Chicken Game / Anti-Coordination Game

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Chicken Game / Anti-Coordination Game

• Players: Player 1 and Player 2.
• Strategies: Each player chooses Straight (ST) or Swerve (SW).
• Rules: Players move simultaneously without observing the other’s choice.

Payoff Details

• ST wins against SW.
• Mutual ST causes the crash outcome.

Payoff Matrix

Derivation (Best Response Analysis)

Player 1

• If Player 2 chooses ST, Player 1 compares $-1$ with $1$, so $BR_1(\text{ST})=\text{SW}$.
• If Player 2 chooses SW, Player 1 compares $2$ with $0$, so $BR_1(\text{SW})=\text{ST}$.

Player 2

• If Player 1 chooses ST, Player 2 compares $-1$ with $1$, so $BR_2(\text{ST})=\text{SW}$.
• If Player 1 chooses SW, Player 2 compares $2$ with $0$, so $BR_2(\text{SW})=\text{ST}$.
• Mutual best responses occur at (ST,SW) and (SW,ST).

Nash Equilibrium

Result:

The pure-strategy Nash equilibria are:

Social Optimum

• Total payoff at (ST,SW) and (SW,ST) is $3$.
• The two pure equilibria are socially optimal.

Insights

Insight:

• Chicken has two asymmetric pure equilibria.
• Anti-coordination drives the game: each player wants the other to yield.
• Mutual commitment to ST is dangerous because both players receive the crash payoff.