A Naïve Bidder in a Common Value Auction

We study a common value auction in which two bidders compete for an item the value of which is a function of three independent characteristics. Each bidder observes one of these characteristics, but one of them is 'naive' in the sense that he does not realize the other bidder's signal contains useful information about the item's value. Therefore, this bidder bids as if this were an Independent Private Values auction. We show that the naive's bidder payoff exceeds that of his fully rational opponent for all symmetric unimodal signal distributions. We also show that naive bidding is persistent in the evolutionary sense.

The University Fruit Farm at Union, Nebraska

The University Fruit Farm may be considered as a substation or detached portion of the Nebraska Experiment Station. It was established to assist in answering questions pertaining to fruit production, and only experiments of this sort are carried on. Supervision of this property rests with the Department of Horticulture of the Nebraska College of Agriculture. This circular has been prepared with the view of furnishing visitors to the farm with a brief outline of the experimental projects. Further information is available from either the local foreman or from the Department. Visitors are always welcome and helpful suggestions are solicited

The Greedy Heuristic Applied to a Class of Set Partitioning and Subset Selection Problems

The greedy heuristic may be used to obtain approximate solutions to integer programming problems. For some classes of problems, notably knapsack problems related to the coin changing problem, the greedy heuristic results in optimal solutions. However, the greedy heuristic does quite poorly at maximizing submodular set functions. This paper considers a class of set partitioning and subset selection problems. Results similar to those for maximizing submodular set functions are obtained for less restricted objective functions. The example used to show how poorly the heuristic does is motivated by a problem arising from an actual auction; the negative results are not mere mathematical pathologies but genuine shortcomings of the greedy heuristic. The greedy heuristic is quite successful at solving a class of knapsack problems related to the coin changing problem. Chang and Korsh [2], Hu and Lenard [5], Johnson and Kernighan [7], and Magazine, Nemhauser, and Trotter [8] show that the greedy heuristic results in optimal solutions for such problems. Problems of optimal subset selection have been studied by Boyce, Farhi, and Weischedel [1], indicating the need for a simply heuristic for obtaining approximate solutions. Fisher, Nemhauser, and Wolsey [4, 9, 10] have shown that the greedy heuristic may result in a solution for problems of maximizing submodular set functions with a value which is a relatively small fraction of the optimum. This paper derives similar results for a wider class of set partitioning and subset selection problems. The problem is formulated in the first section of the paper. Although the motivating problem results in a set partitioning problem, the results of the later sections apply as well to a wider class of subset selection problems. The more general problem statement is given as problem II; however, most of the discussion uses examples from the more restrictive problem I. The second section considers various possible restrictions to be placed on the objective function. The conditions may be stated in terms of either of the problem statements; the two forms of the conditions are shown to be essentially equivalent. Included among the possibilities are submodular set functions and several alternatives which are relaxations of submodularity. The relative generality of the various possibilities is illustrated by a couple of simple examples. The next two sections contain the main results of the paper. Objective functions which are “normal,” “monotonic,” and “discounted” are considered first. For such cases, the greedy heuristic solution is shown to have a value of at least 1/m of the optimal value, where m is the cardinality of the largest feasible subsets. The third section concludes by presenting a class of examples for which the greedy solution value is arbitrarily little more than the bound established above. Similar bounds may be obtained if the “discounted” condition is replaced by “variably discountedness,” although now the bounds must be functions of the variable discounting functions. Again, a lower bound is derived for the greedy solution value. The section concludes by presenting a class of examples for which the greedy solution value is arbitrarily little more than this bound. The last section is an attempt to reassure the reader that the above results are not simply pathological cases. An actual real estate auction [6] is briefly described. This real world problem is used to motivate bidding functions (of two hypothetical bidders) similar to those used to establish the tightness of the bound in sections three and four. This discussion suggests that the results are not mere mathematical pathologies and that, from many a practical viewpoint, the greed heuristic is not a satisfactory algorithm for obtaining optimal solutions to set partitioning and subset selection problems

Auctions and Bidding Models: A Survey

Auctions and bidding models are attracting an ever increasing amount of attention. The Stark and Rothkopf (1977) bibliography includes approximately 500 papers on the subject; additional work has been reported since the bibliography was compiled. This paper presents a general framework for classifying and describing various auctions and bidding models, and surveys the major results of the literature in terms of this framework

Comparing inter-specific competition for continuous corn grown in a living mulch with stover removal

