Stag Hunt

The Stag Hunt is a game theory concept that describes a situation where multiple players must cooperate to achieve a significant payoff. However, the cooperative outcome is fragile, as any individual player can choose to defect and pursue a smaller, but guaranteed, individual payoff. This creates a dilemma: while mutual cooperation yields the highest reward for everyone, the risk of being the only cooperator and receiving nothing makes defection a tempting option.

The game gets its name from Jean-Jacques Rousseau’s Discourse on Inequality, where he presents a scenario involving hunters deciding whether to cooperate to hunt a stag or individually hunt hares. Hunting a stag requires the cooperation of all hunters; if even one hunter defects to hunt a hare, the stag will escape, and the remaining hunters will receive nothing. A hare can be caught by a single hunter, providing a smaller, but certain, payoff.

Formally, the Stag Hunt is a coordination game with at least two Nash equilibria: one where all players cooperate (hunt the stag) and one where all players defect (hunt the hare). The cooperative equilibrium is Pareto-optimal, meaning no player can be made better off without making another player worse off. However, the defecting equilibrium is often considered less risky because it guarantees a minimum payoff regardless of the other players' actions.

Key characteristics of the Stag Hunt include:

• Coordination: Successful hunting of the stag depends on everyone choosing to cooperate.
• Risk Aversion: Players with a higher degree of risk aversion are more likely to choose the safe option of hunting the hare.
• Trust: The decision to cooperate hinges on the trust that other players will also cooperate. A lack of trust can lead to widespread defection.
• Payoff Structure: The stag hunt is defined by the specific payoffs associated with each outcome. The stag reward must be high enough to make cooperation appealing, but not so high that the risk of defection is unbearable. The hare reward should be low enough to incentivize cooperation, but high enough to ensure that defectors are not completely devastated.

The Stag Hunt model is used to analyze a wide range of real-world situations, including international relations, climate change negotiations, technological standards adoption, and even simple social interactions. It highlights the difficulties in achieving collective action and the importance of trust, communication, and commitment in overcoming these difficulties. The game offers insights into why seemingly beneficial cooperative endeavors often fail due to a lack of mutual confidence.