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Playing it Safe: Actions Attractive to the Risk Averse

Marilyn Pease, Mark Whitmeyer

TL;DR

Additional recent technological advances which are making cars safer are pointed out, including energy-absorbing steering wheels, high-mounted brake lights and plastic-lined windshields.

Abstract

We introduce a way to compare actions in decision problems. One action is safer than another if the set of beliefs at which the decision-maker prefers the safer action expands as the decision-maker becomes more risk averse. We provide a full characterization of this relation, show that it is equivalent to robust conceptions of single-crossing and second-order stochastic dominance, and reveal that in monotone decision problems it totally orders the decision-maker's set of actions. We discuss applications to games, insurance, investment hedging, and security design.

Playing it Safe: Actions Attractive to the Risk Averse

TL;DR

Additional recent technological advances which are making cars safer are pointed out, including energy-absorbing steering wheels, high-mounted brake lights and plastic-lined windshields.

Abstract

We introduce a way to compare actions in decision problems. One action is safer than another if the set of beliefs at which the decision-maker prefers the safer action expands as the decision-maker becomes more risk averse. We provide a full characterization of this relation, show that it is equivalent to robust conceptions of single-crossing and second-order stochastic dominance, and reveal that in monotone decision problems it totally orders the decision-maker's set of actions. We discuss applications to games, insurance, investment hedging, and security design.
Paper Structure (27 sections, 19 theorems, 43 equations, 1 figure)

This paper contains 27 sections, 19 theorems, 43 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model
  4. Single-Crossing
  5. Main Result
  6. Intuition
  7. Signed-Ratio Monotonicity
  8. Further Results
  9. Beyond Expected Utility
  10. Monotone Decision Problems
  11. Learning and Incomplete Preferences
  12. Ambiguity
  13. Applications
  14. Games
  15. Contribution Games
  16. ...and 12 more sections

Key Result

Theorem 2.3

Let $u$ be strictly increasing and $F^{\mu}_{a} \succeq_{sc} F^{\mu}_{b}$. Then, whenever $\phi$ is strictly increasing and concave.

Figures (1)

  • Figure 1: Theorem \ref{['thm:central']}. Connecting safety to SOSD and single-crossing.

Theorems & Definitions (38)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Theorem 3.1
  • proof
  • Proposition 3.2
  • proof
  • Definition 4.1
  • Corollary 4.2
  • Proposition 4.3
  • ...and 28 more