Combinatorial auctions are used for the efficient allocation of heterogeneous goods and services. They require appropriate software platforms providing automated winner determination and decision support for bidders. Several promising ascending combinatorial auction formats have been developed throughout the past few years based on primal-dual algorithms and linear programming theory. The Ascending Proxy Auction (Ausubel and Milgrom 2006a) and iBundle (Parkes and Ungar 2000) result in Vickrey payoffs when the coalitional value function satisfies buyer submodularity conditions and bidders bid best-response. These auction formats are based on non-linear and personalized ask prices. In addition, there are a number of designs with linear prices that have performed well in experiments (Bichler et al. 2009, Kwasnica et al. 2005. In this paper, we provide the results of lab experiments testing these different auction formats in the same setting. We analyze aggregate metrics, such as efficiency and auctioneer revenue for small and medium-sized value models. In addition, we provide a detailled analysis not only of aggregate performance metrics, but of individual bidding behavior under alternative combinatorial auction formats.

Forecasts are pervasive in all areas of applications in business and daily life. Hence evaluating the accuracy of a forecast is important for both the generators and consumers of forecasts. There are two aspects in forecast evaluation: (a) measuring the accuracy of past forecasts using some summary statistics, and (b) testing the optimality properties of the forecasts through some diagnostic tests. On measuring the accuracy of a past forecast, this paper illustrates that the summary statistics used should match the loss function that was used to generate the forecast. If there is strong evidence that an asymmetric loss function has been used in the generation of a forecast, then a summary statistic that corresponds to that asymmetric loss function should be used in assessing the accuracy of the forecast instead of the popular root mean square error or mean absolute error. On testing the optimality of the forecasts, it is demonstrated how the quantile regressions set in the prediction–realization framework of Mincer and Zarnowitz (in J. Mincer (Ed.), Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance (pp. 14–20), 1969) can be used to recover the unknown parameter that controls the potentially asymmetric loss function used in generating the past forecasts. Finally, the prediction–realization framework is applied to the Federal Reserve's economic growth forecast and forecast sharing in a PC manufacturing supply chain. It is found that the Federal Reserve values overprediction approximately 1.5 times more costly than underprediction. It is also found that the PC manufacturer weighs positive forecast errors (under forecasts) about four times as costly as negative forecast errors (over forecasts).

We study a non-cooperative game for joint replenishment by n firms that operate under an EOQ-like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We characterize the behavior and outcomes under undominated Nash equilibria.

W e analyze if and when symmetric Bayes Nash equilibrium predictions can explain human bidding behavior in multi-object auctions. We focus on two sealed-bid split-award auctions with ex ante split decisions as they can be regularly found in procurement practice. These auction formats are straightforward multi-object extensions of the firstprice sealed-bid auction. We derive the risk-neutral symmetric Bayes Nash equilibrium strategies and find that, although the two auction mechanisms yield the same expected costs to the buyer, other aspects of the two models, including the equilibrium bidding strategies, differ significantly. The strategic considerations in these auction formats are more involved than in single-lot first-price sealed-bid auctions, and it is questionable whether expected utility maximization can explain human bidding behavior in such multi-object auctions. Therefore, we analyzed the predictive accuracy of our equilibrium strategies in the laboratory. In human subject experiments we found underbidding, which is in line with earlier experiments on single-lot first-price sealed-bid auctions. To control for regret, we organize experiments against computerized bidders, who play the equilibrium strategy. In computerized experiments where bid functions are only used in a single auction, we found significant underbidding on low-cost draws. In experiments where the bid function is reused in 100 auctions, we could also control effectively for risk aversion, and there is no significant difference of the average bidding behavior and the risk-neutral Bayes Nash equilibrium bid function. The results suggest that strategic complexity does not serve as an explanation for underbidding in split-award procurement auctions, but risk aversion does have a significant impact.