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Given n independent random vectors with common density f on R d , we study the weak convergence of three empirical-measure based estimators of the convex λ-level set L λ of f , namely the excess mass set, the minimum volume set and the maximum probability set, all selected from a class of convex sets A that contains L λ. Since these set-valued estimators approach L λ , even the formulation of their weak convergence is non-standard. We identify the joint limiting distribution of the symmetric difference of L λ and each of the three estimators, at rate n −1/3. It turns out that the minimum volume set and the maximum probability set estimators are asymptotically indistinguishable, whereas the excess mass set estimator exhibits "richer" limit behavior. Arguments rely on the boundary local empirical process, its cylinder representation, dimension-free concentration around the boundary of L λ , and the set-valued argmax of a drifted Wiener process. MSC 2010 subject classifications: Primary 62G05, 62G20; secondary 60F05, 60F17.

In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only the absence of arbitrage opportunities. We formulate this as a generalized moment problem and utilize the well-known Moment-Sum-of-Squares (SOS) hierarchy of Lasserre to obtain bounds on the range of the possible prices. A complementary approach (also due to Lasserre) is employed for comparison. We present several numerical examples to demonstrate the viability of our approach. The framework we consider makes it possible to incorporate different kinds of observable data, such as moment information, as well as observable prices of options on the assets of interest., Comment: 20 pages

We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton's method for self-concordant functions, including the case of inexact search directions. The analysis uses semidefinite programming performance estimation, as pioneered by Drori and Teboulle [Mathematical Programming, 145(1-2):451-482, 2014], and extends recent performance estimation results for the method of Cauchy by the authors [Optimization Letters, 11(7), 1185-1199, 2017]. To illustrate the applicability of the tools, we demonstrate a novel complexity analysis of short step interior point methods using inexact search directions. As an example in this framework, we sketch how to give a rigorous worst-case complexity analysis of a recent interior point method by Abernethy and Hazan [PMLR, 48:2520-2528, 2016]., Comment: 22 pages, 1 figure. Title of earlier version was "Worst-case convergence analysis of gradient and Newton methods through semidefinite programming performance estimation"

International audience; The 62nd life cycle assessment (LCA) forum was held on 9 September 2016 to discuss the state of research and application with regard to consequential life cycle assessment. This conference report presents the highlights of the LCA forum. The state of the art of consequential LCA was presented from different viewpoints. It was pointed out that consequential LCA is more than marginal mixes and avoided burdens and involves causal modelling. It was also said that social responsibility calls for consequential LCA. Currently, different models are used to support decision making. It was suggested to make use of the variety of models to check the conclusiveness of their results and thus the reliability of the LCAs. Current and future implementations of consequential LCI models in background databases and linking algorithms were presented. Several speakers presented consequential LCA case studies covering the sectors energy, transport, housing and mining. Some of the LCA models used in the case studies are complemented with general and partial computable equilibrium models and agent-based models and use environmentally extended input-output data or process-based LCA data. Some of the presentations focused on elements such as constrained production, marginal market mixes and technologies or recycling and system expansion. In three parallel workshops, the needs, contents and methodology, and implementation of consequential LCA approaches were discussed. The participants seemed to generally agree on the basic goal that LCA should be able to reflect the consequences of decisions. The inquiry among the participants showed that the demand for consequential LCA studies is hardly existent. The appropriate implementation of consequential modelling in LCA databases and on the appropriate model to be used in consequential LCA case studies was debated. It revealed a need for further and extensive discussions to be able to reach (minimum) consensus.

International audience; Understanding the environmental profile of a product computed from the Life Cycle Assessment (LCA) framework is sometimes challenging due to the high number of environmental indicators involved. The objective here, in guiding interpretation of LCA results, is to highlight the importance of each impact category for each product alternative studied. For a given product, the proposed methodology identifies the impact categories that are worth focusing on, relatively to a whole set of products from the same cumulated database. The approach extends the analysis of Representativeness Indices (RI) developed by Esnouf et al. (2018). It proposes a new operational tool for calculating RIs at the level of impact categories for a Life Cycle Inventory (LCI) result. Impact categories and LCI results are defined as vectors within a standardized vector space and a procedure is proposed to treat issues coming from the correlation of impact category vectors belonging to the same Life Cycle Impact Assessment (LCIA) method. From the cumulated ecoinvent database, LCI results of the Chinese and the German electricity mixes illustrate the method. Relevant impact categories of the EU-standardized ILCD method are then identified. RI results from all products of a cumulated LCI database were therefore analysed to assess the main tendencies of the impact categories of the ILCD method. This operational approach can then significantly contribute to the interpretation of the LCA results by pointing to the specificities of the inventories analysed and for identifying the main representative impact categories.

