Auction Theory

Game Theory · Axiom Academy

LESSON Auction Theory Foundations Understanding value types, bidder models, and auctions as strategic games 1. Types of Values in Auctions A fundamental distinction in auction theory is how bidders derive value from winning an item. The value structure determines bidding behavior and auction outcomes. Each bidder has their own independent valuation, unaffected by others' information. Example: Personal artwork preferences The item has the same objective value to all bidders, but they have different information about it. Each bidder's value depends on both their own signal and others' private information. 2. Independent Private Values (IPV) Model The IPV model is the workhorse of auction theory. It assumes each bidder i draws their valuation independently from a known distribution. Each bidder i has valuation v i drawn independently from distribution F Valuations are private information (only bidder i knows v i ) The distribution F is common knowledge Bidders are risk-neutral expected utility maximizers Under IPV, a bidder's optimal strategy depends only on their own value and the distribution of opponents' values, not on learning from others' bids. 3. Bidder Types and Strategy Spaces In auction theory, we model bidders as strategic players who choose bidding functions based on their private information. Strategy: A bidding strategy is a function b(θ i ) that maps each possible type to a bid amount. Truthful bidding: b(v i ) = v i (bidding your true value)

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