Three essays on auctions

Thesis

The importance of being discrete: on the (in-)accuracy of continuous approximations in auction theory

While auction theory views bids and valuations as continuous variables, real-world auctions are necessarily discrete. In this paper, we use a combination of analytical and computational methods to investigate whether incorporating discreteness substantially changes the predictions of the theory. In some cases, we find that introducing discreteness leaves auction theoretic predictions almost entirely unaffected. In other cases, however, we show that introducing discreteness can rob auctions of their usual symmetric, pure-strategy equilibria; and can even rob them of pure-strategy equilibria altogether (symmetric or otherwise). We discuss the implications of our findings for both theoretical and experimental work on auctions.

Going... going... wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour

In this paper, we design and implement an experiment aimed at testing the level-k model of auctions. We begin by identifying (simple) environments that optimally disentangle the predictions of the level-k model from the natural benchmark of Bayes-Nash equilibrium. We then implement these environments within a virtual laboratory in order to see which theory can best explain observed bidding behaviour. Overall, our findings suggest that, despite its notable success in predicting behaviour in other strategic settings, the level-k model (and its close cousin, cognitive hierarchy) cannot explain behaviour in auctions.

Competitive equilibrium and the double auction

In this paper, we revisit the common claim that double auctions necessarily generate competitive equilibria. We begin by observing that competitive equilibrium has some counterintuitive implications: specifically, it predicts that monotone shifts in the value distribution can leave prices unchanged. Using experiments, we then test whether these implications are borne out by the data. We find that in double auctions with stationary value distributions, the resulting prices can be far from competitive equilibria. However, we also show that double auctions display stronger equilibrating tendencies once traders can leave without replacement as time progresses. Taken together, these findings suggest that the exit of traders over time is a key driver of equilibrium prices in double auctions.

Authors: Rasooly, I

• DOI: 10.5287/ora-brq75g1kz
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford