We develop a probabilistic consumer choice framework based on information asymmetry between consumers and firms. This framework makes it possible to study market competition of several firms by both quality and price of their products. We find Nash m
arket equilibria and other optimal strategies in various situations ranging from competition of two identical firms to firms of different sizes and firms which improve their efficiency.
People in the Internet era have to cope with the information overload, striving to find what they are interested in, and usually face this situation by following a limited number of sources or friends that best match their interests. A recent line of
research, namely adaptive social recommendation, has therefore emerged to optimize the information propagation in social networks and provide users with personalized recommendations. Validation of these methods by agent-based simulations often assumes that the tastes of users and can be represented by binary vectors, with entries denoting users preferences. In this work we introduce a more realistic assumption that users tastes are modeled by multiple vectors. We show that within this framework the social recommendation process has a poor outcome. Accordingly, we design novel measures of users taste similarity that can substantially improve the precision of the recommender system. Finally, we discuss the issue of enhancing the recommendations diversity while preserving their accuracy.
This paper proves a corner occupying theorem for the two-dimensional integral rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given integral rectangles into an integral rectangular container without overl
apping, then we can achieve a feasible packing by successively placing an integral rectangle onto a bottom-left corner in the container. Based on this theorem, we might develop efficient heuristic algorithms for solving the integral rectangle packing problem. In fact, as a vague conjecture, this theorem has been implicitly mentioned with different appearances by many people for a long time.
