PLEASE CHECK THIS HOW TO SOLVE PLEASE TEACH EXPLAIN STEP BY STEP EXAMPLE 176.2 (A synergistic relationship) Consider a variant of the situation inExample 39.1, in which two individuals are involved in a synergistic relationship.Suppose that the players choose their effort levels sequentially, rather than simul-taneously. First individual 1 chooses her effort level a₁, then individual 2 choosesher effort level a2. An effort level is a nonnegative number, and individual i's pref-erences (for i = 1, 2) are represented by the payoff function a¡(c+a; − a;), where jis the other individual and c> 0 is a constant.To find the subgame perfect equilibria, we first consider the subgames of length1, in which individual 2 chooses a value of a2. Individual 2's optimal action afterthe history ay is her best response to a₁, which we found to be. (c + a₁) in Exam-ple 39.1. Thus individual 2's strategy in any subgame perfect equilibrium is thefunction that associates with each history a₁ the action (c+a₁).Now consider individual 1's action at the start of the game. Given individ-ual 2's strategy, individual 1's payoff if she chooses a₁ is a₁(c +(c + a₁) -a₁),or a₁ (3c-a₁). This function is a quadratic that is zero when a₁ = 0 and whena₁ = 3c, and reaches a maximum in between. Thus individual 1's optimal actionat the start of the game is a₁ = c.. We conclude that the game has a unique subgame perfect equilibrium, in whichindividual 1's strategy is a₁ = 3c and individual 2's strategy is the function thatassociates with each history at the action (c+a₁). The outcome of the equilibriumis thåt individual 1 chooses a₁ = 3c and individual 2 chooses a2 = c.

There are 2 playersPlayer 1 and player 2The game is a sequential game. It is not a simultaneous…

EXAMPLE 176.2 (A synergistic relationship) Consider a variant of the situation in Example 39.1, in which two individuals are involved in a synergistic relationship. Suppose that the players choose their effort levels sequentially, rather than simul- taneously. First individual 1 chooses her effort level a₁, then individual 2 chooses her effort level a2. An effort level is a nonnegative number, and individual i's pref- erences (for i= 1, 2) are represented by the payoff function a; (c +a; - a;), where j is the other individual and c> 0 is a constant. To find the subgame perfect equilibria, we first consider the subgames of length

EXAMPLE 176.2 (A synergistic relationship) Consider a variant of the situation in Example 39.1, in which two individuals are involved in a synergistic relationship. Suppose that the players choose their effort levels sequentially, rather than simul- taneously. First individual 1 chooses her effort level a₁, then individual 2 chooses her effort level a2. An effort level is a nonnegative number, and individual i's pref- erences (for i= 1, 2) are represented by the payoff function a; (c +a; - a;), where j is the other individual and c> 0 is a constant. To find the subgame perfect equilibria, we first consider the subgames of length

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

ASAP Please! In a variation of the coin game, there are 22 coins. Two players take turns and take between 1 and 3 coins each time. The player who takes the last coin loses the game. We may consider this a sequential game and thus could model this using an extensive form game. To win this game, the first mover should take Group of answer choices А.2 coins В.1 coin C. Any number, because no matter what, the first player loses the game D.3 coins
Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.
Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?
Jesse and Janie are playing a game. On the table in front of them, there are 50 coins. They take turns removing some of these coins from the table. At each turn, the person moving can remove either 1,2,3,4,5,6, or 7 coins (they cannot remove 0 or 8, etc.). The person to remove the last coin wins. Suppose Janie is the first player to have a turn (a) In the subgame perfect equilibrium, Janie begins by taking _________coins (b) Suppose Janie makes a mistake in play and removes a number of coins that leaves 27 coins on the table when it is jesses turn. To have a chance at winning, Jesse should remove _________ Coins
Consider the following extensive form game between player 1 and player 2. T B (2, 2) L R R (3, 1) (0, 0) (5, 0) (0, 1) (a). Find the normal form representation of this game. (show the bimatrix) (b). Find all pure strategy NE. (c). Which of these equilibria are subgame perfect?
$11. Anne and Bruce would like to rent a movie, but they can't decide what kind of movie to get: Anne wants to rent a comedy, and Bruce wants to watch a drama. They decide to choose randomly by playing "Evens or Odds." On the count of three, each of them shows one or two fingers. If the sum is even, Anne wins and they rent the comedy; if the sum is odd, Bruce wins and they rent the drama. Each of them earns a payoff of 1 for winning and 0 for losing "Evens or Odds." (a) Draw the game table for "Evens or Odds." (b) Demonstrate that this game has no Nash equilibrium in pure strategies.
Two workers are on a production line. They each have two actions: exert effort, E, or shirk, S. Effort costs a worker e > 0 and shirking costs them nothing. If two workers do action E a lot of output is produced and the workers earn £3 each. If only one worker chooses action E less output is produced and they both earn £1. The workers earn nothing if they both shirk. (i) Describe this situation as a strategic form game (assuming the workers do not observe each other's effort choice when making their own decision). (ii) For what values of e does this game have strictly dominant strategies? (iii) Describe the Nash equilibria of this game for e = 0,1, 2, 3. (iv) The workers now are re-arranged into a production line. First worker 1 moves and then worker 2 moves. Worker 2 can now see worker l's effort level before they choose their effort. Draw this extensive form game. (v) Find the subgame perfect equilibria of the production-line game for c = 1/2 and c = 3/2.
In the movie Rebel Without a Cause, James Dean and Buzz Gunderson compete for thefavours of sixteen year old Judy. Buzz's gang members steal two cars. The group of teenagers gathers on aLos Angeles lookout, with a cliff that drops down to the Pacific Ocean. James and Buzz are to drive the stolencars toward the cliff. The first person to jump from his car is declared the chicken (which is bad). The lastperson to jump is the hero (which is good), capturing Judy's affection and the gang's respect. The driverlesscars continue over the cliff and plunge to the rocks at its base.Each driver can make two possible actions. Jump when he feels endangered (be a chicken) or jump AFTERthe other driver jumps (be a rooster). Assuming that both feel endangered at the same moment, the followingmatrix represents the payoffs for James and Buzz for each choice of strategy.BuzzChicken RoosterJames Chicken 3, 3 -10, 20Rooster 20, -10 -50, -50 PLEASE ANSWER THE BELOW QUESTION WITH REFERECE TO THE ABOVE…
UNIT 9 CHAPTER 5 In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
Use the decision tree below to answer the following question Aggression Lee: -10; Cody: -10 Cody Aggression Cooperation Lee: 40; Cody: 0 Lee Соорeration Aggression Lee: 0, Cody: 4o Cody Cooperation Lee: 25; Cody: 25 What is the Subgame Perfect Equilibrium (SPE) of this game? O {Lee: Aggression; Cody: Aggression} O {Lee: Aggression; Cody: Cooperation} O {Lee: Cooperation; Cody: Aggression} O {Lee: Cooperation; Cody: Cooperation}