Exploring the dimensions and transactional outcomes of incomplete business contracts

With an increased emphasis on outsourcing and shortening business cycles, contracts between firms have become more important. Carefully written contracts contribute to the efficiency and longevity of inter-firm relationships as they may constrain opportunism and are often a less costly governance mechanism than maintaining complex social relationships (Larson 1992). This exploratory examination adds to our understanding of how incomplete contracts affect interorganizational exchange. First, we consider the multiple dimensions of contract constraints (safeguards). We also investigate the extent that constraints affect decisions to enforce the relationship by delaying payments, and whether the decision is efficient. Finally, we examine the extent the constraints are effective (and ineffective) at reducing transaction problems associated with enforcement. Based on 971 observations of transactions using explicit, written terms and other secondary data in the context of IT transaction in The Netherlands we test our research propositions.

Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A Distance-Based Method for Attribute Reduction in Incomplete Decision Systems

There are limitations in recent research undertaken on attribute reduction in incomplete decision systems. In this paper, we propose a distance-based method for attribute reduction in an incomplete decision system. In addition, we prove theoretically that our method is more effective than some other methods.

Generalized Discernibility Function Based Attribute Reduction in Incomplete Decision Systems

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditional attributes. Our methods use generalized discernibility matrix and function in tolerance-based rough sets.

An inconsistency control system based on incomplete pairwise comparison matrices

Incomplete pairwise comparison matrix was introduced by Harker in 1987 for the case in which the decision maker does not fill in the whole matrix completely due to, e.g., time limitations. However, incomplete matrices occur in a natural way even if the decision maker provides a completely filled in matrix in the end. In each step of the total n(n–1)/2, an incomplete pairwise comparison is given, except for the last one where the matrix turns into complete. Recent results on incomplete matrices make it possible to estimate inconsistency indices CR and CM by the computation of tight lower bounds in each step of the filling in process. Additional information on ordinal inconsistency is also provided. Results can be applied in any decision support system based on pairwise comparison matrices. The decision maker gets an immediate feedback in case of mistypes, possibly causing a high level of inconsistency.

Cooperation under incomplete contracting

We examine the notion of the core when cooperation takes place in a setting with time and uncertainty. We do so in a two-period general equilibrium setting with incomplete markets. Market incompleteness implies that players cannot make all possible binding commitments regarding their actions at different date-events. We unify various treatments of dynamic core concepts existing in the literature. This results in definitions of the Classical Core, the Segregated Core, the Two-stage Core, the Strong Sequential Core, and the Weak Sequential Core. Except for the Classical Core, all these concepts can be defined by requiring absence of blocking in period 0 and at any date-event in period 1. The concepts only differ with respect to the notion of blocking in period 0. To evaluate these concepts, we study three market structures in detail: strongly complete markets, incomplete markets in finance economies, and incomplete markets in settings with multiple commodities.

On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper.

A fundamentális transzformáció és a referenciapont szerepe a hiányos szerződések elméletében (The role of basic transformation and reference point in the theory of incomplete contracts)

A cikk Oliver Hart és szerzőtársai modelljeinek következtetéseit hasonlítja össze Williamson tranzakciós költségekre vonatkozó nézeteivel. Megmutatja, hogy a két irányzat a vállalat vagy piac kérdéskörében más eszközöket használ, de hasonlóan érvel. Megismerkedhetünk Williamson Harttal szemben megfogalmazott azon kritikájával, hogy Hart modelljeiben az alkunak nincsenek tranzakciós költségei, illetve a kritika kritikájával is. Hart elképzeléseit támasztja alá a tulajdonjogi irányzaton belül nemrégiben kialakult referenciapont-elmélet, amely kísérleti lehetőségeket is nyújt a különböző feltételezések igazolására. ____ The article compares the conclusions from the models of Oliver Hart et al. with the views of Williamson on transaction costs. It shows that the two schools use different means on the question of the firm or the market, but similar reasoning. The author covers Williamson's criticism of Hart that there are no transaction costs in his models, and also the criticism of that criticism. Hart's notions are supported by the recently developed theory of reference point within the property-right trend, which offers chances of experimental proof of the various assumptions.

