Microeconomics
11th Edition
ISBN: 9781260507140
Author: David C. Colander
Publisher: McGraw Hill Education
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Chapter 20, Problem 7IP
To determine
The wealth distribution to change over time.
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In a sealed-bid, second-price auction with complete information, the winner is the bidder who submits the second-highest price, but pays the price submitted by the highest bidder. Do you agree? Explain.
Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.
Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2.
In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid.
a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…
Chapter 20 Solutions
Microeconomics
Ch. 20.1 - Prob. 1QCh. 20.1 - Prob. 2QCh. 20.1 - Prob. 3QCh. 20.1 - Prob. 4QCh. 20.1 - Prob. 5QCh. 20.1 - Prob. 6QCh. 20.1 - Prob. 7QCh. 20.1 - Prob. 8QCh. 20.1 - Prob. 9QCh. 20.1 - Prob. 10Q
Ch. 20.A - Netflix and Hulu each expects profit to rise by...Ch. 20.A - Prob. 2QECh. 20 - Prob. 1QECh. 20 - Prob. 2QECh. 20 - Prob. 3QECh. 20 - Prob. 4QECh. 20 - Prob. 5QECh. 20 - Prob. 6QECh. 20 - Prob. 7QECh. 20 - Prob. 8QECh. 20 - Prob. 9QECh. 20 - Prob. 10QECh. 20 - Prob. 11QECh. 20 - Prob. 12QECh. 20 - Prob. 13QECh. 20 - Prob. 14QECh. 20 - Prob. 15QECh. 20 - Prob. 16QECh. 20 - Prob. 1QAPCh. 20 - Prob. 2QAPCh. 20 - Prob. 3QAPCh. 20 - Prob. 4QAPCh. 20 - Prob. 5QAPCh. 20 - Prob. 6QAPCh. 20 - Prob. 1IPCh. 20 - Prob. 2IPCh. 20 - Prob. 3IPCh. 20 - Prob. 4IPCh. 20 - Prob. 5IPCh. 20 - Prob. 6IPCh. 20 - Prob. 7IP
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- Consider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true? This is a game where players A and B have the same number of strategies. Player A will get a higher payoff than player B as A moves first. This is game will only have one Nash equilibrium. This is a game of perfect information.arrow_forwardHello, please help me to solve this question in Game Theory. Thanks in advance!Consider a first price sealed-bid auction of an object with two bidders. Each bidder i’s valuation of the object is vi, which is known to both bidders. The auction rules are that each player submits a bid in a sealed envelope. The envelopes are then opened, and the bidder who has submitted the highest bid gets the object and pays the auctioneer the amount of his bid. If the bidders submit the same bid, each gets the object with probability 0.5. Bids must be integers. Find a Nash equilibrium for this game and show whether it is unique.arrow_forwardYou have just played rock, paper, scissors with your friend. You chose scissors and he chose paper, so you won. Is this a Nash equilibrium? Explain why or why not.arrow_forward
- Suppose there is a second price sealed bid auction in which the players have the following values: v1=15, v2=4, v3=6, v4=8, v5=10, v6=6. In the symmetric equilibrium, what bid will bidder 4 submit? a. 10 b. 15 c. 4 d. 8arrow_forwardHow to solve this question? Consider an antique auction where bidders have independent private values. There are two bidders, each of whom perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?arrow_forwardThis question is from game theoryarrow_forward
- in every Nash equilibrium, the strategy of every player is a best response to the strategies chosen by the other players. (a) True. (b) False.arrow_forwardExplain why a player in a sealed-bid, second-price auction would never submit a bid that exceeds his or her true value of the object being sold. (Hint: What if all players submitted bids greater than their valuations of the object?)arrow_forwardwhy is a nash equilibrium stablearrow_forward
- Within a voluntary contribution game, the Nash equilibrium level of contribution is zero, but in experiments, it is often possible to sustain positive levels of contribution for a long period. How might we best explain this? A) Participants are altruistic, and so value the payoff which other participants receive, benefiting (indirectly) from making a contribution. B) Participants believe that if they make a contribution, then other participants will be more likely to make a contribution. C) Participants in experiments believe that they have to make contributions in order to receive any payoff from their participation. D) Participants have experience of working in situations in which cooperation can be sustained for mutual benefit and so have internalised a social norm of cooperationarrow_forwardNash equilibrium refers to the optimal outcome of a game where there is no incentive for the players to deviate from their initial strategy. An individual (or player) can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. Given this premise, can there be a no Nash equilibrium?arrow_forwardThe empirical evidence in the dictator games shows that it is most common for ‘dictators’ to share (A) between 10% to 30% of their endowments; (B) between 40% and 60% of their endowments; (C) nothing with the recipients; (D) their entire endowments.arrow_forward
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