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.