Economics (Irwin Economics)
21st Edition
ISBN: 9781259723223
Author: Campbell R. McConnell, Stanley L. Brue, Sean Masaki Flynn Dr.
Publisher: McGraw-Hill Education
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Question
Chapter 14, Problem 3P
Subpart (a):
To determine
Nash equilibrium in extensive form representation.
Subpart (b):
To determine
Nash equilibrium in extensive form representation.
Subpart (c):
To determine
Nash equilibrium in extensive form representation.
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QUESTION 8
Player 1 chooses between Up and Down. Player 2 observes this, then chooses between Up and Down herself. If both players choose the same action, they both get a payoff of 1. If they choose
different actions, the player with Up gets 1 and the player with Down gets -1. How many (pure strategy) Nash equilibria are there in this game?
O 3
O 4
Consider a new card game between 2 players:
Michael (player 1) and Phyllis (player 2)
Michael is dealt two cards : O7 and 8. Phyllis is
also dealt two cards: 09 and 10. Now, each of
the players will play 1 card both at the same
time.
The payoff of Michael is 8 points if he plays a
card of opposite color (red/black) than Phyllis,
and otherwise his payoff is 10 points.
The payoff of Phyllis is 1 points if the difference
of the already played card numbers is smaller
than 4, otherwise her payoff is 5 points.
1. Find the action sets of each player
and the action profile of the game.
2. Represent the game in the Normal
form.
3. Find the Best Responses for
Michael.
4. Find the Best Responses for
Phyllis.
5. Find all the Nash Equilibriums of
the game (if any).
Newfoundland’s fishing industry has recently declined sharply due to overfish- ing, even though fishing companies were supposedly bound by a quota agree- ment. If all fishermen had abided by the agreement, yields could have been maintained at high levels. LO4
Model this situation as a prisoner’s dilemma in which the players are Company A and Company B and the strategies are to keep the quota and break the quota. Include appropriate payoffs in the matrix. Explain why overfishing is inevitable in the absence of effective enforcement of the quota agreement.
Provide another environmental example of a prisoner’s dilemma.
In many potential prisoner’s dilemmas, a way out of the dilemma for a would-be cooperator is to make reliable character judgments about the trustworthiness of potential partners. Explain why this solution is not avail-
able in many situations involving degradation of the environment.
Chapter 14 Solutions
Economics (Irwin Economics)
Ch. 14.2 - Prob. 1QQCh. 14.2 - The D2e segment of the demand curve D2eD1 graph...Ch. 14.2 - Prob. 3QQCh. 14.2 - Prob. 4QQCh. 14 - Prob. 1DQCh. 14 - Prob. 2DQCh. 14 - Prob. 3DQCh. 14 - Prob. 4DQCh. 14 - Prob. 5DQCh. 14 - Prob. 6DQ
Ch. 14 - Prob. 7DQCh. 14 - Prob. 8DQCh. 14 - Prob. 9DQCh. 14 - Prob. 10DQCh. 14 - Prob. 11DQCh. 14 - Prob. 12DQCh. 14 - Prob. 13DQCh. 14 - Prob. 14DQCh. 14 - Prob. 1RQCh. 14 - Prob. 2RQCh. 14 - Prob. 3RQCh. 14 - Prob. 4RQCh. 14 - Prob. 5RQCh. 14 - Prob. 6RQCh. 14 - Prob. 7RQCh. 14 - Prob. 8RQCh. 14 - Prob. 9RQCh. 14 - Prob. 10RQCh. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Prob. 3P
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Similar questions
- 3. Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives £20 and player 2 receives £45. If both move left, player 1 receives £15 and player 2 receives £30. If player 1 moves left and player 2 moves right, player 1 receives £40 and player 2 receives £40. a. Draw the above situation in the form of an extensive form game. b. Find the sub-game perfect Nash equilibrium of the extensive form game.arrow_forward4. Consider a three-player bargaining, where the players are negotiating over a surplus of one unit of utility. The game begins with player 1 proposing a three-way split of the surplus. Then player 2 must decide whether to accept the proposal or to substitute for player 1's proposal his own alternative proposal. Finally, player 3 must decide whether to accept or reject current proposal (it is player 1's if player 2 accepts or player 2's if player 2 offer a new one). If he accepts, then the players obtain the specified shares of the surplus. If player 3 rejects, then the players each get 0. (a) Draw the extensive form game of this perfect-information game. (b) Determine the subgame perfect NE.arrow_forwardSuppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 7 and Deborah will receive a payoff of 6. The only dominant strategy in this game is for ____ to choose ____ . The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses ____ and Deborah chooses ____ .arrow_forward
