Auction Design Quiz
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Questions and Answers

What is the usual answer to the question of how to sell a unique work of art?

To hold an auction.

Procurement auctions are only used by firms for selling goods and services.

False (B)

What broader field does the question of auction design fall into?

Mechanism design

In a first-price auction, who wins the object?

<p>The bidder with the highest bid.</p> Signup and view all the answers

In a first-price auction, what price does the winner pay?

<p>The highest bid.</p> Signup and view all the answers

In a second-price auction, who wins the object?

<p>The bidder with the highest bid.</p> Signup and view all the answers

In a second-price auction, what price does the winner pay?

<p>The second highest bid.</p> Signup and view all the answers

In a Dutch auction, how is the price determined?

<p>The seller announces a very high price and reduces it until a bidder accepts.</p> Signup and view all the answers

In a Dutch auction, what happens if none of the bidders accepts the price?

<p>The seller reduces the price.</p> Signup and view all the answers

In an English auction, how is the price determined?

<p>The seller announces a very low price, and bidders announce if they accept the current price. The price increases until only one bidder remains.</p> Signup and view all the answers

In an English auction, what happens if more than one agent accepts the price?

<p>The seller increases the price, and the process repeats.</p> Signup and view all the answers

In the Independent Private Values model, who knows the valuation $v_i$?

<p>The buyer i knows her valuation $v_i$.</p> Signup and view all the answers

In the Independent Private Values model, what do the seller and other buyers know about $v_i$?

<p>They know that $v_i$ is distributed according to $f(v_i)$.</p> Signup and view all the answers

In a First Price Auction, what is the strategy of each agent $i$?

<p>A bid made for each possible valuation.</p> Signup and view all the answers

First Price Auction and a Dutch Auction are strategically equivalent.

<p>True (A)</p> Signup and view all the answers

Second Price Auction and an English auction are equivalent (as long as the values are private).

<p>True (A)</p> Signup and view all the answers

The FPA and the Dutch auction are equivalent and raise the same revenue.

<p>True (A)</p> Signup and view all the answers

The SPA and the English auctions are equivalent and raise the same revenue.

<p>True (A)</p> Signup and view all the answers

With risk averse agents, First Price Actions (FPA) will tend to raise less revenue than the SPA.

<p>False (B)</p> Signup and view all the answers

With less sophisticated bidders, the English auction is obviously strategy-proof.

<p>True (A)</p> Signup and view all the answers

Flashcards

Competitive Markets

Markets where multiple sellers compete, leading to efficient pricing.

Thin Markets

Markets with few buyers or sellers, often leading to less efficient pricing.

Auction

A public sale where goods are sold to the highest bidder.

First Price Auction (FPA)

Bidders submit sealed bids; the highest bid wins and pays that bid.

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Second Price Auction (SPA)

Bidders submit sealed bids; the highest bid wins but pays the second-highest bid.

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Dutch Auction

The seller starts with a high price and lowers it until a bidder accepts.

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English Auction

Bidders openly bid against each other, with incremental price increases.

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Independent Private Values

Bidders have their own valuations that do not depend on others.

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Utility of Winning

The difference between a winner's value and the final price paid.

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Bayes-Nash Equilibrium

A strategy where each player optimizes their bid based on others' strategies in uncertain conditions.

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Nash Equilibrium in Auctions

A stable state where all bidders are bidding optimally given others' strategies.

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Revelation Principle

Incentive-compatible mechanisms can always be simplified to truthful reporting.

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Revenue Equivalence Theorem

Under certain conditions, different auction formats yield the same expected revenue.

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Inefficient Mechanism

A process that fails to allocate resources efficiently, potentially missing sales.

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Optimal Mechanism

The best method of selling that maximizes seller's revenue while ensuring participation.

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Budget-Constrained Bidders

Participants whose spending is limited by their budgets, affecting bidding behavior.

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Winner's Curse

Bidders may overpay due to overestimating the value of the auctioned item.

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Procurement Auctions

Auctions used by organizations to purchase goods and services.

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Bidding Strategy

The plan a bidder adopts to maximize their chances of winning.

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Sealed Bid

A confidential bid submitted without revealing it to competitors.

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Tied Bid

When two bidders submit the same highest bid in an auction.

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Allocation Function

Defines how the item is allocated among bidders based on reported valuations.

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Cost Function

Represents the payment made by bidders based on their reported prices.

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Incentive Compatibility

A mechanism where truthfully reporting a type leads to optimal outcomes.

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Common Distribution

A probability distribution shared among bidders for their valuations.

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Government Auctions

Auctions held by the government to sell or allocate items.

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Unique Valuation

A bidder's distinct assessment of an item's worth, unshared by others.

