Consider the following version of the Battle of the sexes, called The prince and the gold-digger. Handsome prince Bruce and ambitious young girl Sheila need to decide to go the the polo match or to the beach. Bruce prefers to go to the beach, and Sheila prefers to go to the polo match. Sheila wants to be at the same event as the prince; however, Bruce really wants to avoid gold-digger Sheila.

(a)Draw a suitable 2*2 matrix with appropriate payoffs to represent this interaction as a game.

(b)Find all the Nash equilibria of the game you have built.

(c)If you were a paparazzo hoping to photograph the prince, where would you go?

(d)Suppose the tabloid press has a mole in the prince entourage who is Sheila's friend and tells her what Bruce will do. Bruce knows this, but cannot stop it happening. What happens in this case?

(e)Would Bruce want to stop the mole leaking his choice? Compare this to the original battle of the sexes game.