Mixing sets linked by bidirected paths

Recently there has been considerable research on simple mixed-integer sets, called mixing sets, and closely related sets arising in uncapacitated and constant capacity lot- sizing. This in turn has led to study of more general sets, called network-dual sets, for which it is possible to derive extended formulations whose projection gives the convex hull of the network-dual set. Unfortunately this formulation cannot be used (in general) to optimize in polynomial time. Furthermore the inequalities definining the convex hull of a network-dual set in the original space of variables are known only for some special cases. Here we study two new cases, in which the continuous variables of the network-dual set are linked by a bi- directed path. In the first case, which is motivated by lot-sizing problems with (lost) sales, we provide a description of the convex hull as the intersection of the convex hulls of 2^n mixing sets, where n is the number of continuous variables of the set. However optimization is polynomial as only n + 1 of the sets are required for any given objective function. In the second case, generalizing single arc flow sets, we describe again the convex hull as an intersection of an exponential number of mixing sets and also give a combinatorial polynomial-time separation algorithm.mixing sets, extended formulations, mixed integer programming, lot-sizing with sales

Success: talent, intelligence or beauty ?

We analyze the Celebrity 100 annual list of the world’s most “powerful celebrities” compiled and published by Forbes Magazine. The lists provide an interesting collection of people, that includes their earnings, and the perception of citizens concerning the attributes that made them become celebrities. We analyze the relationship between their earnings and the perceptions on their intelligence, talent, beauty and other attributes, and show that though beauty plays a role, intelligence and talent are more important.earnings, economic success, talent

Compensating the dead? Yes we can!

An early death is, undoubtedly, a serious disadvantage. However, the compensation of short-lived individuals has remained so far largely unexplored, probably because it appears infeasible. Indeed, short-lived agents can hardly be identified ex ante, and cannot be compensated ex post. We argue that, despite the above difficulties, a compensation can be carried out by encouraging early consumption in the life cycle. In a model with heterogeneous preferences and longevities, we show how a specific social criterion can be derived from intuitive principles, and we study the corresponding optimal policy under various informational assumptions. We also study the robustness of our solution to alternative types of preferences and savings policies.compensation, longevity, mortality, fairness, redistribution

Rock and roll bands, (in)complete contracts and creativity

Members of a rock and roll band are endowed with different creativity. They match and eventually obtain credit for song writing as well as a share of the returns from sales. More creative members increase the probability of success but may also claim a larger share of the pie. In our theoretical model, the nature of matching (postive or negative assortative) as well as the covariation between the probability of having a “hit” and the dispersion of credits given to individual members are a function of the completeness of contracting. When members adopt a “gentleman’s agreement” to share credits equally, the covariation between the probability of a hit and the dispersion of credits is negative, which is the consequence of positive assortative matching in creativity. The data show that the relation between dispersion and success is significantly negative, and that rock bands are thus likely to sign incomplete contracts.overlapping generations, resource management, common pool resource, spatial interdependence, strategic behaviour, cooperative behaviour

Unions' relative concerns and strikes in wage bargaining

We consider a model of wage determination with private information in a duopoly. We investigate the effects of unions having relative concerns on the negotiated wage and the strike activity. We show that an increase of unions' relative concerns has an ambiguous effect on the strike activity.relative position, wage bargaining, private information, strike activity

Lower bounds rule!

We propose two axioms that introduce lower bounds into resource monotonicity requirements for rules for the problem of adjudicating conflicting claims. Suppose the amount to divide increases. The first axiom requires that two claimants whose lower bound changes equally experience an equal change in awards. The second axiom requires that extra resources are divided only among those claimants who experience a strictly positive change in their lower bound. We show that, in the two-claimant case, Concede-and-Divide is the only rule that satisfies both axioms when the axioms are defined over a large set of lower bounds that include the minimal rights lower bound and the secured lower bound. We also show that, in the n-claimant case where at least one claimant claims the total amount, the Minimal Overlap rule is the only rule that satisfies both axioms when the axioms are defined over the secured lower bound.claims problems, lower bounds, concede-and-divide, minimal overlap rule

Low-rank matrix approximation with weights or missing data is NP-hard

Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data analysis, has been successfully used in several applications, such as in collaborative filtering to design recommender systems or in computer vision to recover structure from motion. In this paper, we study the computational complexity of WLRA and prove that it is NP-hard to find an approximate solution, even when a rank-one approximation is sought. Our proofs are based on a reduction from the maximum-edge biclique problem, and apply to strictly positive weights as well as binary weights (the latter corresponding to low-rank matrix approximation with missing data).low-rank matrix approximation, weighted low-rank approximation, missing data, matrix completion with noise, PCA with missing data, computational complexity, maximum-edge biclique problem

Foreign languages’ acquisition: self learning and linguistic schools

We examine patterns of acquiring non-native languages in a model with two linguistic communities with heterogeneous learning skills, where every individual faces the choice of self-learning the foreign language or acquiring it at a profit-maximizing linguistic school. We consider a one-school model with divisions in both communities and various two-school settings with a school in each community. We compare the number of learners and welfare implications under self- learning with those obtained under various schooling contexts. In particular, we show that for communities with similar size, introducing language schools always increases the number of learners with respect to the exclusive self-learning option.communicative benefits, linguistic equilibrium, learning costs

Vertical integration and exclusivities in maritime freight transport

A key recent theme in maritime freight transport is the involvement of shipping lines in terminal management. Such investments are costly but allow liners to provide better service. Most of these new terminals are dedicated terminals but some are non-exclusive and let rivals access them for a fee. In this paper, we show that a shipping line that builds its own terminal finds it strategically profitable i) to continue routing part of its cargo through the open port facilities, and ii) to keep its terminal non-exclusive. In this way, the liner investor pushes part of the rival's freight from the open to the new terminal. Besides, under non-exclusivities, the shipping lines offer a wider variety of services, total freight increases and the resulting equilibrium fares are higher than with a dedicated terminal.freight transport, shipping lines, vertical integration

Product innovation and market acquisition of firms

The paper explores the incentives for an incumbent firm to acquire an entrant willing to sell a product innovation, rather than openly compete with this entrant and, in case of acquisition, the incentives to sell simultaneously both the existing products and the new one, rather than specializing on a single variant. We prove that, in some circumstances, an incumbent firm can find it profitable to make an acquisition proposal to the entrant in order to deter entry. Nevertheless, in this acquisition scenario, a product proliferation strategy is never observed at equilibrium. Rather, the incumbent restricts itself to offer either its own variant or the product innovation produced by the entrant, depending on the quality differential existing between them. It follows that, while being available for sale, sometimes the innovation simply remains unexploited