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

Using data from online auctions of train tickets in Sweden, we study the ``declining price anomaly'' in sequential auctions. First, we study a model of sequential second-price auctions with independent private values that closely matched the auctions for train tickets and assume bidders have maxmin expected utilities over multiple priors. In the unique symmetric equilibrium, bidders use their worst-case conditional beliefs to evaluate their payoffs in each round of the auction. This makes bidders underestimate their future payoffs and thus bid relatively more aggressively in earlier rounds and causing prices to decline on average. Also, equilibrium, in general, is history-dependent even in the independent private values paradigm, which is symptomatic of dynamic inconsistency, a common feature of dynamic problems with ambiguity. We show that this latter implication can distinguish the ambiguity aversion explanation from other theoretical explanations of the anomaly depending on the direction of the dependence. A reduce form analysis of the bidding behavior in the train ticket auctions shows that bidding in the auctions is positively history-dependent, which provides evidence in favor of our approach over other models.

Finally, we show that using dynamic bidding data we can identify and disentangle bidders worst-case beliefs from the true distribution of valuations, even in the presence of dynamic inconsistency, using a novel technique that exploits bidders' inter-temporal first order conditions. Employing our identification we estimate the true distribution of valuations and bidders' worst-case beliefs. Our estimation uncovers a first-order stochastic dominance relationship between beliefs and the true distribution as well as changing of beliefs over time, both consistent with ambiguity aversion. Our counterfactuals show that, while ambiguity increases the seller's revenue by at least 18% compared to the common prior case, switching to sequential first-price auctions would further increase revenue by at least 11%.

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.