Abstract

We study the effect of ambiguity on expected revenue in multi-unit auctions where bidders have independent private values, maxmin preferences, and single-unit demand. If the set of priors is suitably rich, we show that the discriminatory or `pay-as-bid' auction has the highest expected revenue followed by the sequential first-price auction and then the sequential second-price auction. The uniform price auction with the `highest losing bid ' pricing rule does the worst. Our results also extend to some open auction formats.

Abstract

We revisit the (non-)identification of affiliated interdependent-value auctions from the perspective of sequential auctions introduced by Milgrom and Weber (2000). In contrast to static auctions, prices in early rounds affect bidding in later rounds in sequential auctions, generating enough variation for testing interdependent against private values and model identification. We develop nonparametric tests and identification results by exploring the functional dependence of the pseudo values in later rounds on the prices in early rounds. We also discuss applications and extensions of our results, including cases of non-identical goods, observed covariates and unobserved heterogeneity.

Abstract

We study sequential auctions of identical units with declining prices. In eBay-style Swedish train-ticket auctions, prices fall 8.5% per round and bids rise with preceding-round prices, patterns inconsistent with standard models. We prove sequential second-price auctions with ambiguity-averse bidders have a unique equilibrium matching both. We establish an identification result using inter-temporal first-order conditions to recover the valuation distribution and history-dependent worst-case beliefs, without an exclusion restriction. Estimated beliefs first-order stochastically dominate valuations at every history and shift with the price path, and the model reproduces both empirical patterns. Counterfactually, first-price auctions raise revenue 19–28%; uniform-price auctions lower it 10–27%.

Abstract

This paper studies an ultimatum game with imperfect information. The players can form a match that generates either a high or low surplus. The sender only has a prior over the size of the surplus, but can acquire costly information about the surplus. The sender has preferences over bundles, and makes proposals that are bundles. The receiver knows the size of the surplus when responding, and accepts as long as the total cost of the bundle is lower than the surplus. It is shown that under these conditions, an equilibrium with two types of inefficiencies exists. The first type of loss is caused by conflict where the sender makes a propositions that is rejected, and the second type of loss is the informational cost incurred by the sender. The inefficiency is bounded by entropy of the prior times the scaling factor of information cost minus the expected payoff of the responder. Given the losses, we then study if there is room for an intermediary, whose interest is to maximize the outcome of the sender. The intermediary's proposed split is only realized if it is accepted by both parties. The parties will otherwise get to the play the ultimatum game with costly information acquisition. It is shown that there exists a proposed split that is accepted by both parties if the intermediary does not introduce new inefficiencies that are larger than the expected losses from the ultimatum game with costly information acquisition.

The model is placed in the context of employer-employee negotiations, where the parties must agree on a compensation package including a wage and other benefits. Understanding the value of the total package is complicated, and the worker must acquire information, which is costly, to make an optimal claim. The role of the intermediary is interpreted as a labor union who provide agency services for the worker by pooling the states. It is then shown that collective bargaining is easier to sustain as an equilibrium outcome if worker preferences are more homogeneous. This result is in line with the cross-country empirical evidence that is provided at the end of the paper.

Abstract

In 1951, the National Collegiate Athletic Association (NCAA) instigated their first TV plan, which restricted the number of college football games that could be broadcasted on TV. The reason for the plan was that unrestricted TV broadcasting was believed to be detrimental for stadium attendance of college football. This paper investigates if TV broadcasting of college football caused stadium attendance to decrease as the NCAA anticipated. To do so I use data on game attendance and accessibility to TV broadcasts of games from the early to mid 1950s. I compare games played by a team in a county when no TV broadcasted game was available, to games played when a TV broadcasted game was accessible. The findings suggest that a small drop in attendance caused by simultaneous broadcasts of games cannot be ruled out, however, the drop is not as large as anticipated and communicated by the NCAA.