We analyze applications of biform games to linear production (LP) and sequencing processes. Biform games apply to problems in which strategic decisions are followed by some cooperative game, where the specific environment of the cooperative game is in turn determined by these strategic decisions. In biform LP-processes, we allow firms to compete for resources, rather than assuming the resource bundles are simply given. With strategy dependent resource bundles that can be obtained from two locations, we show that the induced strategic game has a (pure) Nash equilibrium, using the Owen set or any game-theoretic solution concept that satisfies anonymity to solve the cooperative LP-game. In biform sequencing processes, we no longer assume an initial processing order is given. Instead, this initial order is strategically determined. Solving the second-stage cooperative sequencing game using a gain splitting rule, we fully determine the set of Nash equilibria of the induced strategic game.

We introduce the half-cycle formulation (HCF), a new integer programming (IP) model for the kidney exchange problem, which has life-saving applications. In HCF, a cycle (i.e., set of kidney swaps) is represented by two compatible halves. After giving several algorithmic enhancements for HCF, we show through extensive computational experiments with an IP solver that our new model outperforms existing formulations when the cycle size limit is set to 4, 5, or 6, depending on the density of the compatibility graph.

We study the inter-temporally optimal innovation strategies of incumbent manufacturing firms that compete in an established market and can extend their product line through product innovation. Firms invest in production capacity and R&D knowledge stock, where the R&D knowledge stock and the current R&D investment determine the hazard rate of innovation. Our findings show that the firms’ optimal R&D strategies are driven by a subtle interplay between the relative positions of their R&D knowledge stocks and their current relative positions on the established market. First, we find that under symmetric investment costs the knowledge leader should spend more on R&D than the knowledge laggard only if it has a substantially smaller market share on the established market. If the knowledge leader’s market share is sufficiently large, its optimal investment in R&D is so small that its innovation rate is lower than the knowledge laggard’s. Second, optimal investment in R&D knowledge is negatively affected by the opponent’s production capacity on the established market if the competitor has not innovated yet. However, we find that this effect is reversed after the competitor has successfully introduced the new product on the submarket. Third, the manufacturing firm with higher costs of adjusting production capacity for the established product has a higher incentive to engage in product innovation and might even achieve a higher total discounted profit than its more efficient competitor.

We consider the two bar charts packing problem (2-BCPP), a recent combinatorial optimization problem whose aim is to pack a set of one-dimensional items into the minimum number of bins. As opposed to the well-known bin packing problem, pairs of items are grouped to form bar charts, and a solution is only feasible if the first and second items of every bar chart are packed in consecutive bins. After providing a complete picture of the connections between the 2-BCPP and other relevant packing problems, we show how we can use these connections to derive valid lower and upper bounds for the problem. We then introduce two new integer linear programming (ILP) models to solve the 2-BCPP based on a nontrivial extension of the arcflow formulation. Even though both models involve an exponential number of constraints, we show that they can be solved within a constraint generation framework. We then empirically evaluate the performance of our bounds and exact approaches against an ILP model from the literature and demonstrate the effectiveness of our techniques on both benchmarks inspired by the literature and new classes of instances that are specifically designed to be hard to solve. The outcomes of our experiments are important for the packing community because they indicate that arcflow formulations can be used to solve targeted packing problems with precedence constraints and also that some of these formulations can be solved with constraint generation. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.1256 .

Due to their relation to the linear complementarity problem, absolute value equations have been intensively studied recently. In this paper, we present error bound conditions for absolute value equations. Along with the error bounds, we introduce a condition number. We consider general scaled matrix p-norms, as well as particular p-norms. We discuss basic properties of the condition number, including its computational complexity. We present various bounds on the condition number, and we give exact formulae for special classes of matrices. Moreover, we consider matrices that appear based on the transformation from the linear complementarity problem. Finally, we apply the error bound to convergence analysis of two methods for solving absolute value equations.

The price of anarchy is the most well-known measure for quantifying the inefficiency of equilibrium flows in traffic networks and routing games. In this work, we give unifying price of anarchy bounds for atomic and non-atomic parallel link routing games with polynomial cost functions under various cost objectives including the arithmetic mean, geometric mean and worst-case cost objective. We do this through the study of the generalized p-mean as cost objective, and obtain upper bounds on the price of anarchy in terms of this parameter p. Our bounds unify existing results from the literature, and, in particular, give alternative proofs for price of anarchy results in parallel link routing games with polynomial cost functions under the geometric mean objective obtained by Vinci et al. (ACM Trans Econ Comput 10(2):41, 2022). We recover those simply as a limiting case. To the best of our knowledge, these are the first price of anarchy bounds that capture multiple cost objectives simultaneously in a closed-form expression.

