Question

The matrix below shows payoffs in a stag hunt game. If both hunters hunt stag, each gets a payoff of 4. If both hunt hare, each gets 3. If one hunts stag and the other hunts hare, the stag hunter gets 0 and the hare hunter gets 3.

Hunter B

hunt stag hunt hare

hunt stag 4,4 0,3

Hunter A

hunt hare 3,0 3,3

(a) If you are sure that the other hunter will hunt stag, what is the best thing for you to do? (b) If you are sure that the other hunter will hunt hare, what is the best thing for you to do?

(c) Does either hunter have a dominant strategy in this game? If so, what is it? If not explain why not. (d) This game has two pure strategy Nash equilibria. What are they?

(e) Is one Nash equilibrium better for both hunters than the other? If so, which is the better equilibrium?

Answer 1

A) payoff matrix

	Stag	hare
Stag	(4*,4•)	(0,3)
Hare	(3,0)	(3*,3•)

If other hunts stag, best option for you is to hunt stag.

Bcoz higher payoff is with hunting stag

B) if other hunts hare, then best thing is for you is to hunt hare

C) no one has dominant strategy.

Bcoz if column player hunts stag, then it's best for row player to hunt stag

, Now if column player hunts hare, then row player will hunt hare.

Similarly for row player

thus no one has dominant strategy

.

d) two NE

( Hunt stag, hunt stag)

& (Hunt hare, hunt hare)

.

e) yes, if both hunts stag , both get higher payoff = 4

While with both players hunting hare, each gets = 3

so better NE:

( Hunt stag, hunt stag)

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