Lionheart and Emilia have the same favorite place to pitch his/her tent on Playa del Confital in Las Palmas de Gran Canaria. When they arrive to the beach to built their tents they get into a generosity argument. Each of them wants to leave the best spot for the other. Each of them commits self on how long to argue for and the one who finishes arguing first will get convinced to take the favorite spot to build tent (if both finish arguing simultaneity, then they flip a coin). Each of them gets 10 utility points if (s)he convinces the other to take the best spot, and loses 1 utility point in each minute of arguing. (For example, if Emilia takes the spot, then Lionheart gets 10 utility points, while Emilia gets 0 utility points.)

(a)Describe the set of actions of each player and the utility function of each player. What is the Nash equilibrium in this game?