There is a project for which player 1 can exert effort e ≥ 0 that costs her c(e) = 0.5e². If player 1 and player 2 can come to an agreement, then a total value of v(e) = e is produced, which can be allocated between the two players. Effort also produces a value y(e) = ke, where k = [0, 1], that player 1 can obtain for herself if player 1 and 2 fail to agree. The game has three stages: (I stage) Player 1 chooses effort e ≥ 0; (II Stage) Player 2 observes e and chooses and effort level a = [0, 1]; (III stage) Player 1 observes a and either agrees (a) or rejects (r) the offer. If player 1 accepts the offer, then her payoff is ae - 0.5e² and player 2's payoff (1-a)e. If she rejects the offer, then player 1's payoff is ke - 0.5e² and player 2's payoff is zero. • What is the subgame perfect equilibrium effort choice? • Suppose that player 2 can choose k € [0, 1] before the above game is played. What would he choose? What would be the equilibrium effort? • Suppose now that the government, rather than player 2, can choose k before the above game is played. Assuming that the government aims to maximize total welfare e - 0.5e², what value of k would it choose? What would be the equilibrium effort?

There is a project for which player 1 can exert effort e ≥ 0 that costs her c(e) = 0.5e². If player 1 and player 2 can come to an agreement, then a total value of v(e) = e is produced, which can be allocated between the two players. Effort also produces a value y(e) = ke, where k = [0, 1], that player 1 can obtain for herself if player 1 and 2 fail to agree. The game has three stages: (I stage) Player 1 chooses effort e ≥ 0; (II Stage) Player 2 observes e and chooses and effort level a = [0, 1]; (III stage) Player 1 observes a and either agrees (a) or rejects (r) the offer. If player 1 accepts the offer, then her payoff is ae - 0.5e² and player 2's payoff (1-a)e. If she rejects the offer, then player 1's payoff is ke - 0.5e² and player 2's payoff is zero. • What is the subgame perfect equilibrium effort choice? • Suppose that player 2 can choose k € [0, 1] before the above game is played. What would he choose? What would be the equilibrium effort? • Suppose now that the government, rather than player 2, can choose k before the above game is played. Assuming that the government aims to maximize total welfare e - 0.5e², what value of k would it choose? What would be the equilibrium effort?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Let G₁, G₂ and G3 be the following games. Colin A B Rose A (10,3) (7.5) B (6,6) (8,4) G₁ Rose Rose Colin A Colin A B A (5,8) (4.2) B (9.2) (3,5) G₂ B (3,6) A (4,4) B (5.3) (2,7) G3 Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution.
Which of the above 4 statements is CORRECT?
Consider the following game in extensive form, involving the chance parameter p. PT] =P (0,0) N Answer: U P[H] = 1-p h B P[T] = P h d (-60,60) (20,-20) (40,-40) t (0,0) N P[H] = 1-p (0,0) Suppose that p = 0.75 and the strategy profile (u, h) is played. What expected payoff does player B receive? (Report your answer in decimal form, rounding if necessary to two places.
No hand written solution and no image
Two employees witness fraud committed in their firm. Each has two pure strategies: to become a whistleblower and report a crime, or not to report a crime. Each employee gets a payoff of 1 if the crime is reported by someone (it does not matter if both or only one employee reports). However, reporting the crime is costly. An employee who reports has to pay the cost of reporting equal to 0.5-0.25*d, where d=1 if the other employee also reports, and d=0 otherwise. Suppose that employees simultaneously decide to report or not. There is a unique mixed strategy Nash equilibrium in this game where each employee reports with the same positive probability less than 1. What is the probability that the crime is reported by at least one employee in such an equilibrium? ________
Two hotels are considering a location along a newly constructed highway through the desert. The highway is 500 miles long with an exit every 50 miles (including both ends). The hotels may choose to to locate at any exit. These will be the only hotels for any traveler using the highway. Each traveler has their own most preferred location along the highway (at some exit) for a hotel, and will choose to go the hotel closest to that location. Travelers most preferred locations are distributed evenly, so that each exit has the same number of travelers who prefer that exit. If both hotels are the same distance from a traveler's most preferred location, then that traveler flips a coin to determine which hotel to stay at. A hotel would each like to maximize the number of travelers who stay at it. If Hotel 1 locates at the 100 mile exit, where should Hotel 2 locate? Given Hotel 2's location that you just found, where would Hotel 1 prefer to locate? Which pairs of locations form Nash equilibria?
Consider the following game 1\2 Y Z A 10,3 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (9/10,1/10) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, player 2 should respond by playing _____
A recently discovered painting by Picasso is on auction at Sotheby's. There are two main bidders Amy and Ben {1,2}. Bidding starts at £10M but the value of the painting is certainly not more than £20M. Each bidder's valuation v; is independently and uni- formly distributed on the interval [10M, 20M], and this is common knowledge among the players: A bidder knows their own valuation but not of their opponent. Consider an auction where an object is allocated to the highest bidder but the price paid by the bidder is determined randomly. With probability 3/4, the bidder pays their own bid, and with probability 1/4 the bidder pays the losing bid. The person bidding lowest pays nothing. If the bids are equal, each bidder gets the object with probability one-half, and in this case, pays their bid. Suppose that bidder 1 assumes that bidder 2 will bid a constant fraction, 7, of bidder 2's valuation (and similarly, bidder 2 assumes bidder 1 will bid the same constant propor- tional value of…
Consider two players, designated by i = 1,2, involved in a dynamic bargaining over a perfectly divisible surplus of size 1. At the beginning of the interaction (at timet 1), player 1 chooses x1 in [0, 1]. Player 2 observes this offer and decides whether or not to accept it. If player 2 accepts this offer, the game ends and the utilities of player 1 and 2 equal x1 and 1- x1, respectively. If player 2 does not accept this offer, the game goes into the second round with a probability of \pi = 2|1/2-x11, while with probability 1 -\ pi the game ends and both players get a payoff of 0. If the game reaches the second round, t = 2, player 2 makes a counter-offer x2 in [0, 1] observing the whole past. Player 1 sees this offer and decides whether or not to accept it. If player 1 accepts x2, then the game ends and player 1 gets a payoff of x2 and player 2 a utility of 1 - x2. Both players get a payoff of zero when player 1 rejects player 2's offer x2 and the game ends. We assume that the game is…
(b) Assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game?
Two workers independently choose how much effort to put in their jobs. If worker 1 chooses e₁ ≥ 0 and worker 2 chooses e2 ≥ 0, their payoffs are given by u₁(e₁,e2,01,02) = 0₁e₁ + ße₁e₂ · - 1/² u₁ (e₁,e₂,0₁,0₂) = 0₂ €₂ + ßе₁e₂. = ²2 where 0 <ß < 1 and 0 ≤ 0; ≤ 1 for i: = 1,2. Assume that 0; is player i's private information: each player knows her own 0 and believes that the other player's 0 is drawn from the uniform distribution over [0, 1]. Find the Bayesian Nash equilibria of this game.
In the following decision tree, what choices should player 1 make?