Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Chapter 13, Problem 5E
To determine
To Ascertain:
Explain the outcome if the proposed situation in the previous query varies according to the given scenario.
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Consider the following game, where M > 0: The matrix payoff is shown below Gill Left Right James Accept 0, 0 2, −2 Reject ?, −? 1, −1 a) Do players have a dominant strategy? (b) What is the Nash equilibrium (or equilibria)? (c) Are there any values of M such there is no Nash equilibrium in pure strategy? ( d) Find the mixed strategies Nash equilibrium?
a) How many players does this game have? What are the strategies of each player?
(b) What are the Nash equilibria of this game?
(c) What are the Pareto Efficient outcomes?
(f) Does GaterTools have a dominant strategy? Explain using numbers from the payoff matrix.(g) Identify the Nash equilibrium. Explain why this is a Nash equilibrium using information from the payoff matrix.(h) Suppose HandyBilt makes a credible commitment to GaterTools that if GaterTools maintains its price, then HandyBiltwill pay GaterTools $250. Will this offer result in a Nash equilibrium with different strategies from those identified in part(g) ? Explain using numbers from the payoff matrix.
Chapter 13 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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- In the game depicted below, firms 1 and 2 must independently (no collusion) decide whether to charge high or low prices. (a) What is the Nash equilibrium for the above game? (b) If the firms were able to collude, what outcome would they settle on? (c) Is there any incentive for Firms 1 and 2 to cheat on the collusive outcome? Please explain.arrow_forward(a) Consider a ROCK PAPER SCISSOR game. Two players indicate either Rock, Paper or Scissor simultaneously. The winner is determined by: Rock crushes Scissors, Paper covers Rock, and Scissor cut Paper. In the case of a tie, there is no payoff. In the case of a win, the winner collects 5 dollars. Write the payoff matrix for this game. (b) Find the optimal row and column strategies and the value of the matrix game. 3 2 4 -2 1 -4 5arrow_forwarda) Draw an extensive form game with 4 outcomes (2 moves for player 1 followed by 2 moves for 2 after each of 1's moves) and no pure strategy Nash equilibrium. b) Write the strategic form to verify your answer to (a) c) Draw an extensive form 2-player game, in which both players always move, that has exactly 4 outcomes, 1 subgame perfect Nash equilibrium and no non-subgame perfect Nash equilibrium and no dominant strategies. d) Write the strategic form and use it to verify your answer to (b)arrow_forward
- Explain why the value of a matrix game is positive if all of the payoffs are positive. A. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c)will be negative and ad−bcwill be negative. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive. B. If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will be negative. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. C. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the…arrow_forwardFor the friend-foe game, recall that there were 3 Nash equilibria possible, but the equilibria set didn't include the cooperative outcome, for which both players would win. Friend Foe Friend 500,500 0,1000 Foe 1000,0 0.0 a) If the game is played répeatedly. propose a play strategy that will enforce cooperation. For what valucs of o (discount factor) the equilibrium will be (Friend. Friend)?arrow_forwardConsider a bankruptcy game with two risk neutral players where V =$800,000, C1= $300,000 and C2=$800,000. a) What is the Nash bargaining solution?arrow_forward
- Refer to the payoff matrix in question 8 at the end of this chapter. First, assume this is a one-time game. Explain how the $60/$57 outcome might be achieved through a credible threat. Next, assume this is a repeated game (rather than a one-time game) and that the interaction between the two firms occurs indefifi nitely. Why might collusion with a credible threat not be necessary to achieve the $60/$57 outcome?arrow_forwardif Y = 4 (a) If ⟨a,d⟩ is played in the first period and ⟨b,e⟩ is played in the second period, what is the resulting (repeated game) payoff for the row player? (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?arrow_forwardThe payoff matrix below shows the payoffs for Firm A and Firm B, each of whom can either "cooperate" or "cheat." The numbers in parentheses are (payoff for A, payoff for B). Firm B Cooperate Cooperate (30, 30) (x, 10) Cheat (10, X) (20, 20) Firm A Chent If x = 40, the Nash equilibrium is. O a. (Firm A: cheat, Firm B: cheat) O b. (Firm A: cooperate, Firm B: cheat) O c. (Firm A: cheat, Firm B: cooperate) O d. (Firm A: cooperate, Firm B: cooperate) O e. There is no Nash equilibrium for this value of x.arrow_forward
- Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.arrow_forwardSolve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.arrow_forward(a) Assuming that each fishery chooses fi ∈ (0,F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? (c) Suppose that a benevolent social planner wants maximize the util- ity of both fisheries. In other words, the social planner solves the following problem: max w(f1, f2) = u1(f1, f2) + u2(f1, f2) (f1 ,f2 )= 2ln(f1)+2ln(f2)+2ln(F −f1 −f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?arrow_forward
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