3. Three game theorists work on a team project. Assume they work independently, and it is not possible for them to monitor each other. No one likes working, and the cost of efforts is measured in dollars. Each player can work up to 5 hours, and the cost per working hour is 5 euros. The quality and hence the prot of the project is determined by the joint efforts (total number of working hours) of the three players. For each additional hour that the team invests in the project, up to 10 hours, the total prot will increase by 15 euros. After 10 hours, efforts will not increase prots. Assume players divide the prot equally among them. Hence, ea ch player's payoff is his share of the prot minus his cost. There is common knowledge of rationality. i. Write up this scenario formally as a game. ii. Compute the set of rationalizable effort levels for each player. Provide a reasonable belief for which each effort level can be rationalized. iii. Calculate the best responses of the players considering only pure strategies. iy. Find the Nash equilibria in pure strategies if they exist