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Hierarchies of synergies: an example of two-hand, multi-finger tasks

Gorniak, Stacey L.; Zatsiorsky, Vladimir M.; Latash, Mark L.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.44%
We explored the ability of the central nervous system (CNS) to assemble synergies stabilizing the output of sets of effectors at two levels of a control hierarchy. Specifically, we asked a question: can the CNS organize both two-hand and within-a-hand force stabilizing synergies in a simple two-hand force production task that involves two fingers per hand? Intuitively, one could expect a positive answer; that is, forces produced by each hand are expected to co-vary negatively across trials to bring down the total force variability, while forces produced by each finger within-a-hand are expected to co-vary negatively to reduce the variability of that hand’s contribution to the total force. The subjects were instructed to follow a trapezoidal time profile with the signal corresponding to the force produced by a set of instructed fingers in one-hand tasks with two-finger force production and in two-hand tasks with involvement of both symmetrical and asymmetrical finger pairs in the two hands. Finger force co-variation across trials was quantified and used as an index of stabilization of the force produced by all the instructed fingers, and of the force produced by finger pairs within-a-hand. No major differences were seen between the dominant and the non-dominant hand and between the two-hand tasks with symmetrical and asymmetrical finger involvement. Stronger synergies were seen in the index–middle finger pair as compared to the ring-little finger pair. The main result of the study is the significantly weaker or even lacking two-finger force stabilizing synergies within-a-hand during two-hand tasks while such synergies were present in one-hand tasks. This observation points at a potential limitation in the ability of the CNS to organize synergies at two levels of a control hierarchy simultaneously. It also allows suggesting a hypothesis on two types of synergies in the human motor repertoire...

Hierarchical control of static prehension: II. Multi-digit synergies

Gorniak, Stacey L.; Zatsiorsky, Vladimir M.; Latash, Mark L.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.37%
The purpose of this study was to explore the ability of the central nervous system (CNS) to organize synergies at two levels of a hypothetical control hierarchy involved in two-hand multi-finger prehension tasks with one or more persons participating in the task together. At the higher level of the hierarchy, the total force and moment of force produced on an object are distributed between the thumb and the virtual finger (an imagined finger with mechanical output equal to the involved fingers of the hand), while at the lower level the virtual finger action is distributed among the four fingers. We tested a hypothesis that the CNS is able to organize synergies at only one level of the hierarchy. The subjects held vertically one of the two handles, a narrow one and a wide one. They used the four fingers of the right hand opposed by either the right hand thumb, the left hand thumb, the left hand index finger, the thumb of an experimenter, the index finger of an experimenter, or an inanimate object. Forces and moments of force produced by each digit were recorded. Indices of synergies stabilizing the mechanical output variables at each of the two levels were computed. Contrary to the expectations, force and moment of force stabilizing synergies were found at one or both levels of the hierarchy across all tasks. Unimanual tasks exhibited higher synergy indices compared to all tasks...

Subject-Specific Muscle Synergies in Human Balance Control Are Consistent Across Different Biomechanical Contexts

Torres-Oviedo, Gelsy; Ting, Lena H.
Fonte: American Physiological Society Publicador: American Physiological Society
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.41%
The musculoskeletal redundancy of the body provides multiple solutions for performing motor tasks. We have proposed that the nervous system solves this unconstrained problem through the recruitment of motor modules or functional muscle synergies that map motor intention to action. Consistent with this hypothesis, we showed that trial-by-trial variations in muscle activation for multidirectional balance control in humans were constrained by a small set of muscle synergies. However, apparent muscle synergy structures could arise from characteristic patterns of sensory input resulting from perturbations or from low-dimensional optimal motor solutions. Here we studied electromyographic (EMG) responses for balance control across a range of biomechanical contexts, which alter not only the sensory inflow generated by postural perturbations, but also the muscle activation patterns used to restore balance. Support-surface translations in 12 directions were delivered to subjects standing in six different postural configurations: one-leg, narrow, wide, very wide, crouched, and normal stance. Muscle synergies were extracted from each condition using nonnegative matrix factorization. In addition, muscle synergies from the normal stance condition were used to reconstruct muscle activation patterns across all stance conditions. A consistent set of muscle synergies were recruited by each subject across conditions. When balance demands were extremely different from the normal stance (e.g....

