🆚Game Theory and Economic Behavior Unit 11 – Auction Theory & Mechanism Design

Key Concepts and Definitions

• Auction theory studies how people behave in auction markets and the properties of auction markets
• Mechanism design is a field in economics and game theory that takes an engineering approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally
• Private value is when each bidder has a value for the item that is independent of the values of the other bidders
• Common value is when the value of the item is the same for all bidders, but bidders have different private information about the value
• Winner's curse occurs when the winning bid exceeds the intrinsic value or true worth of an item
  • Happens because the winner is the bidder who has the highest estimate of the item's value, which is likely to be an overestimate
• Reserve price is the minimum price that a seller will accept for an item
• Efficiency in auction design refers to maximizing the total surplus, which is the sum of the buyer's surplus and the seller's surplus

Types of Auctions

• English auction, also known as an open ascending price auction, starts with a low price and bidders successively raise the price until only one bidder remains
• Dutch auction, also known as an open descending price auction, starts with a high price and the auctioneer lowers the price until a bidder accepts the current price
• First-price sealed-bid auction is where bidders submit sealed bids and the highest bidder wins and pays their bid price
• Second-price sealed-bid auction, also known as a Vickrey auction, is where bidders submit sealed bids and the highest bidder wins but pays the second-highest bid price
  • Encourages truthful bidding as the optimal strategy
• All-pay auction is where all bidders pay their bid, regardless of whether they win the item or not
• Combinatorial auction allows bidders to place bids on combinations of items, rather than just individual items

Auction Strategies and Bidding Behavior

• Dominant strategy is a strategy that is optimal regardless of what the other players do
  • In a second-price sealed-bid auction, the dominant strategy is to bid one's true value
• Nash equilibrium is a set of strategies, one for each player, such that no player has an incentive to unilaterally change their strategy
• Winner's curse can be avoided by shading bids, which means bidding less than one's estimate of the item's value
• Collusion among bidders, such as bid rigging or bid rotation, can reduce the seller's revenue
  • Auction design can include measures to prevent or detect collusion
• Jump bidding is when a bidder makes a bid that is significantly higher than the current price, signaling a strong commitment to winning the item
• Sniping is when a bidder waits until the last possible moment to place a bid, giving other bidders little time to respond

Mechanism Design Principles

• Incentive compatibility means that players have an incentive to behave in accordance with the mechanism's goals
  • For example, in a second-price sealed-bid auction, bidding one's true value is incentive compatible
• Individual rationality ensures that players are willing to participate in the mechanism
  • Requires that players expect to gain at least as much by participating as they would by not participating
• Budget balance means that the mechanism does not require an external subsidy or generate a surplus
• Allocative efficiency is achieved when the item is allocated to the bidder who values it the most
• Revelation principle states that any mechanism can be transformed into an equivalent direct mechanism where players truthfully report their private information
• Myerson's optimal auction design principle states that the optimal auction maximizes the expected revenue subject to incentive compatibility and individual rationality constraints

Revenue Equivalence Theorem

• States that any two auction mechanisms that result in the same allocation of the item and meet certain conditions will generate the same expected revenue for the seller
  • Conditions include: bidders are risk-neutral, bidders have independent private values, and the bidder with the lowest possible value expects zero surplus
• Implies that the choice of auction format (English, Dutch, first-price sealed-bid, second-price sealed-bid) does not affect the expected revenue, under certain conditions
• Provides a benchmark for comparing the revenue generated by different auction formats
  • Deviations from the theorem's conditions can lead to differences in revenue
• Allows for the design of optimal auctions by focusing on the allocation rule rather than the payment rule
  • Payment rule can be derived from the allocation rule using the revenue equivalence principle

Optimal Auction Design

• Goal is to design an auction that maximizes the seller's expected revenue while satisfying incentive compatibility and individual rationality constraints
• Myerson's optimal auction design principle provides a framework for designing optimal auctions
  • Involves transforming bidders' values into virtual values, which account for the bidders' information rents
  • Allocates the item to the bidder with the highest non-negative virtual value
  • Sets a reserve price equal to the lowest value for which the virtual value is non-negative
• Optimal auctions may involve setting different reserve prices for different bidders based on their value distributions
• Optimal auctions in the presence of budget constraints or risk-averse bidders may differ from the standard optimal auction design
• Practical considerations, such as simplicity and transparency, may lead to the use of sub-optimal but more easily implementable auction formats

Applications in Economics and Business

• Spectrum auctions are used by governments to allocate radio frequency spectrum licenses to telecommunications companies
  • Often use a combinatorial clock auction format to allow for efficient allocation of multiple licenses
• Timber auctions are used by government agencies to sell the right to harvest timber from public lands
  • Often use a sealed-bid format with a reserve price to ensure a minimum revenue for the agency
• Online advertising auctions, such as Google's AdWords and Facebook's ad auctions, allocate advertising space to advertisers based on a combination of bid price and ad quality
  • Use a generalized second-price auction format to encourage truthful bidding and efficient allocation
• Electricity market auctions are used to match electricity supply and demand in real-time and day-ahead markets
  • Often use a uniform-price auction format to determine the market-clearing price
• Carbon emission permit auctions are used by governments to allocate permits for greenhouse gas emissions to companies
  • Can use a sealed-bid or ascending clock auction format with a reserve price to ensure a minimum price for the permits

Advanced Topics and Current Research

• Multi-unit auctions are used when multiple identical items are being sold
  • Vickrey-Clarke-Groves (VCG) mechanism is an extension of the Vickrey auction for multi-unit settings
• Multi-dimensional auctions consider multiple attributes of the items being sold, such as quality or delivery time, in addition to price
  • Scoring auctions assign a score to each bid based on a pre-determined scoring rule and the highest score wins
• Auctions with externalities occur when a bidder's valuation depends on the identities or actions of other bidders
  • Can lead to inefficient outcomes and require specialized auction designs to address the externalities
• Behavioral auction theory incorporates insights from psychology and behavioral economics to model bidder behavior that deviates from standard economic assumptions
  • Includes models of bounded rationality, loss aversion, and social preferences
• Robust auction design aims to create auction mechanisms that perform well under a range of possible environments and bidder behaviors
  • Involves designing auctions that are robust to variations in bidders' value distributions, risk attitudes, and strategic behavior
• Experimental and empirical studies test the predictions of auction theory and inform the design of real-world auction markets
  • Lab experiments allow for controlled testing of specific auction formats and behavioral hypotheses
  • Field experiments and natural experiments provide evidence on the performance of auctions in real-world settings