Chapter 3: Agronomic Response of Living Mulches in Continuous Corn with Stover Removal A paper to be submitted to Agronomy Journal Dustin R. Wiggans, Jeremy W. Singer, Kenneth J. Moore, and Kendall R. Lamkey Corn stover provides producers a potential additional market for selling biomass for biomass production. However, corn stover returns nutrients to the soil, decreases soil erosion, and helps maintain soil properties. Long term stover removal has been determined to cause detrimental environmental effects (Wilhelm et al., 1986; Mann et al., 2002; Nelson, 2002). Perennial groundcovers or living mulches grow simultaneously with the main row crop and are maintained as living groundcover throughout the growing season. Groundcovers grown in the interrow of row crops may provide beneficial functions such as weed suppression, water infiltration, nutrient cycling, and carbon inputs, but should not disrupt corn development and productivity. The objective of this research was to evaluate management systems including living mulches grown in continuous corn with stover removal. Corn was planted into three perennial groundcovers: creeping red fescue (CF) (Festuca rubra L.), Kentucky bluegrass (KB) (Poa pratensis L.), and a mixture of creeping red fescue and white clover (MX) (Trifolium repens L.) in 2008 and 2009 near Ames, IA. Management treatments were fall strip tillage (ST) and no-tillage (NT), accompanied with either a pre-planting paraquat burn-down followed by two post-planting glyphosate applications (PQ), or a pre-planting glyphosate band followed by two post-planting glyphosate applications (RU). Grain yields ranged from 5620 (MX RU ST) to 11339 (KB PQ ST) kg ha-1 in 2008, and 7611 (CF RU NT) to 12768 (KB PQ NT) kg ha-1 in 2009. Kentucky bluegrass PQ ST produced similar yields compared to the control in 2008, and all treatments were similar to the control in 2009, except CF RU NT. Kentucky bluegrass PQ ST produced the greatest stover dry matter (DM) (6883 kg ha-1) in 2008, and KB PQ NT produced the most in 2009 (10862 kg ha-1), excluding the control. In both years the herbicide significantly affected grain yield and stover DM with PQ producing better yields than RU (except in the MX stover DM treatments in 2008). Tillage did not have similar effects. Kentucky bluegrass, paraquat herbicide, and either no-tillage or strip-tillage provide the most consistent response across these growing seasons and showed the greatest potential to implementing living mulches in corn bioenergy cropping systems. Chapter 4: Corn Water Use in Living Mulch Systems with Stover Removal A paper to be submitted to Agronomy Journal Dustin R. Wiggans, Jeremy W. Singer, Kenneth J. Moore, and Kendall R. Lamkey Corn stover returns nutrients to the soil, decreases soil erosion, and helps maintain overall soil properties. Additionally, corn stover may provide producers an additional market for selling biomass, but long term stover removal has been determined to cause detrimental environmental effects (Wilhelm et al., 1986; Mann et al., 2002; Nelson, 2002). Living mulches, or perennial groundcovers, grow simultaneously with the main row crop and are maintained as living groundcover throughout the growing season. Groundcovers grown in the interrow of row crops can provide beneficial functions such as weed suppression, nutrient cycling, and increase water infiltration, but should not disrupt corn development and productivity. The objectives of this research were to quantify soil and plant water use in continuous corn with and without a living mulch with stover removal. Corn was planted into living mulch groundcovers of creeping red fescue (CF) (Festuca rubra L.), and Kentucky bluegrass (KB) (Poa pratensis L.) in 2008 and 2009 near Ames, IA. Management was no-tillage (NT) with a pre-planting paraquat burn-down followed by two post-planting glyphosate applications (PQ) during the season. Kentucky bluegrass (P = 0.3743) was less competitive than CF (P = 0.0482) compared to a no living mulch control for soil water content (SWC) at the 15 cm soil depth during the vegetative growth period in 2008. Additionally in 2008, both KB (0.3681 m3 m-3) and CF (0.3696 m3 m-3) were significant compared to a no living mulch control (0.3473 m3 m-3) for SWC at the 15 cm soil depth during the post-maturity period. There were no significant affects on SWC at the 15 cm level among treatments in 2009. Soil water content at the 45 cm soil depth and soil temperature (ST) at the 15 cm soil depth were non-significant among treatments both years. Living mulch did affect leaf area index (LAI) at V6, V12, and R1 in 2008, and only at V6 in 2009. Carbon dioxide exchange rate (CER) and corn transpiration rate (TR) were not affected by groundcover either year. Reproductive water use efficiency (RWUE) for KB (50 and 41 g grain cm water-1) was greater compared to the control (41 and 36 g grain cm water-1) by 22 and 14% in 2008 and 2009, respectively. Kentucky bluegrass was less competitive than CF both years, and used water more efficiently during reproductive growth compared to a no-living mulch control. Therefore, KB demonstrates the greatest potential to implementing living mulches in a corn bioenergy cropping systems

Sealed Bid Auctions with Non-Additive Bid Functions

A traditional sealed bid auction of a single item sells the item at the high bid price to a bidder with the highest bid. Such an auction may be used to auction several items; each bidder submits a bid on each item and each item is sold to a high bidder on that item. Implicit in this traditional scheme is the assumption that the bid for a set of items is the sum of the bids on the individual items: there are instances where this restriction appears unreasonable. This paper considers a more general sealed bid auction in which bids are submitted on all possible subsets of the items. The items are partitioned among the bidders to maximize revenue, where each bidder are partitioned among the bidders to maximize revenue, where each bidder pays what was bid on the set of items actually received. In general, the set partitioning problem is an extremely difficult integer programming problem, and there are two alternatives. The “greedy” and “sequential auction” heuristics are shown to result, at least for some examples, in very sub-optimal solutions. However, a class of slightly less general auction problems is presented for which optimal solutions may be calculated relatively easily; suggesting that some form of general sealed bid auctions may be appropriate in some situations

Auctions and Bidding Models: A Survey

Auctions and bidding models are attracting an ever increasing amount of attention. The Stark and Rothkopf (1977) bibliography includes approximately 500 papers on the subject; additional work has been reported since the bibliography was compiled. This paper presents a general framework for classifying and describing various auctions and bidding models, and surveys the major results of the literature in terms of this framework

Strawberries in Nebraska

The strawberry is probably the most important small fruit grown in Nebraska. It thrives well in all sections of the State where the moisture supply is not too limited, being found almost universally in home plantings. It is also produced commercially in certain favored localities but this acreage is limited