Solution
Stag Hunt
Show the problem again
Two hunters each choose Stag or Hare. Payoffs: (Stag, Stag) = (4, 4); hunting Stag alone yields 0 while the defector hunting Hare gets 3; (Hare, Hare) = (3, 3). In the mixed-strategy Nash equilibrium, with what probability does each player hunt Stag? Express as a fraction.
Worked solution
The answer is 3/4. If the opponent hunts Stag with probability p, Stag yields 4p and Hare yields 3 regardless. Indifference requires 4p = 3, so p = 3/4. The game has two pure equilibria: (Stag, Stag) is payoff-dominant while (Hare, Hare) is risk-dominant, making it the standard model of the tension between efficiency and safety in coordination.
Source: The stag hunt, from Jean-Jacques Rousseau's 'Discourse on Inequality' (1755); formalised in the modern game-theory literature. Statement written for AxiomIQ.