Market effects of changes in consumers' social responsibility

In a duopoly model of vertical differentiation, we study market equilibrium and the resulting social welfare following an increase in the consumer's willingness to pay (WTP) for products sold by socially responsible manufacturers. Different types of such changes emerge depending on their effects on consumer heterogeneity. We show that, in most cases, increases in the consumers' social consciousness yield higher profits to socially responsible firms and may lead to higher levels of social welfare, provided that the market structure is left unchanged. However, when an increase in the consumer's social consciousness changes the market structure, welfare may fall, while the duopolists' profits rise. The resulting tension between private and social interest calls for a cautious attitude toward information campaigns aimed at increasing the consumer's social consciousness.

Weighted alpha-rate dominating sets in social networks

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum alpha and alpha-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted alpha-rate domination set problem which is, to the best of our knowledge, the first such algorithm. A theoretical approximation bound based on a simple randomised rounding technique is given. The algorithm is implemented in Python and applied to a UK Twitter mentions networks using a measure of individuals’ influence (klout) as weights. We argue that the weights of vertices could be interpreted as the costs of getting those individuals on board for a campaign or a behaviour change intervention. The minimum weighted alpha-rate dominating set problem can therefore be seen as finding a set that minimises the total cost and each individual in a network has at least alpha percentage of its neighbours in the chosen set. We also test our algorithm on generated graphs with several thousand vertices and edges. Our results on this real-life Twitter networks and generated graphs show that the implementation is reasonably efficient and thus can be used for real-life applications when creating social network based interventions, designing social media campaigns and potentially improving users’ social media experience.