About the game theory

13. A billionaire enters your classroom and plunks down $1 million on a table. He says that he's here to give away money to the least greedy person in the class. The procedure is that all 30 of the students are to write down an integer between 1 and 1,000,000. Whoever writes down the lowest number walks away with an amount of money equal to his or her number. If two or more students write down the same number, and it was the lowest among all students, then those students will equally share the amount that they wrote down. Assume each student's payoff equals how much money he or she wins. a. Assuming students play according to Nash equilibrium, how much of that $1 million does the billionaire give away? Now suppose the student who wrote down the lowest lone number receives an amount equal to that number. If there is no lone number-that is, every number submitted by a student was also submitted by at least one other student-then no money is distributed. b. Find a Nash equilibrium in which the amount paid out is $1. c. Find a Nash equilibrium in which the amount paid out is $15