Stag Hunt

Definition

The stag hunt is a game theory scenario that illustrates the tension between safety and social cooperation. In this game, two players can either choose to hunt a stag together, which requires mutual cooperation for success, or they can hunt a hare individually, which guarantees a smaller but certain payoff. The stag hunt highlights the concept of Nash equilibrium as both players benefit more when they work together, but each may be tempted to act in their self-interest, leading to different possible outcomes.

5 Must Know Facts For Your Next Test

1. In a stag hunt, if both players choose to hunt the stag and succeed, they receive a higher payoff than if they had chosen to hunt hares.
2. If one player chooses to hunt a hare while the other hunts a stag, the hare hunter will receive a payoff while the stag hunter will end up with nothing, creating a risk for cooperation.
3. The stag hunt demonstrates that communication and trust between players are crucial for achieving the optimal outcome of mutual cooperation.
4. The stag hunt can lead to multiple Nash equilibria: one where both players cooperate and hunt the stag, and another where both players choose the safer option of hunting hares.
5. In repeated stag hunt scenarios, players may develop strategies that foster cooperation over time, increasing the likelihood of achieving higher payoffs.

Review Questions

• How does the stag hunt illustrate the conflict between individual interests and collective benefit?
  • The stag hunt shows that while individuals may gain more by working together to hunt the stag, the fear of being left empty-handed can lead them to prioritize their own safety by hunting hares instead. This conflict creates a dilemma where mutual cooperation is the most beneficial outcome, yet individual self-interest can derail this cooperation. Thus, players must weigh their desire for collective success against the temptation of guaranteed but lower individual rewards.
• Discuss how the concept of Nash equilibrium applies to the outcomes of the stag hunt game.
  • In the stag hunt game, Nash equilibria exist at both extremes: when both players cooperate and successfully hunt the stag or when both choose to hunt hares. If both opt for hares, neither player can improve their outcome by unilaterally changing their strategy. Similarly, if both decide to cooperate on the stag hunt, they maximize their payoffs collectively. However, if one player deviates from cooperation while the other remains committed to hunting a stag, this leads to an inefficient outcome for that player. Understanding these equilibria helps explain players' decision-making processes in scenarios characterized by trust and risk.
• Evaluate how repeating the stag hunt game could change player behavior and influence cooperation over time.
  • In repeated stag hunts, players have opportunities to build trust and establish patterns of cooperation that may not be present in a one-time interaction. Through repeated play, individuals may adopt strategies that favor long-term collaboration over short-term gains. This can lead to a stable environment where players increasingly choose to hunt stags due to their past experiences of mutual success. Additionally, social norms and expectations can evolve as players witness cooperative behavior rewarded over time, thereby enhancing overall outcomes in future games.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Cooperative Game: A game where players can form coalitions and negotiate joint strategies to improve their payoffs.

Pareto Efficiency: A state in which resources are allocated in the most efficient manner, meaning that any change would make at least one player worse off.