Muscle synergies as a predictive framework for the EMG patterns of new hand postures

Ajiboye, A B; Weir, R F
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.44%
Synchronous muscle synergies have been suggested as a framework for dimensionality reduction in muscle coordination. Many studies have shown that synergies form a descriptive framework for a wide variety of tasks. We examined if a muscle synergy framework could accurately predict the EMG patterns associated with untrained static hand postures, in essence, if they formed a predictive framework. Hand and forearm muscle activities were recorded while subjects statically mimed 33 postures of the American Sign Language alphabet. Synergies were extracted from a subset of training postures using non-negative matrix factorization and used to predict the EMG patterns of the remaining postures. Across the subject population, as few as 11 postures could form an eight-dimensional synergy framework that allowed for at least 90% prediction of the EMG patterns of all 33 postures, including trial-to-trial variations. Synergies were quite robust despite using different postures in the training set, and also despite using a varied number of postures. Estimated synergies were categorized into those which were subject-specific and those which were general to the population. Population synergies were sparser than the subject-specific synergies, typically being dominated by a single muscle. Subject-specific synergies were more balanced in the coactivation of multiple muscles. We suggest as a result that global muscle coordination may be a combination of higher order control of robust subject-specific muscle synergies and lower order control of individuated muscles...

Motoneuronal and muscle synergies involved in cat hindlimb control during fictive and real locomotion: a comparison study

Markin, Sergey N.; Lemay, Michel A.; Prilutsky, Boris I.; Rybak, Ilya A.
Fonte: American Physiological Society Publicador: American Physiological Society
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.41%
We compared the activity profiles and synergies of spinal motoneurons recorded during fictive locomotion evoked in immobilized decerebrate cat preparations by midbrain stimulation to the activity profiles and synergies of the corresponding hindlimb muscles obtained during forward level walking in cats. The fictive locomotion data were collected in the Spinal Cord Research Centre, University of Manitoba, and provided by Dr. David McCrea; the real locomotion data were obtained in the laboratories of M. A. Lemay and B. I. Prilutsky. Scatterplot representation and minimum spanning tree clustering algorithm were used to identify the possible motoneuronal and muscle synergies operating during both fictive and real locomotion. We found a close similarity between the activity profiles and synergies of motoneurons innervating one-joint muscles during fictive locomotion and the profiles and synergies of the corresponding muscles during real locomotion. However, the activity patterns of proximal nerves controlling two-joint muscles, such as posterior biceps and semitendinosus (PBSt) and rectus femoris (RF), were not uniform in fictive locomotion preparations and differed from the activity profiles of the corresponding two-joint muscles recorded during forward level walking. Moreover...

Task-level feedback can explain temporal recruitment of spatially fixed muscle synergies throughout postural perturbations

Safavynia, Seyed A.; Ting, Lena H.
Fonte: American Physiological Society Publicador: American Physiological Society
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.41%
Recent evidence suggests that complex spatiotemporal patterns of muscle activity can be explained with a low-dimensional set of muscle synergies or M-modes. While it is clear that both spatial and temporal aspects of muscle coordination may be low dimensional, constraints on spatial versus temporal features of muscle coordination likely involve different neural control mechanisms. We hypothesized that the low-dimensional spatial and temporal features of muscle coordination are independent of each other. We further hypothesized that in reactive feedback tasks, spatially fixed muscle coordination patterns—or muscle synergies—are hierarchically recruited via time-varying neural commands based on delayed task-level feedback. We explicitly compared the ability of spatially fixed (SF) versus temporally fixed (TF) muscle synergies to reconstruct the entire time course of muscle activity during postural responses to anterior-posterior support-surface translations. While both SF and TF muscle synergies could account for EMG variability in a postural task, SF muscle synergies produced more consistent and physiologically interpretable results than TF muscle synergies during postural responses to perturbations. Moreover, a majority of SF muscle synergies were consistent in structure when extracted from epochs throughout postural responses. Temporal patterns of SF muscle synergy recruitment were well-reconstructed by delayed feedback of center of mass (CoM) kinematics and reproduced EMG activity of multiple muscles. Consistent with the idea that independent and hierarchical low-dimensional neural control structures define spatial and temporal patterns of muscle activity...

