Stag Hunt

Paul Bril - Chasse au cerf (Louvre)

Stag Hunt is a concept from game theory, a branch of mathematics and economics that studies strategic interactions with formalized incentive structures. The Stag Hunt scenario, often attributed to the philosopher Jean-Jacques Rousseau, illustrates a situation where individuals must choose between cooperation for a significant mutual benefit and acting alone for a lesser, but guaranteed, personal benefit.

Overview

In the Stag Hunt, two hunters can either jointly hunt a stag (an endeavor that requires mutual cooperation to succeed) or individually hunt a rabbit (an act that can be accomplished alone but yields a lesser reward). If one hunter goes for the stag while the other hunts a rabbit, the stag hunter will fail, receiving no payoff, while the rabbit hunter secures a small reward. The dilemma arises because hunting the stag represents the best collective outcome (cooperation), but it involves a risk if the other hunter chooses to defect (hunt the rabbit).

Formal Representation

In game theory, the Stag Hunt is represented as a game with two strategies: "Stag" (cooperate) and "Rabbit" (defect). The payoffs for each player depend on the strategies chosen by both. Typically, the payoff matrix looks something like this:

	Stag	Rabbit
Stag	(A,A)	(C,B)
Rabbit	(B,C)	(D,D)

Where:

• A > D > B > C
• A is the payoff for both hunters if they both choose Stag.
• D is the payoff for both hunters if they both choose Rabbit.
• B is the payoff for a hunter who chooses Rabbit when the other chooses Stag.
• C is the payoff for a hunter who chooses Stag when the other chooses Rabbit.

Applications

The Stag Hunt is used to model various social and economic situations involving coordination and trust, such as:

• Public goods provision, where individuals must decide whether to contribute to a collective benefit or free-ride on the efforts of others.
• Social norms and their enforcement, where individuals must decide whether to comply with a norm or deviate for personal benefit.
• Political science scenarios, such as arms races or treaty compliance, where the decision to cooperate or defect has significant implications.

Philosophical Implications

The Stag Hunt has been used to explore philosophical questions about the nature of society, cooperation, and trust. Rousseau used it to illustrate the social contract as a solution to collective action problems, where individuals forsake personal interests to achieve a greater common good.

See Also

• Prisoner's Dilemma
• Nash Equilibrium
• Coordination Game
• Public Goods Game

Stag Hunt Resources
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