Ab initio computation of the broadening of water rotational lines by molecular hydrogen

Theoretical cross sections for the pressure broadening by hydrogen of rotational transitions of water are compared to the latest available measurements in the temperature range 65-220 K. A high accuracy interaction potential is employed in a full close coupling calculation. A good agreement with experiment is observed above ~80 K while the sharp drop observed experimentally at lower temperatures is not predicted by our calculations. Possible explanations for this discrepancy include the failure of the impact approximation and the possible role of ortho-to-para conversion of H2.Comment: 11 pages, 3 figures, accepted for publicatio

Differentiated duopoly with 'elimination by aspects'

"Elimination by aspects" (EBA) is a discrete model of probabilistic choice worked out by Tversky in 1972 which supposes that decision makers follow a particular heuristic during a process of sequential choice. Options are described by their attributes and, at each decision stage, the individuals eliminate all the options not having an expected given attribute, and so until only one option remains. In this paper, probabilities resulting from the EBA model are used to construct demands of a differentiated duopoly with imperfect rationality. These demands are consistent with partial heterogeneity of tastes and may be linked with a spatial framework in which consumers have convex perception of distance. In this model, a Nash price equilibrium in pure strategies exists if the cost of the highest attributes level firm is not too low. In this case, the "differentiation by attributes" form retained here is both horizontal and vertical, which is not very frequent in the literature. When the equilibrium does not exists, the interaction of best response functions of the firms induces an Edgeworth cycle instead of an exit of the lowest attributes level firm. This result underlines the role of cost difference in the existence of such a cycle.discrete choices ; product differentiation ; imperfect competition ; elimination-by-aspects ; Edgeworth cycles

Product innovation and imitation in a duopoly with differentiation by attributes

This paper considers a probabilistic duopoly in which products are described by their specific attributes, this form of differentiation embodying the horizontal and vertical dimensions. Consumers make discrete choices and follow a random decision rule based on these attributes. A three-stage game is studied in which firms develop new attributes for their products (innovation), then may imitate the attributes of the competing product and finally compete in price. At the equilibrium, the firm selling the less appreciated product is generally incited to imitate its rival. Confronted to a threat of imitation, the benchmark firm sometimes decreases strategically its attribute index in order to diminish its unit cost of innovation and the differentiation on the market, deterring the imitation in this way. This strategy is efficient when imitation costs are sufficiently concave. In the opposite case, it is preferable for the benchmark firm to accept the imitation. Thus, according to the shape of imitation costs, equilibria with "deterrence" or with "accommodation" "accommodation" occur, completing the current typology of strategic responses to a threat of imitation.quality choices ; differentiation by attributes ; product innovation, product imitation

Probalilistic duopoly with differentiation by attributes

This paper proposes a discrete choice duopoly in which products are described and differentiated by their specific attributes. These attributes can be discrete characteristics or differences in continuous variables, such as prices or qualities. Consumers follow a probabilistic reasoning which is consistent with random decision rule models such as Tversky's "Elimination by Aspects" framework (1972a,b). This type of behavior is relevant for small everyday life purchases. The demand system provides a general structure of product differentiation in which special cases are given by classical models of horizontal and vertical differentiation. Existence and uniqueness of a price Nash equilibrium in pure strategies are established in the duopoly. When attributes' utilities vary, comparative statics properties of profits can be explained by "attractiveness" and "differentiation" effects. These effects are combined in a new way compared to the deterministic structures or to the logit duopoly. For example, an increase in the low utility index of attributes strengthens product differentiation.discrete choices ; product differentiation ; imperfect competition ; "Elimination by Aspects"

Choice of new attributes in the 'Elimination by Aspects' duopoly

The "Elimination by aspects" (EBA) duopoly of product differentiation (Laurent, 2006a) was constructed from the discrete model of probabilistic choice worked out by Tversky (1972a,b). In this framework, an unique price equilibrium exists with a "differentiation by attributes", which embodies horizontal and vertical differentiations as possible special cases. This paper extends this analysis by studying a two-stage game in which firms choose the specific attributes of their product and then compete in prices. At the price equilibrium, the "competitive effect", present in pure vertical differentiation models, is replaced by a "differentiation effect" in this EBA duopoly. Subgame perfect Nash equilibria are shown to exist with exogenous costs but also with attributes-dependent unit and fixed costs. At the equilibrium, products are generally differentiated both horizontally and vertically. But a purely vertical outcome may also occur when costs of innovation are strongly convex or when consumers are very sensible to the price levels. When costs are endogenous, the social optimum is achieved for a pure horizontal differentiation. Thus, there is too much differentiation at the equilibrium: the vertical dimension induces a strong raise of prices, which also reduces the welfare.elimination-by-aspects ; product differentiation ; quality choices ; welfare analysis