Equilibrium selection and altruistic behavior in noncooperative social networks

Given their importance in determining the outcome of many economic interactions, different models have been proposed to determine how social networks form and which structures are stable. In Bala and Goyal (Econometrica 68, 1181–1229, 2000), the one-sided link formation model has been considered, which is based on a noncooperative game of network formation. They found that the empty networks, the wheel in the one-way flow of benefits case and the center-sponsored star in the two-way flow case play a fundamental role since they are strict Nash equilibria of the corresponding games for a certain class of payoff functions. In this paper, we first prove that all these network structures are in weakly dominated strategies whenever there are no strict Nash equilibria. Then, we exhibit a more accurate selection device between these network architectures by considering “altruistic behavior” refinements. Such refinements that we investigate here in the framework of finite strategy sets games have been introduced by the authors in previous papers.     

Dynamical behavior for an eco-epidemiological model with discrete and distributed delay

In this paper, the dynamical behavior of an eco-epidemiological model with discrete and distributed delay is studied. Sufficient conditions for the local asymptotical stability of the nonnegative equilibria are obtained. We prove that there exists a threshold value of the feedback time delay τ beyond which the positive equilibrium bifurcates towards a periodic solution. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.     

Unintended consequences of collocation: using agent-based modeling to untangle effects of communication delay and in-group favor

In studies about office arrangements that have individuals working from remote locations, researchers usually hypothesize advantages for collocators and disadvantages for remote workers. However, empirical findings have not shown consistent support for the hypothesis. We suspect that there are unintended consequences of collocation, which can offset well-recognized advantages of being collocated. To explain these unintended consequences, we developed a multi-agent model to complement our laboratory-based experiment. In the lab, collocated subjects did not perform better than the remote even though collocators had faster communication channels and in-group favor towards each other. Results from the multi-agent simulation suggested that in-group favoritism among collocators caused them to ignore some important resource exchange opportunities with remote individuals. Meanwhile, communication delay of remote subjects protected them from some falsely biased perception of resource availability. The two unintended consequences could offset the advantage of being collocated and diminish performance differences between collocators and remote workers. Results of this study help researchers and practitioners recognize the hidden costs of being collocated. They also demonstrate the value of coupling lab experiments with multi-agent simulation.

An outranking-based fuzzy logic model for collaborative group preferences

Some ideas coming from Multi Criteria Decision Aid are here extended to group decision. We present a logical model in order to reflect the degree of truth of the following predicate “group G considers that option x is at least as good as y.” The proposal considers the strength of the majority using its number and the intensity of its preference, and it also acknowledges the importance of the minorities of a certain numerical significance that manifest an intense disagreement with the predicate of the outranking. The effects of the “majority dictatorship” are restricted. Since it considers simultaneously the strength of the majority, the importance of unhappy minorities, and the intensity of the preference/opposition, this model exhibits desirable qualities of the classic methods by Condorcet and Borda. This model can be used to solve problems regarding selection, ranking, classification, and sorting. Various examples are given, which show the quality of the solutions that were obtained.     

Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups

Let G(O_S)\mathbf{G}(\mathcal{O}_{S}) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O_S)\mathbf{G}(\mathcal{O}_{S}) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(O_S)\mathbf{G}(\mathcal{O}_{S}) established in an earlier paper is sharp in this case.     

Oscillation and global asymptotic stability of a discrete haematopoiesis model

In this paper, we study a discrete haematopoiesis model $$\Delta y_{n}=-\alpha y_{n}+\frac{\beta y_{n-k}^{m}}{1+y_{n-k}^{p}}\quad\mbox{for}\ n=0,1,\ldots,$$ where α∈(0,1), β∈(α,∞), m∈(1,∞), p∈[m,∞), k∈?, and establish some results about oscillation and global asymptotic stability of the positive solution of this model.     

An Eberhard-Like Theorem for Pentagons and Heptagons

Eberhard proved that for every sequence (p _k ), 3≤k≤r, k≠6, of nonnegative integers satisfying Euler’s formula ∑ _k≥3(6−k)p _k =12, there are infinitely many values p ₆ such that there exists a simple convex polyhedron having precisely p _k faces of size k for every k≥3, where p _k =0 if k>r. In this paper we prove a similar statement when nonnegative integers p _k are given for 3≤k≤r, except for k=5 and k=7 (but including p ₆). We prove that there are infinitely many values p ₅,p ₇ such that there exists a simple convex polyhedron having precisely p _k faces of size k for every k≥3. We derive an extension to arbitrary closed surfaces, yielding maps of arbitrarily high face-width. Our proof suggests a general method for obtaining results of this kind.     

Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument

We establish a positivity property for the difference of products of certain Schur functions, s _λ (x), where λ varies over a fundamental Weyl chamber in ? ⁿ and x belongs to the positive orthant in ? ⁿ . Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions. We also derive a log-convexity property of the generalized hypergeometric functions of two Hermitian matrix arguments, and we show how that result may be extended to derive higher-order log-convexity properties.     

