[Cheap Talk] Two players must decide whether to implement a project, which has gross value v E {0,100, 200} to each player. Both players think each value is equally likely. Player 1 (the sender) learns the true value of the project. Then, he reports a value {high,medium,low} to player 2 (the decider), and player 2 decides whether or not to implement the project. If the project is not implemented, both players get zero. If a project with value v is implemented, payoffs are P1 : v – 75 P2 : v – 125 (a) Show that there is no Perfect Bayesian Equilibrium (PBE) in which player 1 always reveals the true value to player 2. (b) Find a PBE in which player 1 reports “high" if the project is worth $200, "low" if the project is worth $0 (and either "low" or "high" when the project is worth $100, figure out which one works). (c) Find another PBE (or, if you believe there are no others, explain).

[Cheap Talk] Two players must decide whether to implement a project, which has gross value v E {0,100, 200} to each player. Both players think each value is equally likely. Player 1 (the sender) learns the true value of the project. Then, he reports a value {high,medium,low} to player 2 (the decider), and player 2 decides whether or not to implement the project. If the project is not implemented, both players get zero. If a project with value v is implemented, payoffs are P1 : v – 75 P2 : v – 125 (a) Show that there is no Perfect Bayesian Equilibrium (PBE) in which player 1 always reveals the true value to player 2. (b) Find a PBE in which player 1 reports “high" if the project is worth $200, "low" if the project is worth $0 (and either "low" or "high" when the project is worth $100, figure out which one works). (c) Find another PBE (or, if you believe there are no others, explain).

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

The Nash equilibrium of the accompanying game is Player 1 Multiple Choice O O O (Y. B). (X, B). X Y Z (Z. C). Player 2 A 9, 8 5, 6 10, 9 none of the provided answers because there is no Nash equilibrium in this game. B 10, 12 12, 20 13, 4 C 3, 15 4, 10 8, 12
Tom, Mary and Jill have apartments in the same building. A security system for their building costs $750. Tom is willing to pay $100 for the security system, Mary is willing to pay $300 and Jill is willing to pay $300. They have a meeting to vote on whether to pay $250 each for the security system. At least two of them must vote for the system to be installed before the vote is passed. The efficient outcome is to have the security system installed. After the meeting the security system will, which illustrates_____________________. Question 1 options: be installed, the free rider problem not be installed, the free rider problem be installed, a negative externality not be installed, a negative externality
Only typed answer
None
Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()
In this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant. The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.
BET GAME Each player puts an ante of $1 into the pot. There are four kings and four queens. The professor will randomly draw a card from the dealer, privately observe what it is, and decide whether to fold or to bet.< a) If the professor folds, the game ends, and you wins the pot, gaining the professor's $1 ante.< b) If the professor bets, another dollar will be placed in the pot, after which you has the option to either fold or call.< b-1) if you fold, the game is end and you lose you $1 ante.< b-2) if you call, you need to add another $1 to the pot and the professor need to reveal the card. At this stage, there will be $4 in the pot. You win the pot with a queen and lose the pot with a king.< (1) Draw the Game Tree.< (2) Write down the Payoff Matrix. (3) Find the Bayesian Nash Equilibrium (4) Find the Perfect Bayesian Nash Equilibrium.<
Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000, etc.). How much will…
Taylor, Faith, Jay, and Jessica are college roommates. They're trying to decide where the four of them should go for spring break: Orlando or Las Vegas. If they order the tickets by 11:00 PM on February 1, the cost will be just $500 per person. If they miss that deadline, the cost rises to $1,200 per person. The following table shows the benefit (in dollar terms) that each roommate would get from the two trips. Roommate Taylor Benefit from Orlando Benefit from Las Vegas Faith $1,250 $800 $550 $800 Jay Jessica $650 $600 $850 $1,050 The roommates tend to put off making decisions. So, when February 1 rolls around and they still haven't made a decision, they schedule a vote for 10:00 PM that night. In case of a tie, they will flip a coin between the two vacation destinations. The roommates will get the most total benefit if they choose to go to Given the individual benefits each roommate receives from the two trips, which trip will each roommate vote for? Fill in the table with each…
38. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their divine services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad and become a Doomer. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. We're all the same bro. (C) You meet at the Orthodox church. (D) There is no focal point. 39. Consider a fractional-reserve banking system in which an initial deposit of $1,000 can generate up to $4,000 in money. What is the reserve ratio? (A) 4 percent. (B) 5 percent. (C) 25 percent. (D) 75 percent.
If the players play pure strategies, the game has no Nash equilibrium. But what if they choose their moves randomly? Let each player instead opt for a mixed strategy instead of a pure strategy. The first will play action Z with probability p, and the second will play action L with probability q. At which pair (p, q) are the mixed strategies of the players in equilibrium? At which pair (p, q) does neither player want to change strategy? When are both strategies simultaneously the best response?