Two time series of financial losses may be observed in different overlapping windows, serially dependent, heteroscedastic, and cross-sectionally dependent. Fitting a regression model to each of the two time series, we construct an improved least squares estimator in one series exploiting the cross-sectional dependence with the other series. We employ a random weight bootstrap method to define the new estimator and to establish its asymptotic normality. The developed inference is robust against heteroscedasticity as we do not estimate the GARCH errors. Simulations confirm the efficiency improvement through substantial variance reduction, especially when the cross-sectional dependence is strong and the second series is longer. We illustrate the usefulness of the method by analyzing mutual funds' returns.

Spending time with a spouse is a major gain from marriage. We extend the classical collective model of the household to allow for togetherness between spouses. Togetherness takes the form of joint leisure and joint care for children. Using revealed preference conditions and Dutch data over the years 2009–2012, we find that households are willing to pay €1.20 per hour—10 percent of the average wage—to convert private leisure to joint leisure and €2.10 per hour to convert private childcare to joint childcare. Our results suggest togetherness is an important component of household time use despite being overlooked in the economics literature. (JEL D12, D13, J12, J13, J16, J22)

This paper studies the existence and uniqueness of equilibrium prices in a model of the banking sector in which banks trade contingent convertible bonds with stock price triggers among each other. This type of financial product was proposed as an instrument for stabilizing the global banking system after the financial crisis. Yet it was recognized early on that these products may create circularity problems in the definition of stock prices—even in the absence of trade. We find that, if conversion thresholds are such that bond holders are indifferent about marginal conversions, there exists a unique equilibrium irrespective of the network structure. When thresholds are lower, the existence of equilibrium breaks down, whereas higher thresholds may lead to multiplicity of equilibria. Moreover, there are complex network effects. One bank’s conversion may trigger further conversions—or prevent them, depending on the constellations of asset values and conversion triggers.

Sparse PCA methods are used to overcome the difficulty of interpreting the solution obtained from PCA. However, constraining PCA to obtain sparse solutions is an intractable problem, especially in a high-dimensional setting. Penalized methods are used to obtain sparse solutions due to their computational tractability. Nevertheless, recent developments permit efficiently obtaining good solutions of cardinality-constrained PCA problems allowing comparison between these approaches. Here, we conduct a comparison between a penalized PCA method with its cardinality-constrained counterpart for the least-squares formulation of PCA imposing sparseness on the component weights. We compare the penalized and cardinality-constrained methods through a simulation study that estimates the sparse structure’s recovery, mean absolute bias, mean variance, and mean squared error. Additionally, we use a high-dimensional data set to illustrate the methods in practice. Results suggest that using cardinality-constrained methods leads to better recovery of the sparse structure.

We consider financial networks where agents are linked to each other by financial contracts. A centralized clearing mechanism collects the initial endowments, the liabilities and the division rules of the agents and determinesthe payments to be made. A division rule specifies how the assets of the agentsshould be rationed. Since payments made depend on payments received, weare looking for solutions to a system of equations. The set of solutions isknown to have a lattice structure, leading to the existence of a least and a greatest clearing payment matrix. Previous research has shown how decentralizedclearing selects the least clearing payment matrix. We present a centralizedapproach towards clearing in order to select the greatest clearing paymentmatrix. To do so, we formulate the determination of the greatest clearingpayment matrix as a programming problem. When agents use proportional division rules, this programming problem corresponds to a linear programmingproblem. We show that for other common division rules, it can be written asan integer linear programming problem.

