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

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

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

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."Elimination par attributs" (EPA) est une heuristique utilisée lors d'un processus de choix séquentiel. A chaque étape de décision, les individus éliminent toutes les options ne possédant pas un certain attribut donné, jusqu'à ce qu'une seule option subsiste. Cette règle a servi de base à Tversky (1972a) pour élaborer un modèle discret de choix probabiliste. Dans ce travail, les probabilités issues du modèle EPA sont utilisées pour construire les demandes d'un duopole différencié avec rationalité imparfaite. Ces demandes sont compatibles avec une hétérogénéité partielle des goûts et peuvent être reliées à un modèle spatial dans lequel les consommateurs ont une perception convexe de la distance. Un équilibre de Nash en prix en stratégies pures existe lorsque le coût de la firme avec le plus haut niveau d'attribut est suffisamment élevé. Dans ce cas, la forme de "différenciation par attributs" retenue ici est à la fois horizontale et verticale, ce qui est peu fréquent dans la littérature. De plus, la firme avec le plus haut niveau d'attributs semble fixer un "prix de référence" sur le marché, utilisé par sa rivale pour déterminer son propre prix. Lorsqu'il n'existe pas d'équilibre, l'interaction des fonctions de meilleure réponse des firmes donne lieu à un cycle à la Edgeworth plutôt qu'à une sortie de la firme ayant le plus bas niveau d'attributs. Ce résultat souligne le rôle du différentiel de coûts dans l'existence de tels 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.Cet article considère un duopole probabiliste dans lequel les produits sont décrits par leurs attributs spécifiques, cette forme de différenciation incorporant les dimensions horizontales et verticales. Les consommateurs réalisent des choix discrets en suivant une règle de décision aléatoire fondée sur ces attributs. Nous étudions un jeu en trois étapes dans lequel les firmes proposent d'abord de nouveaux attributs pour leurs produits (innovation), puis ont la possibilité d'imiter les attributs du produit concurrent et finalement se font une concurrence en prix. A l'équilibre, la firme vendant le produit le moins apprécié est généralement incitée à imiter sa rivale. Face à cette menace d'imitation, il arrive que la firme de référence diminue stratééiquement son niveau d'attributs pour réduire son coût unitaire d'innovation et la différenciation sur le marché, dissuadant alors l'imitation. Cette stratégie est efficace lorsque les coûts d'imitation sont suffisamment concaves. Dans le cas contraire, il est préférable pour la firme de référence d'accepter l'imitation. Ainsi, selon la forme des coûts d'imitation, des équilibres avec "dissuasion" ou avec "accommodation" se produisent, complétant ainsi la typologie actuelle des réponses stratégiques face à une menace d'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.Cet article propose un duopole de choix discrets dans lequel les produits sont décrits et différenciés selon leurs attributs spécifiques. Ces attributs peuvent être des caractéristiques discrètes ou des différences de variables continues, comme les prix ou les qualités. Les consommateurs suivent un raisonnement probabiliste issu des structures à règle de décision aléatoire, comme le modèle d'élimination par attributs (Tversky, 1972). Un tel comportement est fréquemment adopté par les agents en présence de petites décisions d'achat. Le système de demande fournit une structure générale de différenciation des produits ayant pour cas particuliers les modèles classiques de différenciation horizontale et verticale. L'existence et l'unicité d'un équilibre de Nash en stratégies pures avec concurrence en prix sont établies dans le duopole. Lorsque les utilités des attributs varient, les propriétés des profits en statique comparative peuvent être expliquées par des effets "attractivité" et "différenciation". Ces effets se combinent de fa&ccdelil;on nouvelle en comparaison des structures déterministes ou du duopole logit. Par exemple, l'amélioration du produit le moins apprécié renforce la différenciation sur le marché

Homology-directed repair in rodent zygotes using Cas9 and TALEN engineered proteins

International audienceThe generation of genetically-modified organisms has been revolutionized by the development of new genome editing technologies based on the use of gene-specific nucleases, such as meganucleases, ZFNs, TALENs and CRISPRs-Cas9 systems. The most rapid and cost-effective way to generate genetically-modified animals is by microinjection of the nucleic acids encoding gene-specific nucleases into zygotes. However, the efficiency of the procedure can still be improved. In this work we aim to increase the efficiency of CRISPRs-Cas9 and TALENs homology-directed repair by using TALENs and Cas9 proteins, instead of mRNA, microinjected into rat and mouse zygotes along with long or short donor DNAs. We observed that Cas9 protein was more efficient at homology-directed repair than mRNA, while TALEN protein was less efficient than mRNA at inducing homology-directed repair. Our results indicate that the use of Cas9 protein could represent a simple and practical methodological alternative to Cas9 mRNA in the generation of genetically-modified rats and mice as well as probably some other mammals

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.Le duopole de produits différenciés avec "Elimination Par Attributs" (EPA) a été construit (Laurent, 2006a), à partir du modèle de choix discrets élaboré par Tversky (1972a,b). L'existence d'un équilibre en prix a été établie avec une "différenciation par attributs", qui incorpore les différenciations horizontales et verticales comme des cas particuliers. Cet article propose une extension de l'analyse précédente à travers un jeu en deux étapes dans lequel les firmes choisissent les attributs spécifiques de leurs produits et se font concurrence en prix. L'"effet concurrentiel" d'un rapprochement des qualités dans les modèles de différenciation verticale est remplacé par un "effet différenciation" dans le duopole avec EPA. Un équilibre de Nash parfait en sous-jeux existe avec des coûts exogènes mais aussi lorsque les coûts unitaires ou fixes dépendent du niveau d'attributs retenu. A l'équilibre, les produits sont généralement différenciés horizontalement et verticalement. Mais la différenciation peut aussi être purement verticale lorsque les coûts d'innovation sont fortement convexes ou lorsque les consommateurs accordent une grande importance aux prix. Quand les coûts sont endogènes, l'optimum social est atteint pour une différenciation horizontale pure. Ainsi, les produits sont trop différenciés à l'équilibre : la dimension verticale provoque une hausse des prix qui diminue le bien-être