A referenciapont-elmélet mint a hiányos információjú szerződések gondolatkörének új irányzata (The concept of ‘reference points’ as a new direction in the ‘incomplete contract’ theory)

A cikk az alig több mint öt éve született referenciapont-elméletet mutatja be, ismerteti és értékeli a témában eddig megjelent cikkeket és a nagyobb horderejű munkaanyagokat. A referenciapont-elmélet arra a kérdésre keresi a választ, hogy mi a vállalat optimális mérete, és mikor érdemesebb a termelési kooperációt nem a vállalaton belül, a különböző egységek koordinációjával megoldani, hanem külső vállalatok segítségével, a piacon keresztül megvalósítani. A referenciapont-elmélet az azonos kérdések megválaszolására törekvő hiányos szerződések elméletét ért kritika hatására született meg, és saját, újonnan megfogalmazott feltételrendszerét számos ponton ötvözi a hiányos szerződések hipotéziseivel, ugyanakkor bizonyításai során felhasználja a standard közgazdasági irányzat több eszközét is. A cikk a friss eredmények bemutatása mellett megkísérli előre becsülni a referenciapont-elmélet várható jövőbeli fejlődési irányait is. ____ The concept of reference points was established slightly more than five years ago, and it deals with the same boundary of firm related questions as the incomplete contract theory. The present review shows the most important journals and research papers in this field. Reference point theory arose out of a criticism of some of the elements of incomplete contract theory. Reference point theory combines newly- formulated hypotheses with some of the assumptions of incomplete contracts. The theory also uses some of the proving tools of standard economics. The author’s study not only shows the main results of the reference point theory, but it also tries to predict some possible future developments within the theory.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Joint-specific changes in locomotor complexity in the absence of muscle atrophy following incomplete spinal cord injury

ackground Following incomplete spinal cord injury (iSCI), descending drive is impaired, possibly leading to a decrease in the complexity of gait. To test the hypothesis that iSCI impairs gait coordination and decreases locomotor complexity, we collected 3D joint angle kinematics and muscle parameters of rats with a sham or an incomplete spinal cord injury. Methods 12 adult, female, Long-Evans rats, 6 sham and 6 mild-moderate T8 iSCI, were tested 4 weeks following injury. The Basso Beattie Bresnahan locomotor score was used to verify injury severity. Animals had reflective markers placed on the bony prominences of their limb joints and were filmed in 3D while walking on a treadmill. Joint angles and segment motion were analyzed quantitatively, and complexity of joint angle trajectory and overall gait were calculated using permutation entropy and principal component analysis, respectively. Following treadmill testing, the animals were euthanized and hindlimb muscles removed. Excised muscles were tested for mass, density, fiber length, pennation angle, and relaxed sarcomere length. Results Muscle parameters were similar between groups with no evidence of muscle atrophy. The animals showed overextension of the ankle, which was compensated for by a decreased range of motion at the knee. Left-right coordination was altered, leading to left and right knee movements that are entirely out of phase, with one joint moving while the other is stationary. Movement patterns remained symmetric. Permutation entropy measures indicated changes in complexity on a joint specific basis, with the largest changes at the ankle. No significant difference was seen using principal component analysis. Rats were able to achieve stable weight bearing locomotion at reasonable speeds on the treadmill despite these deficiencies. Conclusions Decrease in supraspinal control following iSCI causes a loss of complexity of ankle kinematics. This loss can be entirely due to loss of supraspinal control in the absence of muscle atrophy and may be quantified using permutation entropy. Joint-specific differences in kinematic complexity may be attributed to different sources of motor control. This work indicates the importance of the ankle for rehabilitation interventions following spinal cord injury.

Equitably coloured balanced incomplete block designs

In this thesis we determine necessary and sufficient conditions for the existence of an equitably ℓ-colourable balanced incomplete block design for any positive integer ℓ > 2. In particular, we present a method for constructing non-trivial equitably ℓ-colourable BIBDs and prove that these designs are the only non-trivial equitably ℓ-colourable BIBDs that exist. We also observe that every equitable ℓ-colouring of a BIBD yields both an equalised ℓ-colouring and a proper 2-colouring of the same BIBD. We also discuss generalisations of these concepts including open questions for further research. The main results presented in this thesis also appear in [7].