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

TL;DR

This study tests the level-k model of bidding in auctions through experiments, finding it underperforms compared to equilibrium models and is inconsistent with observed bidding behavior and reasoning levels.

Contribution

The paper identifies environments that distinguish level-k from equilibrium models and empirically evaluates their explanatory power in auction bidding behavior.

Findings

Level-k model under-predicts bids compared to observed data.

Equilibrium models outperform level-k in explaining bidding behavior.

Subjects rarely use iterated reasoning in bidding explanations.

Abstract

In this paper, we design and implement an experiment aimed at testing the level-k model of auctions. We begin by asking which (simple) environments can best disentangle the level-k model from its leading rival, Bayes-Nash equilibrium. We find two environments that are particularly suited to this purpose: an all-pay auction with uniformly distributed values, and a first-price auction with the possibility of cancelled bids. We then implement both of these environments in a virtual laboratory in order to see which theory can best explain observed bidding behaviour. We find that, when plausibly calibrated, the level-k model substantially under-predicts the observed bids and is clearly out-performed by equilibrium. Moreover, attempting to fit the level-k model to the observed data results in implausibly high estimated levels, which in turn bear no relation to the levels inferred from a game known to trigger level-k reasoning. Finally, subjects almost never appeal to iterated reasoning when asked to explain how they bid. Overall, these 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.