X 8.7 Return to the game with two neighbors in Problem 8.5. Continue to suppose that player i's average benefit per hour ofwork on landscaping is 10-, +2 Continue to suppose that player 2's opportunity cost of an hour of landscaping work is 4.Suppose that player I's opportunity cost is either 3 or 5 with equal probability and that this cost is player 1's privateinformation. a. Solve for the Bayesian-Nash equilibrium. b. Indicate the Bayesian-Nash equilibrium on a best-responsefunction diagram. c. Which type of player 1 would like to send a truthful signal to player 2 if it could? Which type would like tohide his or her private information?

Answered: Image /qna-images/answer/3e67a2ff-4bee-47c8-bdcd-4a756e02a226.jpg

Answered: X 8.7 Return to the game with two…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.
Consider the two period Repeated Prisoner's Dilemma Game where each player is interested in the SUM of the payoffs she gets in each period. Players see the outcome after the play in each period. (The period payoffs are 10,5,1,0.) (i) Write out this game in its strategic form. (ii) Find all Nash equilibria and all Subgame Perfect Nash Equilibria.
Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 7 and Trinity will receive a payoff of 5. Trinity Up Down Up 4,8 7,5 Antonio Down 3,2 5,6 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses, and Trinity chooses Grade It Now Save & Continue Continue without saving @ 2 F2 #3 80 Q F3 MacBook Air 44 F7 Dll F8 44 F10 74 $ 4 05 Λ & % 5 6 7 8 * 0 Q W E R T Y U 1 A N S X 9 0 -O O D F G H J K L on را H command C > B N M Λ - - P [ H Λ command opti
Use this information for questions 19-22. Consider the Acid Rain Game with new payoffs below. Total net benefits are given in the payoff matrix below. Country B $96 O $108 $90 Low $120 Abatement High Abatement Country A Low Abatement A: $20 B: $10 A: $21 B: $7 Imagine Country B discounts future profits at d=0.9. If you know that Country A will use the grim reaper punishment, what is the present value of net benefits from deviating for Country B? High Abatement A: $14 B: $18 A: $22 B: $12
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 6 units of utility, while the small rival suffers a loss of utility of 2. If the two companies select the same technology, Microsoft suffers a loss of utility of 2 while the rival gains 2 units of utility. Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously. Microsoft Technology A Technology B Rival Technology A Rival: , Microsoft Rival: , Microsoft Technology B Rival: , Microsoft Rival: , Microsoft True or False: There is no equilibrium in pure strategies. True False Note:- Do not provide handwritten…
3. Two individuals are involved in a synergistic relationship. If both individuals devote more effort to the relationship, they are both better off. Specifically, an effort level is a nonnegative number, and player 1's payoff function is e₁(1+€₂-e₁), where ei is player i's effort level. For player 2 the cost of effort is either the same as that of player 1, and hence her payoff function is given by e2(1+e₁ - e₂), or effort is very costly for her in which case her payoff function is given by e₂(1 + e₁ — 2e2). 1 Player 2 knows player 1's payoff function and whether the cost of effort is high for herself or not. Player 1, however, is uncertain about player 2's cost of effort. He believes that the cost of effort is low with probability p, and high with probability 1 - p, where 0 < p < 1. Find the Bayesian Nash equilibrium of this game as a function of p.
Suppose that Jason and Chad each are thinking of opening up a diet coke stand on the fourth floor of this building. Suppose that potential customers are evenly spaced on a distance that is normalized to 1. Customers will buy a diet coke from whichever stand requires the least walking. If they are the same distance the customer will flip a coin. This is depicted below. 1/4 1/2 3/4 Suppose that Jason and Chad are simultaneously choosing the location of their stands, what is the Nash Equilibrium location? a. One of them puts a stand at 3/4 and the other puts a stand at 1/4 b. Chad and Jason put their stands right next to each other at 1/2 c. One of them puts a stand at 0 and the other puts a stand at 1 d. There is no Nash Equilibrium
Suppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the normal-form accompanying game. Worker Work Shirk Manager Monitor -1,1 1,-1 Don't Monitor 1,-1 -1,1 Which of the following pairs of strategies constitutes a Nash equilibrium? Multiple Choice Manager monitors and worker shirks. Manager does not monitor and worker works. Manager monitors and worker works. O None of the answers is correct.
Problem 3 Consider the following simultaneous normal form game: P.2 R 0,0 -1, 1 1, -1 P.1 P 1, -1 0,0 -1, 1 S -1, 1 1, -1 0,0 Now assume the game is not simultaneous and player 1 gets to play first. Create a game tree that represents the sequential game. Also, name each node, define the set of information sets for each player, show which nodes are in which information set and add define action sets at each info set.
Define a new game as a modified version of the game in Problem 1, which we will call the Matching Two Pennies game: each player choose heads (H) or tails (T) for two pennies. In this game, Player 1 wins if both coins show the same combination of heads and tails, while Player 2 wins if they do not. (a) Write the strategy sets S1 and S2 for this game. (b) Give the payoffs for each player in this Matching Two Pennies game, by defining T;(81, 82) for each player and for each strategy pair, either as a list or in matrix form.
1. Consider a game of chicken: two players approach a narrow bridge with room only for one, and each chooses either to go through and hope the other guy backs off (call this action H, for "hawk"), or backs off to let the other go through (call this action D, for "dove"). If both players are normal, then each gets a payoff of -1 from a collision (i.e. if both choose H), 1 if they choose H against D, 0 if they choose D (regardless of what the other player chooses). Now perturb the game as follows: there is a chance p > 0 that P2 is a “violent type", who gets 1 from playing H regardless of Pl's action, and -1 from playing D, again regardless of P1's action. (a) Illustrate the game tree corresponding to the Harsanyi transformation of this game (i.e. the dynamic game of imperfect information in which nature moves first). (b) Illustrate the extended game (i.e. the normal form game corresponding to your game tree in part (a)). (c) Find all values of p for which there is a BNE in which P1…
Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?

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