Abstract
The benchmark risk-averse equilibrium model does not explain some of the outcomes obtained in experiments with first-price auctions. Nonetheless, the presence of non-linear bidding and the wide dispersion of bids have received little attention in the literature. I focus on these issues and revisit previous laboratory evidence with the help of model-based clustering techniques. The rejection of equilibrium models is found to be mostly due to the significance of non-linear bidding rules and the unexplained heterogeneity. With the use of a mixture model, the observations are classified into four groups or clusters. Significant differences between individuals and clusters are found, but so is a persistent within individual variation, which leads us to conclude that subjects do not commit to one particular bidding strategy and alternate across several processes.
Highlights
Equilibrium Bidding with Risk AversionIn a first-price sealed-bid auction, bidders compete for the purchase of a single commodity
We find that the risk aversion equilibrium model is rejected on the basis of a significant non-linear bidding and the unexplained overdispersion mostly coming from individual between and within heterogeneity
We have revisited laboratory auction data aiming to the prevalence of non-linear bidding behavior and identifying noisy or irrational behavior that could be responsible for the observed data dispersion in experiments
Summary
In a first-price sealed-bid auction, bidders compete for the purchase of a single commodity. The distributions Fv, Gr and the number of bidders N are common knowledge, but the value realizations vi and the coefficient or risk aversion ri are information private to the individual In this context, a bidding strategy b(v,r) is a Symmetric Bayes Nash Equilibrium (SBNE) if for all valuations, bidding bi=b(vi,ri) is a best response for bidder i when all bidders j i bid b(vj,rj). The above equation implies that in equilibrium the coefficient of risk aversion must equal the profit per dollar at stake times the elasticity of the chances of winning. This elasticity can be obtained in closed form if we allow Fv to take a specific parametric form.
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