This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: strong compromise admissibility and compromise stability. These two properties allow for a direct, closed formula for the nucleolus. We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover, for each of these two properties, we characterize the family of graphs for which the nucleolus is invariant

We introduce and study a class of optimization problems we call replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Clients with capacity for storing a certain commodity are located at various places; at each client the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations. Clients should never run empty. The natural feature that makes this problem interesting is that we may schedule a replenishment (well) before a client becomes empty, but then the next replenishment will be due earlier also. This added workload needs to be balanced against the cost of routing vehicles to do the replenishments. In this paper, we focus on the aspect of minimizing routing costs. However, the framework of recurring tasks, in which the next job of a task must be done within a fixed amount of time after the previous one is much more general and gives an adequate model for many practical situations. Note that our problem has an infinite time horizon. However, it can be fully characterized by a compact input, containing only the location of each client and a turnover time. This makes determining its computational complexity highly challenging and indeed it remains essentially unresolved. We study the problem for two objectives: min–avg minimizes the average tour cost and min–max minimizes the maximum tour cost over all days. For min–max we derive a logarithmic factor approximation for the problem on general metrics and a 6-approximation for the problem on trees, for which we have a proof of NP-hardness. For min–avg we present a logarithmic factor approximation on general metrics, a 2-approximation for trees, and a pseudopolynomial time algorithm for the line. Many intriguing problems remain open.

We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$. Such maps are known in quantum information theory as the separable bipartite states, while nonseparable states are called entangled. In particular we introduce bounds for the separable rank $\mathrm{rank_{sep}}(\rho)$, defined as the smallest number of rank one states $xx^*\otimes yy^*$ entering the decomposition of a separable state $\rho$. Our approach relies on the moment method and yields a hierarchy of semidefinite-based lower bounds, that converges to a parameter $\tau_{\mathrm{sep}}(\rho)$, a natural convexification of the combinatorial parameter $\mathrm{rank_{sep}}(\rho)$. A distinguishing feature is exploiting the positivity constraint $\rho-xx^*\otimes yy^* \succeq 0$ to impose positivity of a polynomial matrix localizing map, the dual notion of the notion of sum-of-squares polynomial matrices. Our approach extends naturally to the multipartite setting and to the real separable rank, and it permits strengthening some known bounds for the completely positive rank. In addition, we indicate how the moment approach also applies to define hierarchies of semidefinite relaxations for the set $\mathcal{SEP}_d$ and permits to give new proofs, using only tools from moment theory, for convergence results on the DPS hierarchy from (A.C. Doherty, P.A. Parrilo and F.M. Spedalieri. Distinguishing separable and entangled states. Phys. Rev. Lett. 88(18):187904, 2002).

The paper considers a firm that has the option to invest in a project with an unknown profitability, which is affected by general market uncertainty. The project has the adverse effect that it can cause environmental damage. In case the firm has the option to undertake preventive investment at the time of market entry, we get that preventive investment is significant when (i) the project revenue is large, (ii) the environmental incidents potentially cause a huge reduction of firm value, and (iii) when preventive investment substantially decreases the probability of environmental damage occurrence. The optimality of such a preventive investment results in a significant delay of the project investment. When the firm has the possibility to invest in the project first and do the preventive investment later, this will accelerate the project investment and will result in a larger preventive investment when it indeed will decide to do that one later.

We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated explicitly. The primary tool for the proofs is the functional central limit theorem for a weighted tail empirical process. We also present asymptotic normality results for the extreme quantile estimator. A simulation study shows the good finite-sample behavior of our limit theorems. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

We provide three infinite families of graphs in the Johnson and Grassmann schemes that are not uniquely determined by their spectrum. We do so by constructing graphs that are cospectral but non-isomorphic to these graphs.

Sandwich algorithms are commonly used to approximate the Pareto front of a multiobjective (MO) convex problem by enclosing it between an inner and outer approximation. By iteratively improving the approximations, the distance between them is minimized which gives an estimate of how well the Pareto front is approximated. A wellexplainable type of sandwich algorithm is based on weighted sum scalarization (WSS), where the next set of weights is determined by the most promising inner normal of the inner approximation. As these normals can contain negative values, not every optimization will result in finding an efficient point. In order to reduce the number of searches towards the dominated part, we propose an elegant modification of the criterion space which is an advancement on the formulation of Solanki et al. In addition to being well-explainable and easy to integrate within an existing optimization procedure, this modification is theoretically able to obtain all nondominated points of an MO linear programming problem in a finite number of expansions of the inner approximation. Furthermore, we propose two heuristic approaches to determine the distance between the inner and outer approximation that can be used as an alternative for the distance calculation of Solanki et al. These heuristics incorporate the ideas of Solanki et al. And Craft et al. to obtain straightforward and faster methods.

We consider a model of influence over a network with finite-horizon opinion dynamics. The network consists of agents that update their opinions via a trust structure as in the DeGroot dynamics (De Groot (1974)). The model considers two potential external influencers that have fixed and opposite opinions. They aim to maximally impact the aggregate state of opinions at the end of the finite horizon by targeting one agent in one specific time period. In the case of only one influencer, we characterize optimal targets on the basis of two features: shift and amplification. Also, conditions are provided under which a specific target is optimal: the maximum-amplification target. In the case of two influencers, we focus on the existence and characterization of pure strategy equilibria in the corresponding two-person strategic zero-sum game. Roughly speaking, if the initial opinions are not too much in favour of either influencer, the influencers’ equilibrium behaviour is also driven by the amplification of targets.