Common muscle synergies for balance and walking

Chvatal, Stacie A.; Ting, Lena H.
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 02/05/2013 EN
Relevância na Pesquisa
27.44%
Little is known about the integration of neural mechanisms for balance and locomotion. Muscle synergies have been studied independently in standing balance and walking, but not compared. Here, we hypothesized that reactive balance and walking are mediated by a common set of lower-limb muscle synergies. In humans, we examined muscle activity during multidirectional support-surface perturbations during standing and walking, as well as unperturbed walking at two speeds. We show that most muscle synergies used in perturbations responses during standing were also used in perturbation responses during walking, suggesting common neural mechanisms for reactive balance across different contexts. We also show that most muscle synergies using in reactive balance were also used during unperturbed walking, suggesting that neural circuits mediating locomotion and reactive balance recruit a common set of muscle synergies to achieve task-level goals. Differences in muscle synergies across conditions reflected differences in the biomechanical demands of the tasks. For example, muscle synergies specific to walking perturbations may reflect biomechanical challenges associated with single limb stance, and muscle synergies used during sagittal balance recovery in standing but not walking were consistent with maintaining the different desired center of mass motions in standing vs. walking. Thus...

Motor cortical regulation of sparse synergies provides a framework for the flexible control of precision walking

Krouchev, Nedialko; Drew, Trevor
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 11/07/2013 EN
Relevância na Pesquisa
27.48%
We have previously described a modular organization of the locomotor step cycle in the cat in which a number of sparse synergies are activated sequentially during the swing phase of the step cycle (Krouchev et al., 2006). Here, we address how these synergies are modified during voluntary gait modifications. Data were analysed from 27 bursts of muscle activity (recorded from 18 muscles) recorded in the forelimb of the cat during locomotion. These were grouped into 10 clusters, or synergies, during unobstructed locomotion. Each synergy was comprised of only a small number of muscles bursts (sparse synergies), some of which included both proximal and distal muscles. Eight (8/10) of these synergies were active during the swing phase of locomotion. Synergies observed during the gait modifications were very similar to those observed during unobstructed locomotion. Constraining these synergies to be identical in both the lead (first forelimb to pass over the obstacle) and the trail (second limb) conditions allowed us to compare the changes in phase and magnitude of the synergies required to modify gait. In the lead condition, changes were observed particularly in those synergies responsible for transport of the limb and preparation for landing. During the trail condition...

Task constraints and minimization of muscle effort result in a small number of muscle synergies during gait

De Groote, Friedl; Jonkers, Ilse; Duysens, Jacques
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 18/09/2014 EN
Relevância na Pesquisa
27.41%
Finding muscle activity generating a given motion is a redundant problem, since there are many more muscles than degrees of freedom. The control strategies determining muscle recruitment from a redundant set are still poorly understood. One theory of motor control suggests that motion is produced through activating a small number of muscle synergies, i.e., muscle groups that are activated in a fixed ratio by a single input signal. Because of the reduced number of input signals, synergy-based control is low dimensional. But a major criticism on the theory of synergy-based control of muscles is that muscle synergies might reflect task constraints rather than a neural control strategy. Another theory of motor control suggests that muscles are recruited by optimizing performance. Optimization of performance has been widely used to calculate muscle recruitment underlying a given motion while assuming independent recruitment of muscles. If synergies indeed determine muscle recruitment underlying a given motion, optimization approaches that do not model synergy-based control could result in muscle activations that do not show the synergistic muscle action observed through electromyography (EMG). If, however, synergistic muscle action results from performance optimization and task constraints (joint kinematics and external forces)...

