A master student interested in pursuing a PhD is deciding between two courses: advanced game theory x = A and introduction to game theory x = I. The student can be one of two types: 0= L or 0= H. The PhD admission officer can observe the courses chosen by the student x = {A, I} but not the type of the student 0. Before observing the course chosen by the student, she believes both types are equally likely. She admits students only if she is sure that they are type 0 = H (that is if she believes P(0 = H|x) = 1). The student gets 10 units of utility from being admitted to a PhD and 0 units if not admitted, and pays costs c(0) if she chooses advanced game theory and costs 0 if she chooses introduction to game theory. We assume that c(H) = 0 < c(L) = 15. 1) How do we call a situation of asymmetric information in which the informed player moves first? What if the uninformed player moves first?

There are two types of (college graduate) workers in financial industry: A (able) type and C (challenged) type. Potential employers in finance will pay $160,000 a year to a type A and $60,000 to a type C. Unfortunately, employers cannot observe the worker's type while each worker knows his or her own type. However, a market research informs all employers and workers that 60% of the population is type A and 40% is type C. Additionally, it is known to everyone that the worker types differ in their tolerance for taking an analytical course rather than easy ones in college. The A types regard the cost of each analytical course as equivalent to $3,000 a year of salary, while the C types regard it as $15,000 a year of salary. Alternative employment opportunities outside of the financial industry yield the A types a salary of $125,000 and the C types a salary of $30,000. Suppose an employer in this industry use this differential to screen his applicants and tell the A types from the C types.…

A master student interested in pursuing a PhD is deciding between two courses: advanced game theory x = A and introduction to game theory x = I. The student can be one of two types: 0 = L or 0 = H. The PhD admission officer can observe the courses chosen by the student x = {A, I} but not the type of the student 0. Before observing the course chosen by the student, she believes both types are equally likely. She admits students only if she is sure that they are type 0 = H (that is if she believes P(0 = H|x) = 1). The student gets 10 units of utility from being admitted to a PhD and 0 units if not admitted, and pays costs c(0) if she chooses advanced game theory and costs 0 if she chooses introduction to game theory. We assume that c(H) = 0 < c(L) = 15. 1) What is a separating equilibrium? What does it mean in the game above? 2) What is a pooling equilibrium? What does it mean in the game above?

There are two types of workers in financial industry: A (able) type and C (challenged) type. Potential employers in finance will pay $160,000 a year to a type A and $60,000 to a type C. Unfortunately, employers cannot observe the worker's type while each worker knows his or her own type. However, a market research informs all employers and workers that 60% of the population is type A and 40% is type C. a) Assume that employers in finance treat every applicant as a random draw from the population and pay all the same salary. Then, the pooling salary is $ thousands separator). (Hint: omit the b) Alternative employment opportunities outside of the financial industry yield the A types a salary of $125,000 and the C types a salary of $30,000. If the pooling salary in a) is offered to any applicant in finance, type workers will leave the financial industry and only type workers will stay in the industry. When this continues, the salary in finance will eventually reduce to $ (Hint: omit the…

Exercise 1.4. There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or $300 of his own money or $600. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Represent this game frame with two alternative tables: the first table showing in each cell the amount of money distributed to Player 1 and the amount of money distributed to Player 2, the second table showing the change in wealth of each player (money received minus contribution). (b) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. Represent the corresponding game using a table. (c) Is there a strict dominant-strategy equilibrium?

When a new machine is functioning properly, only 6% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found. (a) Describe the conditions under which this situation would be a binomial experiment. (Select all that apply.) For each part selected, the probability of a defective part being produced must be 0.06. The parts must be selected independently. The selection of a part is dependent on the first part selected. The number of successes and failures in this experiment are equal. The probability of choosing a part that is defective must be 0.94. (b) Draw a tree diagram similar to this section's example showing this problem as a two-trial experiment. Tree Diagram Description ---Select--- ---Select--- ---Select--- ---Select--- Not Defective Defective ---Select--- Not Defective ---Select--- ---Select--- O O O 0 O