Two individuals are in negotiations to terminate a contract. Person A, was the signatory to the control that she had to execute in partnership with Person B and is in possession of the pay- out. The contract is worth R1 000. The mediator asks Person A to choose how much of this contract value she is willing to offer person B. Person B, will then be asked to decide whether to accept the offer or reject it. If Person B rejects the offer, neither player receives any money. Using table or decision tree illustrate the possible payoffs. Determine if Nash equilibrium exist.

Two individuals are in negotiations to terminate a contract. Person A, was the signatory to the control that she had to execute in partnership with Person B and is in possession of the pay- out. The contract is worth R1 000. The mediator asks Person A to choose how much of this contract value she is willing to offer person B. Person B, will then be asked to decide whether to accept the offer or reject it. If Person B rejects the offer, neither player receives any money. Using table or decision tree illustrate the possible payoffs. Determine if Nash equilibrium exist.

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

An object is sold in a first-price auction – thus, the highest bidder wins the object and price is equal to the highest bid. There are two bidders, an "Odd" bidder (player 1) and an "Even" bidder (player 2). The odd bidder must bid an odd integer between 1 and 9, while the Even bidder must bid an even integer between 2 and 10. (So the strategy sets are {1,3, ...,9} and {2,4, ..., 10}.) The value of the object to the Odd bidder is 8, and value of the object to the Even bidder is 7. The payoff to the winner is the value of the object minus the price, and the payoff to the loser is 0. (a) Write the game in its strategic form. (b) Find all Nash equilibria.
Two travelers own an identical suitcase that contains identical antiques. The airline is liable for a maximum of $100 per suitcase. To determine how much to reimburse each traveler, the airline puts them in different rooms (so that they cannot communicate), and ask them to write down an amount (an integer number) between $2 and $100. If both write down the same number, the airline will reimburse both travelers that amount. However, if the two amounts are different, both travelers will be paid the lowest of the two numbers along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount. What are the travelers’ best response functions? What are the Nash equilbria of the game? Are they Pareto efficient? Explain the intuition why.
P1| P2 Left Middle Right Left 4,2 3,3 1,2 Middle 3,3 5,5 2,6 Right 2,1 6,2 3,3 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played in the first period, followed by (Left, Left). e) (Middle, Middle) is played in the first period, followed by (Right, Right).
Question 4 Consider allocating an object to one of two players when each player's pref- erences are her private information. Player 1's value for the object, denoted by vị is drawn from a continuous distribution with (1. 2] as its support. Player 2's value for the object, denoted by v2, is likewise drawn from the interval 0, 1]. 1. What is the equilibrium in dominant strategies if a second price auction is used to allocate the object. Is the outcome ex-post efficient? 2. For what pairs (v1, v2) should Player 1 and Player 2 respectively be allocated the object in a mechanism that maximizes expected revenue for the seller? 3. Comment on the differing allocations you obtained in the previous two parts.
Brown’s TV Production is considering producing a pilot for a comedy series for a major network. While the network may reject the pilot and series, it may also purchase the program for 1 or 2 years. Brown may produce the pilot or transfer the rights for the series to a competitor for $100,000. Brown’s profits are summarized in the following payoff table (profits in thousands). sate of nature reject 1 year 2 years produce pilot -100 50 150 sell to competitor 100 100 100 If the probability estimates for the states of nature are, P(reject)=0.20, P(1 year)=0.30, and P(2 years)=0.5, what is the maximum Brown should be willing to pay for inside information on what the network will do?
A country’s market for new motor vehicles is dominated completely by two firms, Fastcars Ltd and Slowcars Ltd. Market revenue is fixed at $10 billion. Each firm can choose whether to advertise. Advertising costs $1 billion for each firm that advertises. If one firm advertises and the other does not, then the firm that advertises receives 100% of market revenue and pays for its advertising. If both firms advertise, they split the market revenue 50:50 and pay for their respective advertising. If neither advertises, they split the market revenue 50:50 but without the expense of advertising. a) What strategy would you advise that Fastcars Ltd should follow? b) What would you predict will be the strategy chosen by each firm? c) Is there an outcome that would make both firms better off? In case you find that there is such an outcome, is it achievable?
Problem 4: Consider an infinitely repeated game, where the base game is the following 2-person 2x2 game: A A 0,0 10, 10 S1: choose A always S2: choose B always B 10, 10 0,0 Assume both players discount the future at the same rate of r, 0 < r < 1. Limiting each player's strategies to the following six possibilities, S3: Choose A then mimic the other player's previous choice S4: Choose B, then mimic the other player's previous choice S5: Choose A, then choose the opposite of the other player's previous choice S6: Choose B, then choose the opposite of the other player's previous choice a. present the strategic form of this game, b. identify all pure-strategy Nash equilibria c. does repetition with these strategies "solve" the coordination dilemma that confronts the players in the single play of the above game.
During a grand prix car race with 20 competitors, Driver 1 and Driver 2 are currently in 1st and 2nd place, respectively, Driver 2 is catching up to Driver 1, and is thinking about overtaking Driver 1 on the next corner. Driver 1 has two strategies: Driver 1 can either "BLOCK" Driver 2 from overtaking, or "ALLOW" Driver 2 to overtake. Driver 2 (currently in second place) also has two possible strategies: Driver 2 can either try to "OVERTAKE" Driver 1, or "STAY" in 2nd place. Both drivers desperately want to win, but unsuccessful overtaking wastes fuel and increases the risk of falling behind other drivers in the race. Blocking manoeuvres can increase a driver's lead if the other driver decides to stay back, but these manoeuvres can also damage the car if another driver is trying to overtake. The only situation under which Driver 1 will be overtaken by Driver 2 is if Driver 2 attempts to overtake and Driver 1 allows it. The resulting payoff matrix for these various strategies is shown…
Player A and B each announce a color (red, white, blue, or green) simultaneously. The winner is determined by the following rules: red beats white, white beats blue, blue beats green, and green beats red. If both players announce the same color the game is a draw. The payoffs work as follows, if player A wins with red, she wins 5, if player A wins with white or blue, she wins 2, and if player A wins with green, she wins 3. If player B wins with red or white, he wins 4, if player B wins with blue he wins 3, and if player B wins with green he wins 5. The above description leaves out the cases where players announce colors that are not directly comparable. For example, there is no rule for what happens if one player announces white and the other announces green. In these situations, the winner is determined by examining the number of letters in each color that is announced. If both colors have the same number of letters, then the game is a draw. If there are a different number of letters…