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Study Notes

Chapter 9: Auctions

  • Competitive markets for private goods are covered.

  • Competitive markets work efficiently, matching demand and supply.

  • Market "thinness" and private information impact market efficiency.

  • Auctions are often used for unique or specialized goods:

    • Artwork
    • Used phones
    • Sponsorship rights
    • Radio spectrum rights
    • Government-owned firms

  • Auctions involve many distinct formats, each designed for specific purposes.

  • Optimal auction design is a critical concern.

  • Firms and governments use auctions to acquire goods and services.

Ch 9.1: Introduction

  • Competitive markets for private goods were previously discussed.
  • The efficiency of markets in general was previously explored.
  • The impact of private information and thin markets on efficiency is considered.

Ch 9.2: The four common auctions

First Price Auction (FPA)

  • Each buyer submits a sealed bid.
  • The highest bidder wins the object.
  • The price is the highest bid.

Second Price Auction (SPA)

  • Each buyer submits a sealed bid.
  • The highest bidder wins the object.
  • The price is the second-highest bid.

Dutch Auction

  • The seller starts with a high price and lowers it.
  • The first bidder to accept the price wins the object.
  • The price is the price the first person accepts.

English Auction

  • The seller starts with a low price and raises it.
  • Bidders announce whether they accept each price, and continue bidding.
  • The final bidder wins at the stated price.

Ch 9.3: Independent Private Values

  • Single, risk-neutral seller and indivisible object.
  • Multiple risk-neutral buyers.
  • Seller values the object at 0.
  • Each buyer's value is a random variable.
  • Values are drawn form the interval [0, 1] with an associated CDF and density. -These values are statistically independent, not correlated.
  • Oil field example to illustrate the impact on bidding.
  • Private value assumption – an agent's value doesn't depend on other agents' information.

Ch 9.4: First Price Auction

  • Auction format as a game, analyzed in terms of Bayes-Nash equilibrium.
  • Agents want to win an object, but prefer to pay a lower price.
  • Bidders must balance their winning probability with price.
  • Bidding function for each agent (bi).
  • Equilibrium bidding strategy depends on the distribution of agents' types in this symmetric auction case.
  • The seller can determine the optimal bid if all other agents are truthful in their bids.

Ch 9.5: Dutch Auction

  • In a dutch auction, the buyer states a single price.
  • The optimal strategy for a buyer is the same as for a first-price auction.
  • First price and dutch auctions are strategically equivalent.
  • The optimal pricing strategy in a dutch auction is the same as that of a first prize auction.

Ch 9.6: Second Price Auction

  • The simplicity of the SPA equilibrium makes it easy to calculate.
  • Bidders bid their true value in equilibrium.
  • Bidders have no incentive to bid other than their true value in this format of auction.
  • This argument holds if the highest bid among others is known to the agent.
  • In conclusion, bidders have an incentive to bid their valuation truthfully in the SPA.

Ch 9.7: English Auction

  • The optimal behavior in an English auction is to continue bidding until the price reaches an agent's value.
  • If one drops out before reaching one's valuation, potential benefits may be lost.
  • The equilibrium is that one drops out when one reaches one's valuation.
  • Second highest bidder wins the item.

Ch 9.8: Revenue comparison

  • Expected revenue in the FPA vs. the SPA is shown to be equivalent.

Ch 9.9: Extensions and qualifications

  • Correlated values lead to possibilities of "winner's curse".
  • English auction can reveal values which is a benefit.
  • Risk averse agents might favor second price auctions.
  • Budget-constrained bidders might also favor second price auctions.

Ch 9.10: General mechanisms

  • Four standard auctions are specific methods of selling items.
  • Is there a better mechanism theoretically than the four standard options.

Ch 9.11: Direct mechanisms

  • Direct mechanisms involve agents reporting their valuation directly to the seller.
  • Incentive compatibility (IC) is needed in a direct mechanism for truthful reporting strategy.

Ch 9.12: Optimal mechanisms

  • Using the Revelation Principle, the problem of mechanism design is simplified to finding the optimal IC direct mechanism.
  • maximizing expected revenue.
  • Finding a way to satisfy the constraints: IC constraint and IR constraints (participation constraint)
  • The optimal mechanism for independent private values with bidders is a second price auction.

Ch 9.13: Conclusion

  • Auctions, a specific type of mechanism, are found everywhere in various contexts.
  • Design is valuable for optimizing outcomes.
  • Mechanisms aren't always efficient.

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Description

Test your knowledge on auction design and strategies with this quiz. Explore various auction types, their mechanics, and outcomes in detail. Perfect for anyone interested in economics and bidding processes.

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