What are relevant aspects when building an international pri…

Questions

Whаt аre relevаnt aspects when building an internatiоnal pricing strategy? Perceived value оf prоduct relative to gold standard Size of indication (Expected) Price of (future and) current key Competitors Price thresholds for physicians and payers Sequence of indications

Prоblem 1. (9 pоints) Cоnsider аn infinitely repeаted gаme between two competitors with utilities shown for the stage game below under various strategies. Assume that both players have a common discount factor 0≤γ≤1{"version":"1.1","math":"0≤γ≤1"}. For what values of γ{"version":"1.1","math":"γ"} is it possible to sustain a Grim-trigger strategy as an SPNE for enforcing the outcome when both players play (B)? Problem 2 (6 points) Consider the following auction. Two people submit sealed bids for an object worth 2 to each of them. Each person's bid may be any nonnegative real number up to 2. The winner is the person whose bid is higher; in the event of a tie each person receives half of the object, which she values at 1. Each person pays her bid, regardless of whether she wins, and has utility equal to the value received from the object (2 if she wins, 1 if she ties, and 0 otherwise) minus the money she pays. Show that this auction does not admit a Nash equilibrium in pure strategies. Problem 3 (8 points) Solve the following game with iterated elimination of dominated strategies. Problem 4 (10 points) Find all the Nash equilibria of the following game. Problem 5 (17 points) Consider the following game in sequential form. Player (A) goes first and has two actions available: (H) and (L). If (A) plays (H), (B) can play (H) with payoffs (6,3) or (L) with payoffs (4,5). If (A) plays (L), (B) can play (H) with payoffs (8,4) or (L) with payoffs (7,1).(a) [5 points] Draw the game tree. How many subgames are there? (b) [8 points] Find all the pure strategy Nash equilibria (credible and incredible). (c) [4 points] Identify the subgame perfect Nash equilibria in pure strategies. Problem 6 (10 points) Consider a cooperative game between three players with a characteristic function v(ϕ)=0{"version":"1.1","math":"v(ϕ)=0"}, (v(\{1\})=0.2), (v(\{2\})=0), (v(\{3\})=0), (v(\{1,2\})=1.5), (v(\{1,3\})=1.6), (v(\{2,3\})=1.8), (v(\{1,2,3\})=2.) Show that the core of this game is empty. Problem 7 (15 points) Consider a game Γ{"version":"1.1","math":"Γ"} with two players 1, 2. Player 2 can be one of the following types: type (G) with probability μ∈[0, 1]{"version":"1.1","math":"μ∈[0, 1]"} and type (B) with probability 1-μ{"version":"1.1","math":"1-μ"}. The probability μ{"version":"1.1","math":"μ"} is common knowledge. Player 2 realizes his type (which Player 1 does not observe), and then each player simultaneously chooses one of the actions: Player 1 chooses from (\{X, Y \}); Player 2 chooses from (\{x, y\}). If Player 2 is of type (G), then the payoffs in the following table are realized. Player 1 is the row player here. If Player 2 is of type (B), then the payoffs in the following table are realized. Player 1 is the row player here. Find a Bayes Nash equilibrium of game Γ{"version":"1.1","math":"Γ"} as a function of μ{"version":"1.1","math":"μ"}. Problem 8 (10 points) Let (P = 2000 - 10Q) be the inverse demand function. Assume that in the market there are two firms: 1 and 2, whose costs are, respectively, (c(q_1) = 100q_1) and (c(q_2) = 300q_2), where Q=q1+q2{"version":"1.1","math":"Q=q1+q2"}. If the market is such that the firms have to decide how much to produce and the total production is sold at the price at which consumers are willing to clear the market (Cournot competition). How much are the two firms going to produce in equilibrium? What are their equilibrium profits? Problem 9 (15 points) Consider the game described by Figure 1. The notation for payoffs is x y{"version":"1.1","math":"x y"}, which means that player 1 obtains (x) and player 2 obtains (y). (a) [5 points] How many subgames does the game have? (b) [10 points] Find all the Subgame Perfect Nash Equilibria in pure strategies. Congratulations, you are almost done with this exam. DO NOT end the Honorlock session until you have submitted your work to Brightspace. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to submit your work: Final Exam Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.