9. Consider the following statements: I. Every game has at least one pure-strategy Nash equilibrium. II. If the game of rock-paper-scissors were played sequentially, the first mover would have an ad- vantage. III. Stackelberg leader can earn higher profit than a Stackelberg follower. IV. Cournot oligopoly generates higher deadweight loss the fewer firms there are in the market. V. Under Bertrand duopoly, firms selling identical goods can never earn positive profits. Which of the above statements are FALSE? (a) (I) and (II) and (III) (b) (I) and (II) and (V) (c) (I) and (IV) and (V) (d) (II) and (III) and (IV) (e) (II) and (III) and (IV) and (V) Answer: 9b.

Who first established the basic principles of game theory? Select one: a. Nash b. Bernoulli с. Кеynes d. Savage e. von Neumann Who developed a duopoly model to show how two firms compete in the price of a good they supply? Select one: a. Cournot b. Keynes c. Bertrand d. Robinson e. Chamberlain What pair provided the most complete formula for options pricing? Select one: a. von-Neumann-Morgenstern b. Black-Scholes c. Fischer Black d. Cournot-Nash e. Modigliani-Miller

11. Suppose there is a duopoly of two identical firms, A and B, facing a market inverse demand of P = 140 – 0.5Q, and cost functions of CA = 20QA and Cg = 20QB respectively. a. Find the Cournot-Nash equilibrium and profit for each firm. b. Suppose that A acts as the leader in a Stackelberg model and B responds. What are the respective quantities and profits of each firm now? Is it advantageous to move first? c. If the firms were able to collude, how much additional profit could they earn if they switch from simple single pricing to perfect price discrimination? d. Graph and label equilibria on the inverse demand.

15. Match the description provided in the bank of options with the appropriate concept in the second table. Bank of options Letter A Consumers agree X is prefered to Y when both have equal prices Consumer preferences are changed Consumers obtain more information about product characteristics Consumers are targeted with advertising Characteristic that is consumed as complementary to product itself One time cost to enter an industry changes when the market size increases A firm that is a leader obtains a higher profit in a dynamic game One time cost to enter an industry is treated as a parameter of model A firm that is a follower obtains a higher profit in a dynamic game Consumers do not agree X is prefered to Y when both have equal prices Industry with monopoly and perfect competition characteristics An empirical model used to estimate product differentiation В C E F G H I J K Concept Second mover advantage First mover advantage Vertical product differentiation Horizontal product…

3) Recently, a major question in the news is why the Afghan army collapsed so quickly and unexpectedly in the face of the Taliban offensive. To help understand the situation, consider the following simplified model of the situation. Assume that there are two Afghan soldiers in the same unit. Each can stay and fight the Taliban or desert. If both stay and fight, they will win any battle against the Taliban, which each values at 100 utility. If either soldier deserts, the Taliban wins, which they each values at 0 utility. In addition, if only one soldier stays, that soldier will be killed by the Taliban, which he values at -1000 utility. In addition, the Taliban is offering a bounty to any soldier that deserts. ne soldier does not care about this, and would not take the bounty, while the other values the bounty at 50 utility. a. Draw the game based on this scenario. b. Find all pure strategy Nash equilibria c. Find the mixed strategy Nash equilibrium d. What does this game and the…

In an oligopoly, each firm’s share of the total market is typically determined by which of the following ? Explain a. scarcity and competition. b. kinked-demand curves and payoff matrices. c. homogeneous products and import competition. d. product development and advertising