An optimal replenishment policy for an EOQ model with partial backlogging

We study an inventory system where demand on the stockout period is partially backlogged. The backlogged demand ratio is a mixture of two exponential functions. The shortage cost has two significant costs: the unit backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general procedure to determine the optimal policy and the minimum inventory cost for all the parameter values is developed. This model generalizes several inventory systems analyzed by different authors. Numerical examples are used to illustrate the theoretical results.     

Lefschetz properties and basic constructions on simplicial spheres

The well known g-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the strong-Lefschetz property is preserved under the following constructions on homology spheres: join, connected sum, and stellar subdivisions. The last construction is a step towards proving the g-conjecture for piecewise-linear spheres.     

Functional continuity and large deviations for the behavior of single-class queueing networks

We consider a single-class queueing network in which the functional network primitives describe the cumulative exogenous arrivals, service times and routing decisions of the queues. The behavior of the network consisting of the cumulative total arrival, cumulative idle time, and queue length developments for each node is specified by conditions which relate the network primitives to the network behavior. For a broad class of network primitives, including discrete customer and fluid models, a network behavior exists, but need not be unique. Nevertheless, the mapping from network primitives to the set of associated network behavior is upper semicontinuous at network primitives with continuous routing. As an application we consider a sequence of random network primitives satisfying a sample path large deviation principle. We take advantage of the partial functional set-valued upper semicontinuity in order to derive a large deviation principle for the sequence of associated random queue length processes and to identify the rate function. This extends the results of Puhalskii (Markov Process. Relat. Fields 13(1), 99–136, 2007) about large deviations for the tail probabilities of generalized Jackson networks. Since the analysis is carried out on the doubly-infinite time axis ?, we can directly treat stationary situations.     

Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model

For a discrete time network of generalized Bernoulli servers with unreliable nodes we derive the steady state probabilities for the joint queue length vector for all nodes and the availability status of the network. This allows us to assess the performance behavior and the reliability, resp. availability, of the network in an integrated model. Because our result exhibits a product form for the steady state distribution it opens the path to fast algorithmic evaluation of the desired performance and reliability indices.     

Stability in predator – prey models and discretization of a modified Volterra – Lotka model

We consider n  2 populations of animals that are living in mutual predator – prey relations or are pairwise neutral to each other. We assume the temporal development of the population densities to be described by a system of differential equations which has an equilibrium state solution. We derive sufficient conditions for this equilibrium state to be stable by Lyapunov's method. The results supplement those published elsewhere.

Further we consider a modification of the Volterra – Lotka model which admits an asymptotically stable steady state solution. This model is discretized in two ways and we investigate how small the time step size has to be chosen in order to guarantee that the steady state solution is an attractive fixed point of the discretized model. This investigation is connected with the determination of the model parameters from given data.     

Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions

The paper provides a condition for differentiability as well as an equivalent criterion for Lipschitz continuity of singular normal distributions. Such distributions are of interest, for instance, in stochastic optimization problems with probabilistic constraints, where a comparatively small (nondegenerate-) normally distributed random vector induces a large number of linear inequality constraints (e.g. networks with stochastic demands). The criterion for Lipschitz continuity is established for the class of quasi-concave distributions which the singular normal distribution belongs to.     

Agency and structure: a social simulation of knowledge-intensive industries

Modern knowledge-intensive economies are complex social systems where intertwining factors are responsible for the shaping of emerging industries: the self-organising interaction patterns and strategies of the individual actors (an agency-oriented pattern) and the institutional frameworks of different innovation systems (a structure-oriented pattern). In this paper, we examine the relative primacy of the two patterns in the development of innovation networks, and find that both are important. In order to investigate the relative significance of strategic decision making by innovation network actors and the roles played by national institutional settings, we use an agent-based model of knowledge-intensive innovation networks, SKIN. We experiment with the simulation of different actor strategies and different access conditions to capital in order to study the resulting effects on innovation performance and size of the industry. Our analysis suggests that actors are able to compensate for structural limitations through strategic collaborations. The implications for public policy are outlined.     

Directed graphs and combinatorial properties of completely regular semigroups

In this paper, we investigate the divisibility graphs and power graphs of completely regular semigroups. We give the structures of these two kinds of graphs and describe a combinatorial property of completely regular semigroups defined in terms of divisibility graphs and power graphs, respectively.     

Deterministic shock vs. stochastic value-at-risk — an analysis of the Solvency II standard model approach to longevity risk

In general, the capital requirement under Solvency II is determined as the 99.5% Value-at-Risk of the Available Capital. In the standard model’s longevity risk module, this Value-at-Risk is approximated by the change in Net Asset Value due to a pre-specified longevity shock which assumes a 25% reduction of mortality rates for all ages. We analyze the adequacy of this shock by comparing the resulting capital requirement to the Value-at-Risk based on a stochastic mortality model. This comparison reveals structural shortcomings of the 25% shock and therefore, we propose a modified longevity shock for the Solvency II standard model. We also discuss the properties of different Risk Margin approximations and find that they can yield significantly different values. Moreover, we explain how the Risk Margin may relate to market prices for longevity risk and, based on this relation, we comment on the calibration of the cost of capital rate and make inferences on prices for longevity derivatives.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.