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The network of brain structures engaged in motor sequence learning comprises the same structures as those involved in tremor, including basal ganglia, cerebellum, thalamus, and motor cortex. Deep brain stimulation (DBS) of the ventrointermediate nucleus of the thalamus (VIM) reduces tremor, but the effects on motor sequence learning are unknown. We investigated whether VIM stimulation has an impact on motor sequence learning and hypothesized that stimulation effects depend on the laterality of electrode location. Twenty patients (age: 38–81 years; 12 female) with VIM electrodes implanted to treat essential tremor (ET) successfully performed a serial reaction time task, varying whether the stimuli followed a repeating pattern or were selected at random, during which VIM‐DBS was either on or off. Analyses of variance were applied to evaluate motor sequence learning performance according to reaction times (RTs) and accuracy. An interaction was observed between whether the sequence was repeated or random and whether VIM‐DBS was on or off (F[1,18] = 7.89, p =.012). Motor sequence learning, reflected by reduced RTs for repeated sequences, was greater with DBS on than off (T[19] = 2.34, p =.031). Stimulation location correlated with the degree of motor learning, with greater motor learning when stimulation targeted the lateral VIM (n = 23, ρ = 0.46; p =.027). These results demonstrate the beneficial effects of VIM‐DBS on motor sequence learning in ET patients, particularly with lateral VIM electrode location, and provide evidence for a role for the VIM in motor sequence learning. [ABSTRACT FROM AUTHOR]

Supply-then-price competition is common in settings in which capacity commitments precede pricing decisions. We provide a characterization of when and why equilibria of such games clear the market at the Cournot outcomes. The paper extends the seminal work of Kreps and Scheinkman (1983) to differentiated product settings with an arbitrary number of firms and general demand and spill functions. We identify two new fundamental properties that drive the result: independence from irrelevant supply and spill inertia. These properties are satisfied by common demand and spill models. Our result provides a shortcut approach to analyzing supply-then-price games and highlights the importance of demand specification, compared with spill specification, in determining the outcome of such games. We study a two-stage deterministic differentiated-product oligopoly competition game, called the quantity precommitment game, in which firms compete on quantity in the first stage and then compete on price in the second stage. We compare this game with a single-stage Cournot game, in which firms compete on quantity only and prices are set to clear the market. We show that any equilibrium of the quantity precommitment game is an equilibrium of the Cournot game under certain conditions that allow for commonly used demand functions and general spill models. Our approach yields insight into key properties that enable this relationship to hold. The electronic companion is available at https://doi.org/10.1287/opre.2018.1760. [ABSTRACT FROM AUTHOR]

We address the multiproduct newsvendor problem under a general specification of customer choice behavior.We develop a methodology that yields upper bounds on the optimal value as well as feasible inventory solutions. The methodology is based on an approximate Jordan decomposition of the state transition matrix. Two specializations of the methodology are presented: one leads to a decomposition by customer into a sequence of assortment optimization problems and the second leads to a decomposition by product into a collection of independent newsvendor problems. We conduct computational experiments and find that the proposed methodology outperforms existing bounds. [ABSTRACT FROM AUTHOR]