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. BH\GF Early Aug Late Aug Early Aug 30,24,32 14,12,24 Late Aug 13,30,27 8,16,50 BH\GF Early Aug Late Aug Early Aug 16,24,30 30,23,14 Late Aug 30,16,24 14,24,32 Find the rationalizable set of strategies (hint: use iterated dominance!). You can restrict your answer to pure strategies only.

Answer 1

Wild pheasant dominant strategy is ‘Early August’. Thus wild pheasant will eliminate Late August

BLue Heron will eliminate Late August. As Blue Heron has strictly dominated strategy as Early August after 1st round of elimination.

Similarly Grey Fox will eliminate Early August

Thus (Early August, Late August, Early August) is a nash  equilibrium after elimination of three round.