Optimal Mechanism Design with Risk-loving Agents

TL;DR

This paper explores how risk-loving behavior, modeled by convex utility functions, affects optimal auction design, revealing that randomization can increase revenue and leading to simple auction formats for exponential utility functions.

Contribution

It characterizes the optimal auction for risk-loving agents with exponential utility, showing the effectiveness of randomization and simple auction formats for revenue maximization.

Findings

Randomized take-it-or-leave-it pricing can outperform traditional auctions.

Optimal auction for exponential utility involves simple randomized mechanisms.

Results do not extend to general convex utility functions beyond exponential.

Abstract

One of the most celebrated results in mechanism design is Myerson's characterization of the revenue optimal auction for selling a single item. However, this result relies heavily on the assumption that buyers are indifferent to risk. In this paper we investigate the case where the buyers are risk-loving, i.e. they prefer gambling to being rewarded deterministically. We use the standard model for risk from expected utility theory, where risk-loving behavior is represented by a convex utility function. We focus our attention on the special case of exponential utility functions. We characterize the optimal auction and show that randomization can be used to extract more revenue than when buyers are risk-neutral. Most importantly, we show that the optimal auction is simple: the optimal revenue can be extracted using a randomized take-it-or-leave-it price for a single buyer and using a loser-pay auction, a variant of the all-pay auction, for multiple buyers. Finally, we show that these results no longer hold for convex utility functions beyond exponential.