Price of Anarchy for Mechanisms with Risk-Averse Agents

TL;DR

This paper extends the analysis of the price of anarchy to mechanisms with risk-averse agents, showing that many positive results from the risk-neutral case still hold under certain conditions, but some mechanisms like all-pay auctions can perform arbitrarily poorly.

Contribution

It generalizes the smoothness framework to risk-averse agents and identifies conditions under which positive price-of-anarchy bounds are maintained or broken.

Findings

Many positive price-of-anarchy results hold for risk-averse agents.

First-price and second-price auctions satisfy the sufficient condition for good efficiency.

All-pay auctions can have arbitrarily bad social welfare in equilibrium.

Abstract

We study the price of anarchy of mechanisms in the presence of risk-averse agents. Previous work has focused on agents with quasilinear utilities, possibly with a budget. Our model subsumes this as a special case but also captures that agents might be less sensitive to payments than in the risk-neutral model. We show that many positive price-of-anarchy results proved in the smoothness framework continue to hold in the more general risk-averse setting. A sufficient condition is that agents can never end up with negative quasilinear utility after playing an undominated strategy. This is true, e.g., for first-price and second-price auctions. For all-pay auctions, similar results do not hold: We show that there are Bayes-Nash equilibria with arbitrarily bad social welfare compared to the optimum.