A seller will run a second-price, sealed-bid auction for an object. Thereare two bidders, a and b, who have independent, private values v; whichare either 0 or 1. For both bidders the probabilities of v; = 0 and v; = 1 areeach 1/2. Both bidders understand the auction, but bidder b sometimesmakes a mistake about his value for the object.%3|Half of the time his value is 1 and he is aware that it is 1; the other half of thetime his value is 0 but occasionally he mistakenly believes that his value is 1.Let's suppose that when b's value is 0 he acts as if it is 1 with probability 1/2and as if it is zero with 2 probability. So in effect bidder b sees value 0 withprobability 1/4 and value 1 with probability 4.Bidder a never makes mistakes about his value for the object, but he is awareof the mistakes that bidder b makes. Both bidders bid optimally given theirperceptions of the value of the object. Assume that if there is a tie at a bid of xfor the highest bid the winner is selected at random from among the highestbidders and the price is x.Is bidding his true value still a dominant strategy for bidder a? What is theseller's expected revenue?

In a sealed-bid auction, competitors enter their bids simultaneously in sealed envelopes, keeping…

A seller will run a second-price, sealed-bid auction for an object. There are two bidders, a and b, who have independent, private values v₁ which are either 0 or 1. For both bidders the probabilities of v₁ = 0 and v₁ = 1 are each 1/2. Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. Half of the time his value is 1 and he is aware that it is 1; the other half of the time his value is 0 but occasionally he mistakenly believes that his value is 1. Let's suppose that when b's value is 0 he acts as if it is 1 with probability 1/2 and as if it is zero with ½ probability. So in effect bidder b sees value 0 with probability 1/4 and value 1 with probability 3/4.

A seller will run a second-price, sealed-bid auction for an object. There are two bidders, a and b, who have independent, private values v₁ which are either 0 or 1. For both bidders the probabilities of v₁ = 0 and v₁ = 1 are each 1/2. Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. Half of the time his value is 1 and he is aware that it is 1; the other half of the time his value is 0 but occasionally he mistakenly believes that his value is 1. Let's suppose that when b's value is 0 he acts as if it is 1 with probability 1/2 and as if it is zero with ½ probability. So in effect bidder b sees value 0 with probability 1/4 and value 1 with probability 3/4.

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

Question 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm (Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm 1's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted below. Build Not Build Enter 0, -1 2,1 Not Enter 2,0 3,0 High Cost Build Not Build 1 Enter 1.5, -1 2,1 Not Enter 3.5,0 3,0 Low Cost This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in, but Firm 1 does now it. As we have seen in class, there are 5 things that define this Bayesian game. 1. Set of players: N {Firm 1, Firm 2}. = 2. Set of actions for each player: A₁ = {Build, Not Build}, A2 3. Type space of Firm 1: ₁ = {H, L}. {Enter, Not Enter}.…
Respond to the question with a concise and accurate answer, along with a clear explanation and step-by-step solution, or risk receiving a downvote.
please only do: if you can teach explain each part
Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 30% chance of actually realizing that cost reduction and a 70% chance of realizing no cost reduction. Assume the customer has an initial total cost of $300. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is . Suppose the sales representative initially offers the accounting system to the customer for a price of $19.50. The information asymmetry stems from the fact that the has more information about the efficacy of the accounting system than does the . At this price, the customer purchase the accounting system, since the expected…
Faris Co. and Fahad Co. are rivalry in Bahrain's market. Suppose the payoff to each of four strategic interactions are as follows: Faris Co. Response Action Reduce Price Don't Reduce Price Gain = BD 30,000 Reduce Price Loss = BD 1,000 Don't Reduce Price Loss = BD 5,000 No loss or gain The probability of Faris Co. to reduce price is 95 % (otherwise, probability of Faris Co. for not reducing price is 5 %), assume that Fahad Co. choose "reduce price" strategy a. What is size of loss from "reduce price" for Fahad Co.? b. What is size of gain from "don't reduce price" for Fahad Co? c. What is the expected payoff of a "reduce price" for Fahad Co.? and give an example (application) of d. Explain the concept of 'game theory' game theory Fahad Co. Response
Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 20% chance of actually realizing that cost reduction and a 80% chance of realizing no cost reduction. Assume the customer has an initial total cost of $200. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is $____ . Suppose the sales representative initially offers the accounting system to the customer for a price of $12.00. The information asymmetry stems from the fact that the ______(sales rep or buyer) has less information about the efficacy of the accounting system than does the ______(sales rep or buyer) . At this price, the…
There are three bidders participating in a first-price auction for a painting. Each bidder has a private, independent value vi for such a painting that is drawn uniformly from [0,1] Assume that each bidder i has a linear bidding function bi=avi, where a>0. What is the bidding strategy of bidder i , namely bi in the Bayesian equilibrium?
Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.6 0.4 0.9 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.
The ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes a fair proposal (F - 5;5) or unfair proposal (U - 8;2). The second player (the responder) chooses to either accept (A) or reject (R) this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. 1 A 5:5 2 F R 0:0 U A 8:2 2 1. Find the subgame perfect Nash Equilibrium using backward induction. R 0;0
Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions. The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Find the Nash Equilibria (or Equilibrium) of the “research and development”…
(ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D
There are N>=2 collectors who engage in the auction of an antique. The collectorshave a common valuation of the antique, denoted by v, which is known to all. Thecollectors make a simultaneous bid. Let pn denote the bid by collector n = 1,....,N. The one with the highest bid wins the antique. The winner receives payoff v-pi.The other(s) receive zero payoff. If more than one collectors make the same highestbid, then they have an equal chance of winning the item. Prove that: A) It is not a Nash Equilibrium (NE) if the highest bid is v and onlyone collector bids this price.(b) It is not a NE if the highest bid is less than v.(c) It is a NE that the highest bid is v and more than one collector bidsthis price