Question

		Jon is king	Daenerys is queen
Jon	Jon is king	Jon: 100 Daenerys: 50	Jon: -50 Daenerys: -50
	Daenerys is queen	Jon: -50 Daenerys: -50	Jon: 50 Daenerys: 100

1. he above game is a derivation of a popular game in economics called “battle of the sexes” or “the dating game.” In this game, Jon Snow and Daenerys Targaryen are both contenders for the Iron Throne of Westeros. Jon loves Daenerys, but wants to be king. Daenerys loves Jon, but wants to be queen. If they both try to be the ruler, it will lead to war. What is the Nash Equilibrium/Equilibria of this game?
   1. a)1 N.E.: Jon is King.
   2. b) N.E.: Dany is Queen.
   3. c)N.E.: War—Jon King/Dany Queen and Dany Queen/Jon King
   4. d) N.E.: Peace—Jon King or Dany Queen.

Answer 1

d) N.E.: Peace—Jon King or Dany Queen.

(If Jon chooses to be king, Daenerys's best response is for Jon to be the king (50).
If Jon chooses Daenerys to be queen, Daenerys's best response is for Daenerys to be the queen (100).
If Daenerys chooses Jon to be king, Jon's best response is for Jon to be the king (100).
If Daenerys chooses to be queen, Jon's best response is for Daenerys to be the queen (500).
Thus, there are two Nash equilibria. They are either for Jon to be the king or for Dany to be the queen as best response of both players occur simultaneously at these choices. So. there would be peace.)