Abstract
This paper theoretically investigates which auctions are selected by competing sellers when they can choose between first-price auctions and second-price auctions, and when homogeneously risk averse bidders endogenously enter one of the auctions. In order to study this, we first consider bidders’ entry decisions between exogenously given auctions. We find that there exists a symmetric entry equilibrium that is unique and is characterized by a mixed strategy, which depends on whether bidders exhibit constant, decreasing or increasing absolute risk aversion. In a next step, we endogenize the sellers’ choice of auctions. We show that competing sellers have a dominant strategy to select first-price auctions if bidders exhibit nondecreasing absolute risk aversion. If bidders exhibit decreasing absolute risk aversion, other equilibria may exist in which sellers select second-price auctions as well. For instance, we demonstrate that sellers may select second-price auctions if the distribution of private values is sufficiently skewed.
Highlights
Nowadays, a vast array of commodities and services is being sold through online auctions
The main objective of this paper is to investigate which auctions are selected by competing sellers when they may choose between first-price and second-price auctions and when risk averse bidders endogenously enter one of the auctions
We show that when bidders may choose between entering first-price and second-price auctions, a symmetric entry equilibrium exists involving mixed strategies, where the mixing probabilities depend on whether bidders exhibit constant, decreasing or increasing absolute risk aversion
Summary
A vast array of commodities and services is being sold through online auctions. Bidders do not know their own value for the good, but they do know the distribution of values This is a common assumption in much of the theoretical and experimental literature studying entry into auctions (e.g., McAfee and McMillan 1987b; Engelbrecht-Wiggans 1987, 1993; Levin and Smith 1994; Smith and Levin 1996; Pevnitskaya 2004; Palfrey and Pevnitskaya 2008; Ivanova-Stenzel and Salmon 2004a, b, 2008a, b). The second strand of the literature assumes that bidders obtain some type of private information before making their entry decisions This includes bidders’ private values (Menezes and Monteiro 2000) and bidders’ heterogeneous rates of risk aversion (Pevnitskaya 2004; Palfrey and Pevnitskaya 2008). Stant absolute risk attitudes, but who assume exogenous random participation (McAfee and McMillan 1987a) They find that sellers prefer to select a first-price auction when bidders exhibit constant absolute risk aversion. We use these outcomes to analyze the entry decisions in Stage 2 and the selection of auctions in Stage 1
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