- 4 Consider an extensive game where player 1 starts with choosing of two actions, A or B. Player 2 observes player 1’s move and makes her move; if the move by player 1 is A, then player 2 can take three actions, X, Y or Z, if the move by player 1 is B, then player 2 can take of of two actions, U or V. Write down all teminal histories, proper subhistories, the player function and strategies of players in this game.arrow_forward14. You have baked a cake, but your two dear daughters won't stop fighting on who gets the biggest slice. To settle the dispute, to ask your dear daughter one (DD1) to cut the cake and your dear daughter two (DD2) to choose which piece she wants. (a) Draw the extensive form of the game. Let dear daughter one's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what is on the platter, dear daughter two's strategies might in- clude "Take Big Slice", "Take Small Slice", or "Take Equal Slice". Assign payoffs to dear daughter one and dear daughter two that grow with the size of the slice that they receive. (b) Use backward induction to find the equilibrium outcome of this game. (c) Is the promise to take a small slice by DD2, if DD1 cuts unevenly, credible? Explain carefully. (d) After the rules are announced, dear daughter two says "It is not fair! I want to be the one who gets to cut the cake, not the one who chooses the slice!". Is dear daughter two's complaint valid? You are…arrow_forwardWal-Mart's dominant strategy is to pick a price of $. Target Price = $30 Price = $17 %3D What is the Nash equilibrium for this game? $6,000 $1,500 O A. The Nash equilibrium is for Target to choose a price of $17 and Wal-Mart to choose a price of $30. Price = $30 $6,000 $11,000 O B. The Nash equilibrium is for Target and Wal-Mart to both choose a price of $30. Wal - Mart C. The Nash equilibrium is for Target to choose a price of $30 and Wal-Mart to choose a price of $17. $11,000 $4,500 Price = $17 %3D $1,500 $4,500 O D. The Nash equilibrium is for Target and Wal-Mart to both choose a price of $17. South OE. O E. A Nash equilibrium does not exist for this game.arrow_forward
- 9. For the payoff matrix below, consider a sequential version of the game in which Player 2 moves first and then Player 1 moves second. Which of the following is not a correct statement? Player 1 Top Center Bottom Left 1,2 5,1 6,0 Player 2 Middle 7,1 11,2 -4,3 Right 10,4 1,0 8,5 The subgame perfect payoffs coincide with those of a Nash equilibrium b. Depending on Player 2's move, Player 1 will sometimes optimally choose Bottom c. Player 2 will choose Right in the subgame perfect equilibrium d. Player 2 would be willing to pay a positive $ amount to move first rather than second e. Player 1 would be willing to pay a larger $ amount than Player 2 to move firstarrow_forward2. Consider the following "centipede game." The game starts with player 1 choosing be- tween terminate (T) and continue (C). If player 1 chooses C, the game proceeds with player 2 choosing between terminate (t) and continue (c). The two players choose be- tween terminate and continue in turn if the other player chooses continue until the terminal nodes with (player l's payoff, player 2's payoff) are reached as shown below. TTTT Player 1 Player 2 Player 1 Player 2 (3, 3) t (1, 1) (0, 3) (2, 2) (1, 4) (a) List all possible strategies of each player. (b) Transform the game tree into a normal-form matrix representation. (c) Find all pure-strategy Nash equilibria. (d) Find the unique pure-strategy subgame-perfect equilibrium.arrow_forwardConsider the following Extended Form Game: 0 1 O O 5 8 A' a (9,5) A P2 P1 B' A' (5,2) (8,5) B A (1,6) What payoff does player 1 derives if player 1 chooses the strategy (B,A) and player 2 chooses the strategy (A, B')? P2 B' P1 B (6,7)arrow_forward
- Consider the following game with strategies A or B for both players 1 and 2. A> 0 applies. Spieler 2 A В А| 2, а 0, 3 Spieler 1 B 3, 0 1, 1 (For the respective strategy combination, the left number corresponds to the payouts from player 1 and the right number to the payouts from player 2. Which of the following statements is correct? O 1. For a = 2 the strategy combination (A, A) is a Nash equilibrium. O 2. For all a> 0 it holds that the strategy combination (B, B) is the only Nash equilibrium. O 3. For a = 4 there are several Nash equilibria. O 4. Fora4, Aisthe dominant strategy for player 2. 5. For a = 2, player 2 has no dominant strategy.arrow_forwardQUESTION 1 Consider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? O Either 1 or 2 O Exactly 2 O Exactly 1 O None QUESTION 2 In a Cournot duopoly firm 1's best-response function is downward sloping because when firm 2 produces more: O Firm 1's marginal cost goes up, so firm 1 produces less. O Firm 1's total cost goes up, so firm 1 produces less. O Firm 1's marginal revenue goes down, so firm 1 produces less. O Firm 1's average cost goes up, so firm 1 produces less. QUESTION 3 In a pure exchange economy if the price of good x goes up, all consumers are worse off. O True O False QUESTION 4 Which of the following is true if good x is an externality exhibiting good. O Consumers consume too much good x relative to what is socially optimal. O If consumption of good x by person 1 exhibits a positive externality, then consumption of good x by person 2…arrow_forward7. Solving for dominant strategies and the Nash equilibrium Suppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 6 and Beth will receive a payoff of 5. Andrew Left Right Left 8,4 5,4 Beth Right 4,5 6,5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Andrew chooses and Beth choosesarrow_forward
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