Stag-Hare Game, AKA Stag Hunt

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MTIME: [2025-05-03 Sat 15:30],[2024-12-25 Wed 16:03]

	Stag	Hare
Stag	a,a	d,b
Hare	b,d	c,c

where a > b > c > d. In the classical stag hunt game, players don't know what the other player will choose.

A game of positive-sum defection. There are two pure strategy Nash equilibrium for the oneshot stag-hare game: (Stag, Stag) and (Hare, Hare), and sometimes one mixed-strategy equilbrium that depends on the ratio of the payoffs:

pa + (1-p)d = p(a-d) + d pb + (1-p)c = p(b - c) + c

p(a - d) + d = p(b - c) + c p(a - b + c - d) = c -d p = c - d / (a - b + c - d)

EV = (a - d)(c - d)/(a - b + c - d) + d

Example:

	Stag	Hare
Stag	3,3	0,1
Hare	1,0	1,1

In this case the mixed-strategy is (p=1/3 Stag, 1-p=2/3 Hare). The expected payoff for the mixed strategy is 1 – equivalent to the pure Hare-only equilibrium.

Example:

	Stag	Hare
Stag	3,3	2,0
Hare	2,0	1,1

In this case the mixed-strategy is ((p=1/2 Stag, p=1/2 Hare), (p=1/2 Stag, p=1/2 Hare)). The expected payoff for the mixed strategy is 3/2.