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On Risk Aversion in Auctions

Marilyn Pease, Mark Whitmeyer

Abstract

We provide a unifying way to analyze how risk aversion changes bidding in auctions by asking which bids become more attractive as bidders become more risk averse. In first-price auctions, under two payoff conditions--winning is never worse than the outside option, and winning with a low bid is preferable to winning only with a high bid--greater risk aversion makes high bids more appealing. In second-price auctions with a known outside option, bidding more increases risk exposure conditional on winning, so greater risk aversion favors lower bids. We show these bid-level forces translate into corresponding equilibrium comparative statics.

On Risk Aversion in Auctions

Abstract

We provide a unifying way to analyze how risk aversion changes bidding in auctions by asking which bids become more attractive as bidders become more risk averse. In first-price auctions, under two payoff conditions--winning is never worse than the outside option, and winning with a low bid is preferable to winning only with a high bid--greater risk aversion makes high bids more appealing. In second-price auctions with a known outside option, bidding more increases risk exposure conditional on winning, so greater risk aversion favors lower bids. We show these bid-level forces translate into corresponding equilibrium comparative statics.
Paper Structure (12 sections, 9 theorems, 43 equations)

This paper contains 12 sections, 9 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. Auxiliary Results
  3. Bidding and Risk Aversion
  4. First-Price Auctions
  5. Second-Price Auctions
  6. Equilibrium Analysis: First-price Auctions
  7. Equilibrium Analysis: Second-price Auctions
  8. Uniform-Price Auctions
  9. Omitted Proofs
  10. \ref{['fpa']} Proof
  11. \ref{['thm:fpa_safety_equilibrium_cs']} Proof
  12. \ref{['thm:spa_safety_equilibrium_cs']} Proof

Key Result

Theorem 2.2

Let $a$ and $b$ be two distinct actions that do not dominate each other. Then, action $a$ is safer than action $b$ if and only if for each $\theta \in \mathcal{A}$ and $\theta' \in \mathcal{B}$, $b_{\theta'} \geq a_{\theta}$ and $a_{\theta'} \geq b_{\theta}$.

Theorems & Definitions (23)

  • Definition 2.1
  • Theorem 2.2: Theorem 3.1 in safety
  • Lemma 3.1
  • proof
  • Definition 3.2
  • Proposition 3.3
  • Corollary 3.4
  • proof
  • Lemma 3.5
  • proof
  • ...and 13 more