Evidence for altered upper extremity muscle synergies in chronic stroke survivors with mild and moderate impairment

Roh, Jinsook; Rymer, William Z.; Beer, Randall F.
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 11/02/2015 EN
Relevância na Pesquisa
27.5%
Previous studies indicate that motor coordination may be achieved by assembling task-dependent combinations of a few muscle synergies, defined here as fixed patterns of activation across a set of muscles. Our recent study of severely impaired chronic stroke survivors showed that some muscle synergies underlying isometric force generation at the hand are altered in the affected arm. However, whether similar alterations are evident in stroke survivors with lesser impairment remains unclear. Accordingly, we examined muscle synergies underlying spatial patterns of elbow and shoulder muscle activation recorded during an isometric force target matching protocol performed by 16 chronic stroke survivors, evenly divided across mild and moderate impairment levels. We applied non-negative matrix factorization to identify the muscle synergies and compared their structure across groups, including previously collected data from six age-matched control subjects and eight severely impaired stroke survivors. For all groups, EMG spatial patterns were well explained by task-dependent combinations of only a few (typically 4) muscle synergies. Broadly speaking, elbow-related synergies were conserved across stroke survivors, regardless of impairment level. In contrast...

Differences between kinematic synergies and muscle synergies during two-digit grasping

Tagliabue, Michele; Ciancio, Anna Lisa; Brochier, Thomas; Eskiizmirliler, Selim; Maier, Marc A.
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 26/03/2015 EN
Relevância na Pesquisa
27.48%
The large number of mechanical degrees of freedom of the hand is not fully exploited during actual movements such as grasping. Usually, angular movements in various joints tend to be coupled, and EMG activities in different hand muscles tend to be correlated. The occurrence of covariation in the former was termed kinematic synergies, in the latter muscle synergies. This study addresses two questions: (i) Whether kinematic and muscle synergies can simultaneously accommodate for kinematic and kinetic constraints. (ii) If so, whether there is an interrelation between kinematic and muscle synergies. We used a reach-grasp-and-pull paradigm and recorded the hand kinematics as well as eight surface EMGs. Subjects had to either perform a precision grip or side grip and had to modify their grip force in order to displace an object against a low or high load. The analysis was subdivided into three epochs: reach, grasp-and-pull, and static hold. Principal component analysis (PCA, temporal or static) was performed separately for all three epochs, in the kinematic and in the EMG domain. PCA revealed that (i) Kinematic- and muscle-synergies can simultaneously accommodate kinematic (grip type) and kinetic task constraints (load condition). (ii) Upcoming grip and load conditions of the grasp are represented in kinematic- and muscle-synergies already during reach. Phase plane plots of the principal muscle-synergy against the principal kinematic synergy revealed (iii) that the muscle-synergy is linked (correlated...

The effect of arm weight support on upper limb muscle synergies during reaching movements

Coscia, Martina; Cheung, Vincent CK; Tropea, Peppino; Koenig, Alexander; Monaco, Vito; Bennis, Caoimhe; Micera, Silvestro; Bonato, Paolo
Fonte: BioMed Central Publicador: BioMed Central
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
37.27%
Background: Compensating for the effect of gravity by providing arm-weight support (WS) is a technique often utilized in the rehabilitation of patients with neurological conditions such as stroke to facilitate the performance of arm movements during therapy. Although it has been shown that, in healthy subjects as well as in stroke survivors, the use of arm WS during the performance of reaching movements leads to a general reduction, as expected, in the level of activation of upper limb muscles, the effects of different levels of WS on the characteristics of the kinematics of motion and of the activity of upper limb muscles have not been thoroughly investigated before. Methods: In this study, we systematically assessed the characteristics of the kinematics of motion and of the activity of 14 upper limb muscles in a group of 9 healthy subjects who performed 3-D arm reaching movements while provided with different levels of arm WS. We studied the hand trajectory and the trunk, shoulder, and elbow joint angular displacement trajectories for different levels of arm WS. Besides, we analyzed the amplitude of the surface electromyographic (EMG) data collected from upper limb muscles and investigated patterns of coordination via the analysis of muscle synergies. Results: The characteristics of the kinematics of motion varied across WS conditions but did not show distinct trends with the level of arm WS. The level of activation of upper limb muscles generally decreased...

