On the Impossibility of Protecting Risk‐takers

Abstract

Risk‐neutral sellers can extract high profits from risk‐loving buyers using lotteries. To limit risk‐taking, gambling is heavily regulated in most countries. In this article, I show that protecting risk‐loving buyers is essentially impossible. Even if sellers are restricted from using mechanisms that resemble lotteries, they can still construct selling mechanisms that ensure unbounded profits as long as buyers are risk‐loving, at least asymptotically. Asymptotically risk‐loving preferences are both sufficient and necessary for unbounded profits. Buyers are asymptotically risk‐loving, for example, when they are globally risk‐loving, when they have cumulative prospect theory preferences, or when their utility is bounded from below.

Optimal Mechanism Design with Risk-Loving Agents

“…To the best our knowledge, the only work on mechanism design under risk-loving behavior is by Hinnosaar [2017], who shows that in the absence of regulations, the seller can extract infinite revenue from the buyer with asymptotically risk-loving behavior under both the expected utility theory and prospect theory models.…”

“…Therefore, the expected payment the seller receives will increase to $55. In fact, it has been shown by Hinnosaar [2017] that in the absence of any regulation, the seller is able to extract infinite expected revenue from a risk-loving buyer by simply taking advantage of this trick -offering a menu option that asks the buyer to pay a very high amount with a very small probability. Therefore, in this paper, we will mainly focus on the bounded transfer setting, i.e.…”

“…Without this assumption, it can be shown that there exists a mechanism that attains infinite revenue from riskloving buyersHinnosaar [2017].…”