Question

QUESTION 5. (20 pts) Three music festivals compete for the same regional audience, Blue Heron (BH), Grey Fox (GF), and Wild Pheasant (WP). They can select a weekend in early August or in late August. The following is a normal form representation of the game (payoffs are in the order (BH, GF, WP). The organizers of these festivals make their choices independently and simultaneously. WP Early Aug. Late Aug. BHAGF Early Aug Late Aug Early Aug 16,24,30 30,23,14 Late Aug 30,16,24 14,24,32 BH GF Early Aug Early Aug 30,24,32 Late Aug 14,16,24 Late Aug 13,30,27 8,12,50 Find the rationalizable set of strategies (hint: use iterated dominance!) You can restrict your answer to pure strategies only.

Answer 1

WP will always play late  August. Thus early August can be eliminated by WP.

In second round, Early August will be played and late August will be eliminated.

After two round of elimination, early August will be eliminated.

Thus (Early August, Late August and late August) is a pure strategy Nash equilibrium