1. Three people, Dora, Ellen, and Fabian are offered to participate in a contest to win a $120 gift card. They may refuse the contest, or purchase either the gold or the silver ticket. Tickets' prices are $120 for the gold and $60 for the silver. Players make their choices simultaneously and independently. Once the ticket purchase decisions have been made, the gift card is awarded to the person with the highest cost ticket among all purchased. In case there is no such player, the gift card is split equally between those who are the highest cost ticket buyers. The gift card is not awarded to anyone when neither Dora, Ellen nor Fabian purchases a ticket.

a. Represent this game in its normal form.

b. Find all the Nash equilibria in pure strategies.

2. The contest proposer has decided to create an incentive for Dora, Ellen and Fabian to purchase the gold ticket by decreasing its price to $100. Repeat the same steps of the previous question to argue whether the contest proposer was successful in this attempt.