BACKGROUND: Diarrhea, pneumonia, malnutrition, tuberculosis, measles, and fever are the leading causes of mortality in children under five-years of age (0-59 months), whereas diarrhea alone is the world's second-biggest cause of mortality in this population. This study is particularly important for Pakistan as it focuses on one of the main causes of infant mortality, diarrhea, which is a major challenge for Pakistan to achieve the Sustainable Development Goals to reduce infant mortality to 12/1000 live births by 2030.AIM: This study was planned to investigate the various household, parental, environmental, and child-related factors causing diarrheal diseases in children aged 0-59 months in Punjab Pakistan.METHODS: The study used the data of 38,405 households from the Multiple Indicator Cluster Survey (MICS) 2017-18, directed by the Punjab Bureau of Statistics. Comprehensive descriptive statistics, i.e., cross-tabulations and logistic regression were used for the detailed analysis.FINDINGS: The results showed that infants are more probable to get diarrhea than older children. A wide range of influences were found to affect the probability of a child getting diarrhea, including child-specific, mother-specific and environment-specific ones. One prominent finding was that, at the mother level, the education of the mother played a significant role in reducing diarrhea among children under five-years of age (0-59 months).DISCUSSION: The results of the study contribute to the literature by highlighting that it is an interplay of factors that result in diarrhea. Hence, improving the source of drinking water, e.g., tap water and bottled water, can decrease the occurrence of diarrhea, especially in poor households. It was also revealed that households with a toilet facility of flush have less probability of their children being diagnosed with diarrhea than toilet facilities in open drains and fields. On the child level, results suggested that birth order matters as well, with the firstborn child having a lower probability of contracting diarrhea than siblings born after.APPLICATION TO PRACTICE: Interventions targeting infants and mothers of infants aimed at reducing diarrhea are expected to be very effective to reduce child mortality, one of the main child health challenges faced by Pakistan.

This paper studies a new type of interactive Operations Research problem, called a graph machine scheduling problem (GMS-problem). A GMS-problem combines aspects from minimum cost spanning tree problems and sequencing problems. Given a graph, we aim to first establish a connection order on the players such that the total cost of connecting them to a source is minimal and second to find a cost allocation of such an optimal order among the players involved. We restrict attention to GMS-problems on trees and propose a recursive method to solve these tree GMS-problems integrated with an allocation approach. This latter mechanism consistently and recursively uses myopic reference orders to determine potential cost savings, which will then be appropriately allocated. Interestingly, the transition process from a myopic reference order to an optimal one will be smooth using the switching of blocks of agents based on the basic notion of merge segments.

Let $$S \subseteq \mathbb {R}^n$$ S ⊆ R n be a compact semialgebraic set and let f be a polynomial nonnegative on S. Schmüdgen’s Positivstellensatz then states that for any $$\eta > 0$$ η > 0 , the nonnegativity of $$f + \eta$$ f + η on S can be certified by expressing $$f + \eta$$ f + η as a conic combination of products of the polynomials that occur in the inequalities defining S, where the coefficients are (globally nonnegative) sum-of-squares polynomials. It does not, however, provide explicit bounds on the degree of the polynomials required for such an expression. We show that in the special case where $$S = [-1, 1]^n$$ S = [ - 1 , 1 ] n is the hypercube, a Schmüdgen-type certificate of nonnegativity exists involving only polynomials of degree $$O(1 / \sqrt{\eta })$$ O ( 1 / η ) . This improves quadratically upon the previously best known estimate in $$O(1/\eta )$$ O ( 1 / η ) . Our proof relies on an application of the polynomial kernel method, making use in particular of the Jackson kernel on the interval $$[-1, 1]$$ [ - 1 , 1 ] .

Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converges to the so-called Gibbs distribution over the set of all strategy profiles, when interpreted as a Markov chain. In general, logit dynamics might converge slowly to the Gibbs distribution, but beyond that, not much is known about their algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: i) Is there an efficient algorithm for sampling from the Gibbs distribution? ii) If yes, do there also exist natural randomized dynamics that converges quickly to the Gibbs distribution? We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics (in which we in addition are allowed to randomly interchange the strategies of two players) that converges quickly to the Gibbs distribution in such games. This answers both questions above affirmatively. We also address the first question for the class of so-called capacitated $k$-uniform congestion games. To prove our results, we rely on the recent breakthrough work of Anari, Liu, Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base of a matroid according to strongly log-concave probability distribution., Accepted at the 22nd ACM Conference on Economics and Computation (EC 2021)

Technical developments in the last few decades have created new opportunities for social science research. Internet interviewing has grown in prominence, and several online panels have been setup for scientific research purposes. Technical developments that have driven the development of online panels have also improved coordination and increased the capacity of survey scientists to deploy large scale, complex general social surveys. The landscape, however, is fragmented and integration of existing social science surveys into existing online panels may resolve the duplication of efforts and potential inefficiencies, as well as open up opportunities for more intensive data linkage and interoperability. Linking survey data to other forms of data, such as administrative data, has numerous benefits. There have already been several successful examples of such linkages. But linkages are predominantly post-hoc. A new trend is the move towards surveys that are linkable by design, with complex, relational administrative data. A rapid development of innovative technologies and intensified efforts of linkage and integration will offer opportunities to answer questions that have so far been out of reach for social scientists.

This paper provides a multi-actor perspective on the realization of new infrastructures, motivated by the necessity for infrastructures to support the ongoing climate and energy transition in general, and CO2 transport infrastructures for carbon capture, utilization and storage (CCUS) in particular. We develop a general model to represent infrastructures that allows for a unique decomposition into `elementary infrastructure components' based on heterogeneous user requirements. Notably, it incorporates a cost function with a very generic and adaptable structure, for which we can still explicitly determine the costs of each individual component. As a direct consequence an intuitive cost allocation rule is obtained: equal component cost sharing. This allocation rule is in line with existing game-theoretic concepts and satisfies the desirable properties of advantageous scaling and coalitional rationality. Advantageous scaling guarantees that the costs allocated to each existing user do not increase if the number of users grows larger and coalitional rationality ensures that there is no subgroup of infrastructure users that would have a financial reason to object to the cost allocation. Additionally, we examine the application of our model to a prospective CO2 transport infrastructure for CCUS in the port of Rotterdam and the adjoining industry area.

The graph partition problem (GPP) aims at clustering the vertex set of a graph into a fixed number of disjoint subsets of given sizes such that the sum of weights of edges joining different sets is minimized. This paper investigates the quality of doubly nonnegative (DNN) relaxations, i.e., relaxations having matrix variables that are both positive semidefinite and nonnegative, strengthened by additional polyhedral cuts for two variations of the GPP: the k-equipartition and the graph bisection problem. After reducing the size of the relaxations by facial reduction, we solve them by a cutting-plane algorithm that combines an augmented Lagrangian method with Dykstra's projection algorithm. Since many components of our algorithm are general, the algorithm is suitable for solving various DNN relaxations with a large number of cutting planes. We are the first to show the power of DNN relaxations with additional cutting planes for the GPP on large benchmark instances up to 1,024 vertices. Computational results show impressive improvements in strengthened DNN bounds.

The subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept in applications of stochastic games, making it imperative to develop efficient methods to compute an SSPE. For this purpose, this paper develops an interior-point differentiable path-following method (IPM), which establishes a connection between an artificial logarithmic barrier game and the stochastic game of interest by adding a homotopy variable. IPM brings several advantages over the existing methods for stochastic games. On the one hand, IPM provides a bridge between differentiable path-following methods and interior-point methods and remedies several issues of an existing homotopy method called the stochastic linear tracing procedure (SLTP). First, the starting stationary strategy profile can be arbitrarily chosen. Second, IPM does not need switching between different systems of equations. Third, the use of a perturbation term makes IPM applicable to all stochastic games rather than generic games only. Moreover, a well-chosen transformation of variables reduces the number of equations and variables by roughly one half. Numerical results show that the proposed method is more than three times as efficient as SLTP. On the other hand, the stochastic game can be reformulated as a mixed complementarity problem and solved by the PATH solver. We employ the proposed IPM and the PATH solver to compute SSPEs. Numerical results evince that for some stochastic games the PATH solver may fail to find an SSPE, whereas IPM is successful in doing so for all stochastic games, which confirms the reliability and stability of the proposed method. Summary of Contribution: This paper incorporates the interior-point methods into a differentiable path-following method for computing stationary equilibria for stochastic games. This novel method brings excellent computational advantages and remedies several issues with the existing methods for stochastic games. We prove the global convergence of the proposed method and employ this method to solve numerous randomly generated stochastic games with different scales. Numerical results further confirm the high efficiency, stability, and universality of this method for stochastic games.

