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Auctions — A Brief Introduction

Economics Sneak Peak

In 2020, Robert Wilson and Paul Milgrom were awarded the 2020 Nobel Memorial Prize in Economic Sciences. Over the last decades, they improved auction theory and invented multiple new auction formats. If designed correctly, auctions can contribute to a fair resource distribution. In this blog post, we give a short introduction to the fascinating world of auction theory, which we will pick up throughout the next articles to find new ways of looking at the value of data.

An auction allocates a set of resources to a group of people (formally called agents). For simplicity, in the following, we assume that only one resource is auctioned. An auction is considered to be fair if the resource is allocated to the agent who values the resource the most. Formally, an auction is a protocol that lets agents indicate their interest for the resource and turns those indications to an allocation scheme. In particular, an auction consists of the following rules:

  • Bidding rules: Who can bid, when and how?
  • Clearing rules: Who gets what and how much do they need to pay?
  • Information rules: What is known about the auction and especially the auctioned resource?

Auction types and the winner’s curse

The following are the most frequently used auctions:

Source: Jehle, G.A. and P.J. Reny, Advanced Microeconomic Theory, 3rd ed., Prentice Hall

Every auction format has advantages and disadvantages: e.g., an english auction usually is more advantageous for the seller. The effect of a Dutch auction primarily depends on the speed of the clock: a fast clock (meaning fast decreasing prices) leads to lower bids and prices compared to e.g. a first-price sealed-bid auction while a slow clock leads to higher prices. Usually, in an auction, different agents have different information about the resource leading to different individual values and therefore bids. The agent with the most optimistic evaluation of the asset tends to overestimate it´s value and is therefore most likely to win the auction. This phenomenon is called the winner’s curse. Either the winning bid exceeds the actual value of the auctioned resource leading to a net loss for the winner or the value of the resource is actually less than anticipated, which might still lead to a net gain but smaller than originally anticipated.

Second price auctions: incentive compatible and strategy proof

Second price auctions have two very strong advantages:

  • Incentive compatible: agents have an incentive to bid according to their true valuation.
  • Strategy proof: agents have an incentive to show their true valuation.

Dutch and English auctions do not contain the strategy proof as an agent might have an advantage though hiding their true valuation of the ressource. Why is a second price auction incentive compatible? For simplification, let us assume that two agents participate in a (sealed) second-price auction for a unique good. The first agent has a private value v1 for the resource and bids b1in a sealed-bid second price auction. Given the auction design, underbidding (b1<v1) is not advantageous for the agent as he does not have to pay his/her own bid anyway. Therefore, (s)he has two different strategies at hand: either overbidding b1>v1 or truthful bidding b1=v1. Depending on the second agent’s bid b2, we have the following scenarios:

While in scenario I and III, truthful bidding leads to the same result as overbidding, in scenario II truthful bidding is advantageous over overbidding — in other words, truthful bidding is a weakly dominant strategy.

Truthfulness is an obvious desirable property of a mechanism and can be implemented by design by choosing the right auction format. Vickrey-Clarke-Groves (VCG) mechanisms are an important class of truthful mechanisms. Those mechanisms align incentives of the individual agents with the overall group optimising overall social welfare. Within the next few weeks, we will follow this approach to find new ways of looking at data value.

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