Unbalanced Allocations

We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set. Applications of this generic algorithm range from cost minimization to condensed matter physics. In this paper, we analyze the distribution of the bin loads produced by this algorithm, considering, for example, largest and smallest loads, loads of subsets of the bins, and the likelihood of bins having equal loads

On robustness and dynamics in (un)balanced coalitional games

We build upon control theoretic concepts like robustness and dynamics to better accommodate all the situations where the coalitions’ values are uncertain and subject to changes over time. The proposed robust dynamic framework provides an alternative perspective on the study of sequences of coalitional games or interval valued games. For a sequence of coalitional games, either balanced or unbalanced, we analyze the key roles of instantaneous and average games. Instantaneous games are obtained by freezing the coalitions’ values at a given time and come into play when coalitions’ values are known. On the other hand, average games are derived from averaging the coalitions’ values up to a given time and are key part of our analysis when coalitions’ values are unknown. The main theoretical contribution of our paper is a design method of allocation rules that return solutions in the core and/or $\epsilon$-core of the instantaneous and average games. Theoretical results are then specialized to a simulated example to shed light on the impact of the design method and on the performance of the resulting allocation rules

An Approximate "Law of One Price" in Random Assignment Games

Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion

Aid and AIDS: a delicate cocktail

Development assistance targeting health overwhelmingly concentrates on HIV/AIDS. This column argues that that focus neglects critical demographic issues and degrades health infrastructure, particularly in Sub-Saharan Africa. The prime rule for AIDS aid should be “First, do no harm”.

Detecting unbalanced bids via an improved grading-based model

Unbalanced bidding, also known as skewed bidding, is the process of increasing and/or decreasing the prices of various bid items without altering the total offered bid price. Bids can be unbalanced either mathematically (front-end loading) or materially (quantity error exploitation). Owners should be very careful when evaluating the tenders as awarding a contract to an unbalanced bid may result in severe cost overruns because the prices of those items do not reflect their true costs and markup allocations. Unbalanced bidding is still a contentious issue in the construction industry. While some researchers consider it as a legal bidding strategy in such a fierce competitive business environment, others view it as an unethical practice and claim that unbalanced bids should be disqualified. Studies regarding unbalanced bidding can be categorized into two groups: (1) the ones focusing on detecting or preventing this practice to help owners; and 2) the ones focusing on optimizing unbalanced bidding to help contractors. This study aims to develop a model, which consists of eight grading systems, to assist owners in detecting materially unbalanced bids. The proposed model is the improved version of the previous model, which was composed of five grading systems. In order to demonstrate how this grading-based model can be used by owners, an illustrative example is presented. It was found that owners can easily and successfully detect unbalanced bids via the proposed mode