3. (26 points) There are three students each from each of the three following departments: economics, computer science, and statistics (for a total of 9 students). They are trying to put together ideas for projects. If any of the students work alone or in a group of two or three with other students from their major, their project generates $20 each. If an econ student collaborates with either a computer science or statistics student, their team generates $50. In a collaboration of a computer science student and statistics student, $45 is generated. In a team of three consisting of a student from each major, $130 is generated. In a team of four or more, no output is generated because one person always attempts to free-ride and other team members are disheartened. (a) i. Is the allocation of $30 to each econ student, $45 to each com- puter science student, and $55 to each statistics student in the core of this game? Why or why not? ii. Find the core of this game. (b) Now suppose that there are only two econ students instead of three. i. Is the allocation of $50 to each econ student and $35 to each computer science and statistics student in the core? Why or why not? ii. Find the core of this game