Sensory modulation of muscle synergies for motor adaptation during natural behaviors

Cheung, Vincent Chi-Kwan
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 170 p.
ENG
Relevância na Pesquisa
27.44%
To achieve any motor behavior, the central nervous system (CNS) must coordinate the many degrees of freedom in the musculoskeletal apparatus. It has been suggested that the CNS simplifies this formidable task of coordination by grouping multiple muscles together into units of activation, or muscle synergies. Previous studies have shown that electromyogram (EMG) signals collected from many muscles during natural behaviors can be reconstructed by linearly combining a few synergies, identified by the non-negative matrix factorization algorithm. But to what extent synergies are neural constraints, or merely structures reflecting experimental constraints, has remained an open question. I address this question with the hypothesis that, muscle synergies are robust neural patterns constraining motor outputs. The strategy adopted was that of analyzing EMGs collected before and after delivery of a perturbation to the motor system. In my first experiment, EMGs from bullfrog muscles were recorded during locomotor behaviors before and after deafferentation. Systematic comparison of intact and deafferented synergies suggests that most of the synergies remained unchanged after afferent removal.; (cont.) In my second experiment, the frog hindlimb was perturbed by either an inertial load or an elastic load. Using a novel algorithm capable of simultaneously extracting shared and specific synergies...

Effective force control by muscle synergies

Berger, Denise J.; d'Avella, Andrea
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 17/04/2014 EN
Relevância na Pesquisa
27.41%
Muscle synergies have been proposed as a way for the central nervous system (CNS) to simplify the generation of motor commands and they have been shown to explain a large fraction of the variation in the muscle patterns across a variety of conditions. However, whether human subjects are able to control forces and movements effectively with a small set of synergies has not been tested directly. Here we show that muscle synergies can be used to generate target forces in multiple directions with the same accuracy achieved using individual muscles. We recorded electromyographic (EMG) activity from 13 arm muscles and isometric hand forces during a force reaching task in a virtual environment. From these data we estimated the force associated to each muscle by linear regression and we identified muscle synergies by non-negative matrix factorization. We compared trajectories of a virtual mass displaced by the force estimated using the entire set of recorded EMGs to trajectories obtained using 4–5 muscle synergies. While trajectories were similar, when feedback was provided according to force estimated from recorded EMGs (EMG-control) on average trajectories generated with the synergies were less accurate. However, when feedback was provided according to recorded force (force-control) we did not find significant differences in initial angle error and endpoint error. We then tested whether synergies could be used as effectively as individual muscles to control cursor movement in the force reaching task by providing feedback according to force estimated from the projection of the recorded EMGs into synergy space (synergy-control). Human subjects were able to perform the task immediately after switching from force-control to EMG-control and synergy-control and we found no differences between initial movement direction errors and endpoint errors in all control modes. These results indicate that muscle synergies provide an effective strategy for motor coordination.

A computational analysis of motor synergies by dynamic response decomposition

Alessandro, Cristiano; Carbajal, Juan Pablo; d'Avella, Andrea
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 16/01/2014 EN
Relevância na Pesquisa
27.41%
Analyses of experimental data acquired from humans and other vertebrates have suggested that motor commands may emerge from the combination of a limited set of modules. While many studies have focused on physiological aspects of this modularity, in this paper we propose an investigation of its theoretical foundations. We consider the problem of controlling a planar kinematic chain, and we restrict the admissible actuations to linear combinations of a small set of torque profiles (i.e., motor synergies). This scheme is equivalent to the time-varying synergy model, and it is formalized by means of the dynamic response decomposition (DRD). DRD is a general method to generate open-loop controllers for a dynamical system to solve desired tasks, and it can also be used to synthesize effective motor synergies. We show that a control architecture based on synergies can greatly reduce the dimensionality of the control problem, while keeping a good performance level. Our results suggest that in order to realize an effective and low-dimensional controller, synergies should embed features of both the desired tasks and the system dynamics. These characteristics can be achieved by defining synergies as solutions to a representative set of task instances. The required number of synergies increases with the complexity of the desired tasks. However...

