
Stag hunt: fear, no greed.
| Column stag | Column hare | |
|---|---|---|
| Row stag | 4, 4 | 1, 3 |
| Row hare | 3, 1 | 2, 2 |
Chicken (game): greed, no fear.
| Column swerve | Column straight | |
|---|---|---|
| Row swerve | 3, 3 | 2, 4 |
| Row straight | 4, 2 | 1, 1 |
Each has one of the two ingredients of the Prisoner's Dilemma (Greed and fear). Both have two pure equilibria, but of different kinds.
| Stag hunt | Chicken | |
|---|---|---|
| Equilibria | Symmetric: all cooperate, or none | Asymmetric: one gives way, the other doesn't |
| Ranked? | Yes: all-stag is better for everyone | No: each prefers the one where the other yields |
| The problem | Trust: will the others come? | Who pays |
| Best response to others cooperating | Cooperate | Defect |
| Fix | Assurance: make the good equilibrium a focal point through custom or convention (Dixit, Skeath and Reiley, Games of Strategy, 4th ed., 2015, p. 445) | Allocation where one is enough: designate, rotate, share the cost (p. 449) |
| Effect of assurance | Solves it | Backfires: if I know you'll act, I wait |
| Effect of committing first | Reassures others | Gains: a credible refusal pushes the other to yield, though in the n-person game the rush to commit can overshoot (Taylor, The Possibility of Cooperation, 1987, pp. 39, 43) |
The two-player chicken game is mostly a fight over terms:
The essential problem in a chicken game is bargaining
— Douglas Heckathorn, "The Dynamics and Dilemmas of Collective Action" (1996), p. 258
Where they meet
- Thresholds. When a good needs a fixed number of contributors, it behaves like a stag hunt below the number (each needs assurance that enough others will come) and like chicken above it (each would rather someone else made up the number). Taylor's third n-person chicken variant has a sub-game that is an assurance game (pp. 41–43).
- Shape of the return. Heckathorn (pp. 257–258) ties an accelerating return to joining to assurance and a decelerating one to chicken.
- Cases that fit both: playground bystanders ("we'd all have stood up if we knew the others would" is a stag hunt; "one person telling a teacher is enough" is a volunteer's dilemma), and the Plataean breakout.
See also Aggregation technologies, Chicken vs prisoner's dilemma, Prisoner's dilemma vs stag hunt, Patterns of collective action.
