Long-Term Contracts Under the Threat of Supplier Default

Contracting with suppliers prone to default is an increasingly common problem in some industries, particularly automotive manufacturing. We model this phenomenon as a two-period contracting game with two identical suppliers, a single buyer, deterministic demand, and uncertain production costs. The suppliers are distressed at the start of the game and do not have access to external sources of capital; hence, revenues from the buyer are crucial in determining whether default occurs. The production cost of each supplier is the sum of two stochastic components: a common term that is identical for both suppliers (representing raw materials costs, design specifications, etc.) and an idiosyncratic term that is unique to a given supplier (representing inherent firm capability). The buyer chooses a supplier and then decides on a single- or two-period contract. Comparing models with and without the possibility of default, we find that, without the possibility of supplier failure, the buyer always prefers short-term contracts over long-term contracts, whereas this preference is typically reversed in the presence of failure. Neither of these contracts coordinates the supply chain. We also consider dynamic contracts, in which the contract price is partially tied to some index representing the common component of production costs (e.g., commodity prices of raw materials such as steel or oil), allowing the buyer to shoulder some of the risk from cost uncertainty. We find that dynamic long-term contracts allow the buyer to coordinate the supply chain in the presence of default risk. We also demonstrate that our results continue to hold under a variety of alternative assumptions, including stochastic demand, allowing the buyer the option of subsidizing a bankrupt supplier via a contingent transfer payment or loan and allowing the buyer to unilaterally renegotiate contracts. We conclude that the possibility of supplier default offers a new reason to prefer long-term contracts over short-term contracts.supply chain management, financial default, contracting, game theory

Grid cells on the ball

What sort of grid cells do we expect to see in rodents who have spent their developmental period inside a large spherical cage? Or, in a different experimental paradigm, toddling on a revolving ball, with virtual reality simulating a coherently revolving surround? We consider a simple model of grid firing map formation, based on firing rate adaptation, that we have earlier analyzed when playing out on a flat environment. The model predicts that whether experienced on the outside or inside, a spherical environment induces one of a succession of grid maps realized as combinations of spherical harmonics, depending on the relation of the radius to the preferred grid spacing, itself related to the parameters of firing rate adaptation. Numerical simulations concur with analytical predictions

Unilateral subthalamic nucleus stimulation has a measurable ipsilateral effect on rigidity and bradykinesia in Parkinson disease

BACKGROUND: Bilateral deep brain stimulation (DBS) of the subthalamic nucleus (STN) improves motor function in Parkinson disease (PD). However, little is known about the quantitative effects on motor behavior of unilateral STN DBS. METHODS: In 52 PD subjects with STN DBS, we quantified in a double-blinded manner rigidity (n= 42), bradykinesia (n= 38), and gait speed (n= 45). Subjects were tested in four DBS conditions: both on, left on, right on and both off. A force transducer was used to measure rigidity across the elbow, and gyroscopes were used to measure angular velocity of hand rotations for bradykinesia. About half of the subjects were rated using the Unified Parkinson Disease Rating Scale (part III) motor scores for arm rigidity and repetitive hand rotation simultaneously during the kinematic measurements. Subjects were timed walking 25 feet. RESULTS: All subjects had significant improvement with bilateral STN DBS. Contralateral, ipsilateral and bilateral stimulation significantly reduced rigidity and bradykinesia. Bilateral stimulation improved rigidity more than unilateral stimulation of either side, but there was no significant difference between ipsilateral and contralateral stimulation. Although bilateral stimulation also increased hand rotation velocity more than unilateral stimulation of either side, contralateral stimulation increased hand rotation significantly more than ipsilateral stimulation. All stimulation conditions improved walking time but bilateral stimulation provided the greatest improvement. CONCLUSIONS: Unilateral STN DBS decreased rigidity and bradykinesia contralaterally as well ipsilaterally. As expected, bilateral DBS improved gait more than unilateral DBS. These findings suggest that unilateral STN DBS alters pathways that affect rigidity and bradykinesia bilaterally but do not support the clinical use of unilateral STN DBS since bilateral DBS clearly provides greater benefit

Subthalamic nucleus stimulation-induced regional blood flow responses correlate with improvement of motor signs in Parkinson disease

Deep brain stimulation of the subthalamic nucleus (STN DBS) improves motor symptoms in idiopathic Parkinson's disease, yet the mechanism of action remains unclear. Previous studies indicate that STN DBS increases regional cerebral blood flow (rCBF) in immediate downstream targets but does not reveal which brain regions may have functional changes associated with improved motor manifestations. We studied 48 patients with STN DBS who withheld medication overnight and underwent PET scans to measure rCBF responses to bilateral STN DBS. PET scans were performed with bilateral DBS OFF and ON in a counterbalanced order followed by clinical ratings of motor manifestations using Unified Parkinson Disease Rating Scale 3 (UPDRS 3). We investigated whether improvement in UPDRS 3 scores in rigidity, bradykinesia, postural stability and gait correlate with rCBF responses in a priori determined regions. These regions were selected based on a previous study showing significant STN DBS-induced rCBF change in the thalamus, midbrain and supplementary motor area (SMA). We also chose the pedunculopontine nucleus region (PPN) due to mounting evidence of its involvement in locomotion. In the current study, bilateral STN DBS improved rigidity (62%), bradykinesia (44%), gait (49%) and postural stability (56%) (paired t-tests: P < 0.001). As expected, bilateral STN DBS also increased rCBF in the bilateral thalami, right midbrain, and decreased rCBF in the right premotor cortex (P < 0.05, corrected). There were significant correlations between improvement of rigidity and decreased rCBF in the SMA (rs = –0.4, P < 0.02) and between improvement in bradykinesia and increased rCBF in the thalamus (rs = 0.31, P < 0.05). In addition, improved postural reflexes correlated with decreased rCBF in the PPN (rs = –0.38, P < 0.03). These modest correlations between selective motor manifestations and rCBF in specific regions suggest possible regional selectivity for improvement of different motor signs of Parkinson's disease