This paper is an in-depth analysis of the generalized $\vartheta$-number of a graph. The generalized $\vartheta$-number, $\vartheta_k(G)$, serves as a bound for both the $k$-multichromatic number of a graph and the maximum $k$-colorable subgraph problem. We present various properties of $\vartheta_k(G)$, such as that the sequence $(\vartheta_k(G))_k$ is increasing and bounded from above by the order of the graph $G$. We study $\vartheta_k(G)$ when $G$ is the strong, disjunction or Cartesian product of two graphs. We provide closed form expressions for the generalized $\vartheta$-number on several classes of graphs including the Kneser graphs, cycle graphs, strongly regular graphs and orthogonality graphs. Our paper provides bounds on the product and sum of the $k$-multichromatic number of a graph and its complement graph, as well as lower bounds for the $k$-multichromatic number on several graph classes including the Hamming and Johnson graphs.

In this paper, we investigate the relationships between proper efficiency and the solutions of a general scalarization problem in multi-objective optimization. We provide some conditions under which the solutions of the dealt with scalar program are properly efficient and vice versa. We also show that, under some conditions, if the considered general scalar problem is unbounded, then the original multi-objective problem does not have any properly efficient solution. In another part of the work, we investigate a general transformation of the objective functions which preserves proper efficiency. We show that several important results existing in the literature are direct consequences of the results of the present paper.

We consider a funded pension system where collective risks, in a simple Black-Scholes financial market, are allocated to the retirement savings of individual participants. In particular, we consider an allocation in such a way that the relative effect on total retirement wealth, that is, the sum of financial wealth and human capital, is the same for each participant. We show that this allocation is Pareto efficient. This stylized life-cycle fact inspired the new Dutch retirement system. Subsequently, we extend the allocation rule to a setting that includes annuity risk. This risk can be a traded risk (e.g., interest rate risk) as well as a non-traded risk (e.g., longevity risk). From our closed-form solutions, we identify the similarities between our optimal allocation rule and the allocation rule in the new Dutch retirement system. A numerical example illustrates our findings.

We develop a universal econometric formulation of empirical power laws possibly driven by parameter heterogeneity. Our approach extends classical extreme value theory to specifying the tail behavior of the empirical distribution of a general dataset with possibly heterogeneous marginal distributions. We discuss several model examples that satisfy our conditions and demonstrate in simulations how heterogeneity may generate empirical power laws. We observe a cross-sectional power law for the U.S. stock losses and show that this tail behavior is largely driven by the heterogeneous volatilities of the individual assets.

The maximum k-colorable subgraph (MkCS) problem is to find an induced k-colorable subgraph with maximum cardinality in a given graph. This paper is an in-depth analysis of the MkCS problem that considers various semidefinite programming relaxations, including their theoretical and numerical comparisons. To simplify these relaxations, we exploit the symmetry arising from permuting the colors, as well as the symmetry of the given graphs when applicable. We also show how to exploit invariance under permutations of the subsets for other partition problems and how to use the MkCS problem to derive bounds on the chromatic number of a graph. Our numerical results verify that the proposed relaxations provide strong bounds for the MkCS problem and that those outperform existing bounds for most of the test instances. Summary of Contribution: The maximum k-colorable subgraph (MkCS) problem is to find an induced k-colorable subgraph with maximum cardinality in a given graph. The MkCS problem has a number of applications, such as channel assignment in spectrum sharing networks (e.g., Wi-Fi or cellular), very-large-scale integration design, human genetic research, and so on. The MkCS problem is also related to several other optimization problems, including the graph partition problem and the max-k-cut problem. The two mentioned problems have applications in parallel computing, network partitioning, floor planning, and so on. This paper is an in-depth analysis of the MkCS problem that considers various semidefinite programming relaxations, including their theoretical and numerical comparisons. Further, our analysis relates the MkCS results with the stable set and the chromatic number problems. We provide extended numerical results that verify that the proposed bounding approaches provide strong bounds for the MkCS problem and that those outperform existing bounds for most of the test instances. Moreover, our lower bounds on the chromatic number of a graph are competitive with existing bounds in the literature.