A model-based approach to predict muscle synergies using optimization: application to feedback control

Sharif Razavian, Reza; Mehrabi, Naser; McPhee, John
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 06/10/2015 EN
Relevância na Pesquisa
27.41%
This paper presents a new model-based method to define muscle synergies. Unlike the conventional factorization approach, which extracts synergies from electromyographic data, the proposed method employs a biomechanical model and formally defines the synergies as the solution of an optimal control problem. As a result, the number of required synergies is directly related to the dimensions of the operational space. The estimated synergies are posture-dependent, which correlate well with the results of standard factorization methods. Two examples are used to showcase this method: a two-dimensional forearm model, and a three-dimensional driver arm model. It has been shown here that the synergies need to be task-specific (i.e., they are defined for the specific operational spaces: the elbow angle and the steering wheel angle in the two systems). This functional definition of synergies results in a low-dimensional control space, in which every force in the operational space is accurately created by a unique combination of synergies. As such, there is no need for extra criteria (e.g., minimizing effort) in the process of motion control. This approach is motivated by the need for fast and bio-plausible feedback control of musculoskeletal systems...

Measuring financial synergies in cross-border M&A transactions using diffusion processes

Brailsford, Timothy John; Liao, Szu-Lang; Penm, Jack HW
Fonte: Inderscience Publishers Publicador: Inderscience Publishers
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
37.1%
In a cross-border M&A framework, the question and measurement of financial synergy can be important in the analysis of the transaction and consideration needs to be given to whether the specific cross-border financial risks outweigh operational synergies.

On the Origin of Muscle Synergies: Invariant Balance in the Co-activation of Agonist and Antagonist Muscle Pairs

Hirai, Hiroaki; Miyazaki, Fumio; Naritomi, Hiroaki; Koba, Keitaro; Oku, Takanori; Uno, Kanna; Uemura, Mitsunori; Nishi, Tomoki; Kageyama, Masayuki; Krebs, Hermano Igo
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 24/11/2015 EN
Relevância na Pesquisa
27.41%
Investigation of neural representation of movement planning has attracted the attention of neuroscientists, as it may reveal the sensorimotor transformation essential to motor control. The analysis of muscle synergies based on the activity of agonist–antagonist (AA) muscle pairs may provide insight into such transformations, especially for a reference frame in the muscle space. In this study, we examined the AA concept using the following explanatory variables: the AA ratio, which is related to the equilibrium-joint angle, and the AA sum, which is associated with joint stiffness. We formulated muscle synergies as a function of AA sums, positing that muscle synergies are composite units of mechanical impedance. The AA concept can be regarded as another form of the equilibrium-point (EP) hypothesis, and it can be extended to the concept of EP-based synergies. We introduce, here, a novel tool for analyzing the neurological and motor functions underlying human movements and review some initial insights from our results about the relationships between muscle synergies, endpoint stiffness, and virtual trajectories (time series of EP). Our results suggest that (1) muscle synergies reflect an invariant balance in the co-activation of AA muscle pairs; (2) each synergy represents the basis for the radial...

Auctions with synergies and asymetric buyers

Menezes, Flavio; Monteiro, Paulo K
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.95%
In this paper we consider sequential auctions with synergies where one player wants two objects and the remaining players want one object each. We show that expected prices may not necessarily decrease as predicted by Branco [Econ. Lett. 54 (1997) 159]. Indeed we show that expected prices can actually increase.

Synergies and price trends in sequential auctions

Menezes, Flavio; Monteiro, Paulo K
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
37.46%
In this paper we consider sequential second-price auctions where an individual's value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies declining expected prices. When synergies are negative, expected prices are increasing. There are several corollaries. First, the seller is indifferent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the first object is never exercised in the symmetric equilibrium and the seller's revenue is unchanged. Under negative synergies, in contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net effect on the seller's revenue of the introduction of an option is ambiguous. Finally, we examine a special case with asymmetric players who have distinct synergies. In this example...