Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a manager whose preferences are represented by the following payoff function u(91, 92) = II₁ (91, 92) + aq₁ and the marked demand function is P = 1 - Q. The game is played as follows. In the first stage the owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes a and choose q₁ and q2 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium levels of a, q₁ and 92?

Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a manager whose preferences are represented by the following payoff function u(91, 92) = II₁ (91, 92) + aq₁ and the marked demand function is P = 1 - Q. The game is played as follows. In the first stage the owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes a and choose q₁ and q2 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium levels of a, q₁ and 92?

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

Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 3 units of utility, while the small rival suffers a loss of utility of 1. If the two companies select the same technology, Microsoft suffers a loss of utility of 1 while the rival gains 1 units of utility.
For various values of X(for player1 and player 2), find all Nash equilibria of the following game with von Neumann-Morgenstern preferences:
find all Nash equilibria in this game using von Neumann-Morgenstern preferences:
The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Which game (in the attachment) describes the “research and development game” properly? Remember that investment costs $6, and that this should be reflected, whenever appropriate, in the correct game matrix. (Note: Firm A chooses the row and Firm B chooses the column.)
Three firms share a market. The demand function is P(q1, 92, 93) = 10 – q1 – 92 – 93, where q; is the output of firm i, Player i. The marginal cost per unit for each firm is zero. Suppose firm 1 is a market leader, and that firm 2, and firm 3 choose q2 and q3 simultaneously after observing q1 Find the SPE of this game. How much is produced by firm 2? Numerical answer How much is produced by firm 1, 2, and 3?
Consider a variation of the television station broadcast game of Exercise 4 in Chapter 7. Suppose the stations interact sequentially. First, MBC chooses between 6:00 and 7:00. Then, after observing MBC’s choice, RBC decides between 6:00 and 7:00. Finally, after observing the behavior of both MBC and RBC, CBC chooses either 6:00 or 7:00. Payoffs are as given before. Draw the extensive form of this sequential game and compute the subgame perfect equilibrium.
Superstore (S) and Megastore (M) are two competing discount supermarkets. If neither store advertises, S makes $115 in profits and M makes $165. If both stores advertise, S makes $80 and M makes $95. If M advertises and S does not, they make $305 and $55 respectively. If S advertises and M does not, they make $285 and $65 respectively. Based on Game Theory, what will the two firms do? Hint: illustrate the Nash equilibrium to support your answer.
PLEASE CHECK THIS HOW TO SOLVE
a) Find the Nash equilibria in the game (in pure and mixed strategies) and the associated payoffs for the players. b) Now assume that the game is extended in the following way: in the beginning Player 1 can decide whether to opt out (this choice is denoted by O) or whether to play the simultaneous-move game in a) (this choice is denoted by G). If Player 1 opts out (plays O) then both Player 1 and Player 2 get a payoff of 4 each and the game ends. If Player 1 decides to play G, then the simultaneous-move game is played. Find the pure-strategy Nash equilibria in this extended version of the game. (Hint: note that Player 1 now has 4 strategies and write the game up in a 4x2 matrix.) c) Write the game in (b) up in extensive form (a game tree). Identify the subgames of this game.
For various values of X(for player1 and player 2), find all Nash equilibria of the following game with von Neumann-Morgenstern preferences:
Consider the following situation: five individuals are participating in an auction for an old bicycle used by a famous cyclist. The table below provides the bidders' valuations of the cycle. The auctioneer starts the bid at an offer price far above the bidders' values and lowers the price in increments until one of the bidders accepts the offer. Bidder Value ($) Roberto 750 Claudia 700 Mario 650 Bradley 600 Michelle 550 What is the optimal strategy of each player in this case? Who will win the auction if each bidder places his or her optimal bid? If Claudia wins the auction, how much surplus will she earn?
5