We consider a large-scale service system where incoming tasks have to be instantaneously dispatched to one out of many parallel server pools. The user-perceived performance degrades with the number of concurrent tasks and the dispatcher aims at maximizing the overall quality-of-service by balancing the load through a simple threshold policy. We demonstrate that such a policy is optimal on the fluid and diffusion scales, while only involving a small communication overhead, which is crucial for large-scale deployments. In order to set the threshold optimally, it is important, however, to learn the load of the system, which may be unknown. For that purpose, we design a control rule for tuning the threshold in an online manner. We derive conditions which guarantee that this adaptive threshold settles at the optimal value, along with estimates for the time until this happens. In addition, we provide numerical experiments which support the theoretical results and further indicate that our policy copes effectively with time-varying demand patterns., Comment: 51 pages, 6 figures

This paper studies a firm’s investment decision in production capacity where product demand follows a product life cycle (PLC), implying that demand first grows and then declines. The starting point of the decline phase is uncertain. The investment decision involves deciding about the timing and the size of the investment. We make a distinction between the firm being a product life cycle leader and a product life cycle follower. A PLC-leader will always first experience demand growth before the decline kicks in. In case of a PLC-follower, the firm enters an existing product life cycle, implying that the decline can already start before this firm even has invested. It turns out that it makes a major difference whether the firm is a PLC-leader or PLC-follower. To benefit from a period of demand growth, the PLC-follower has an incentive to invest early, thus when the current demand level is still low. This forces the firm to limit the investment size. The PLC-leader, on the contrary, always chooses the investment size corresponding to demand growth throughout, where the probability of demand decline simply delays the moment of investment.

We consider financial networks where agents are linked to each other via mutualliabilities. In case of bankruptcy, there are potentially many bankruptcy rules, ways to distribute the assets of a bankrupt agent over the other agents. One common approach is to first apply pairwise netting of agents that have mutual liabilities and next use the proportional rule to determine the payments on the basis of the net liabilities. We refer to this as the pairwise netting proportional rule. The pairwise netting proportional rule satisfies the basic requirements of claims boundedness, limited liability, priority of creditors, and continuity. It also satisfies the desirable properties of net impartiality, an agent that has two creditors with the same net claims pays the same amount to both creditors on top of pairwise netting, and invariance to mitosis, an agent that splits into a number of identical agents is not a_ecting the payments of the other agents. We demonstrate that if net impartiality and invariance to mitosis, together with the basic requirements, are regarded as imperative properties, then payments should be determined by the pairwise netting proportional rule.

Multivariate regular variation is a common assumption in the statistics literature and needs to be verified in real-data applications. We develop a novel hypothesis test for multivariate regular variation, employing localized empirical likelihood. We establish the weak convergence of the test statistic to a non-standard, distribution-free limit and hence can provide universal critical values for the test. We show the very good finite-sample behavior of the procedure through simulations and apply the test to several real-data examples.

Kidney exchange programmes (KEPs) across the world help match donors and recipients to identify kidney transplantations. Almost all KEPs use a hierarchical set of objectives to determine an optimal set of transplants to perform, and integer linear programming is often used to find such optimal matchings. In this work, we identify the barriers in existing mathematical models and we propose innovative techniques to remove these barriers, vastly reducing solution times and allowing us to significantly increase the potential size of KEPs. Our techniques include two methods to avoid unnecessary variables, as well as a diving algorithm that reduces the need to solve multiple complex integer linear programming models while still guaranteeing the optimality of a final solution. We also show that it is possible to transition between two distinct existing formulations (namely the cycle formulation and the position-indexed chain-edge formulation) between the optimisation of two successive objective functions. We use this technique to devise a new algorithm which, among other features, intelligently exploits the different advantages of the prior two models. We demonstrate the performance of our new algorithms with extensive computational experiments modelling the UK KEP, where we show that our improvements reduce running times by three orders of magnitude compared to the cycle formulation. We also provide substantial empirical evidence that the new methodology offers equally spectacular improvements when applied to modelling the objectives used by Spain and the Netherlands, suggesting that our approach is not just viable, but a significant performance improvement, for many different KEPs across the globe.

In this paper, we study asymptotic expansions for distorted probabilities under ambiguity, revisiting the framework and analysis of Izhakian (2020b). We argue that the first order terms in these expansions need to be corrected and provide alternatives. We also revisit later results in this paper on the separation of ambiguity and ambiguity attitudes. We argue that a crucial lemma is flawed implying that Izhakian's ambiguity measure ℧ 2 is not an equivalent way of representing the preferences it is supposed to represent.

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component which contains more than one agent is called a cycle and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a positive endowment. The division rule used by a cyclical agent with a positive endowment should be positive monotonic and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Since division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. We also show how uniqueness of clearing payment matrices is related to continuity of bankruptcy rules.