Meaningful and Meaningless Solutions for Cooperative N-person Games

Game values often represent data that can be measured in morethan one acceptable way (e.g. monetary amounts). We point out thatin such a case a statement about cooperative n-person game modelmight be "meaningless" in the sense that its truth or falsity depends onthe choice of an acceptable way to measure game values. In particularwe analyze statements about solution concepts such as the core, stablesets, the nucleolus, the Shapley value (and its generalizations).Keywords: Cooperative n-person Games, Measurement, SensitivityAnalysis

Sequential vs. Single-Round Uniform-Price Auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k1 objects are sold in the first round and k2 in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces first-round revenue. Thus, revenue is greater in a single-round, uniform auction for k = k1 + k2 objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify two informational effects: a positive effect on second-round price and an ambiguous effect on first-round price. The expected first-round price can be greater or smaller than with no bid announcement, and greater or smaller than the expected price in a single-round uniform auction. As a result, total expected revenue in a sequential uniform auction with winning-bids announcement can be greater or smaller than in a single-round uniform auction.Multi-unit auctions, Sequential auctions, Uniform-price auction, Affiliated values, Information revelation

Sequential vs. Single-Round Uniform-Price Auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k1 objects are sold in the first round and k2 in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces the first-round price. Total revenue is greater in a single-round, uniform auction for k = k1 + k2 objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify a positive informational effect on the second-round price. Total expected revenue in a sequential uniform auction with winning-bids announcement may be greater or smaller than in a single-round uniform auction, depending on the model’s parameters.Multi-Unit Auctions; Sequential Auctions; Uniform-Price Auction; Affiliated Values; Information Revelation

Information Aggregation in Auctions with an Unknown Number of Bidders

Information aggregation, a key concern for uniform-price, common-value auctions with many bidders, has been characterized in models where bidders know exactly how many rivals they face. A model allowing for uncertainty over the number of bidders is essential for capturing a critical condition for information to aggregate: as the numbers of winning and losing bidders grow large, information aggregates if and only if uncertainty about the fraction of winning bidders vanishes. It is possible for the seller to impart this information by precommitting to a specified fraction of winning bidders, via a proportional selling policy. Intuitively, this makes the proportion of winners known, and thus provides all the information that bidders need to make winners curse corrections.information aggregation, common-value auctions, uncertain level of competition

Scalings in Linear Programming: Necessary and Sufficient Conditions for Invariance

We analyze invariance of the conclusion of optimality for the linear programming problem under scalings (linear, affine,...) of various problem parameters such as: the coefficients of the objective function, the coefficients of the constraint vector, the coefficients of one or more rows (columns) of the constraint matrix. Measurement theory concepts play a central role in our presentation and we explain why such approach is a natural one

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This document in subdirectory RS/96/48 / Scalings in Linear Programming: Necessary and Sufficient Conditions for Invariance

is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRIC