Price of Anarchy for First Price Auction with Risk-Averse Bidders

Inquiry into the price of anarchy (POA) for auctions is almost confined within the risk-neutral setting. Nonetheless, empirical and experimental studies suggest that real-world agents are more or less risk-averse rather than strictly risk-neutral. In this paper, we study the POA of first-price single-item auctions (FPA) with risk-averse bidders. For completeness, we consider both risk-averse and risk-neutral sellers. In the former, we establish that the POA is 1/2 for both the symmetric FPA and FPA in general. In the latter, we show that the POA can be arbitrarily bad for the symmetric FPA and characterise the conditions for the POA to be constant. In response to a fairness issue in the case of risk-neutral sellers, we propose the notion of suboptimal social welfare. We subsequently derive POA bounds with respect to this new notion where the bounds are parameterised by two variables that capture the value range of the utility function.