3 research outputs found
Pricing in Social Networks with Negative Externalities
We study the problems of pricing an indivisible product to consumers who are
embedded in a given social network. The goal is to maximize the revenue of the
seller. We assume impatient consumers who buy the product as soon as the seller
posts a price not greater than their values of the product. The product's value
for a consumer is determined by two factors: a fixed consumer-specified
intrinsic value and a variable externality that is exerted from the consumer's
neighbors in a linear way. We study the scenario of negative externalities,
which captures many interesting situations, but is much less understood in
comparison with its positive externality counterpart. We assume complete
information about the network, consumers' intrinsic values, and the negative
externalities. The maximum revenue is in general achieved by iterative pricing,
which offers impatient consumers a sequence of prices over time.
We prove that it is NP-hard to find an optimal iterative pricing, even for
unweighted tree networks with uniform intrinsic values. Complementary to the
hardness result, we design a 2-approximation algorithm for finding iterative
pricing in general weighted networks with (possibly) nonuniform intrinsic
values. We show that, as an approximation to optimal iterative pricing, single
pricing can work rather well for many interesting cases, but theoretically it
can behave arbitrarily bad
Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach
We consider the problem of allocating multiple indivisible items to a set of
networked agents to maximize the social welfare subject to network
externalities. Here, the social welfare is given by the sum of agents'
utilities and externalities capture the effect that one user of an item has on
the item's value to others. We first provide a general formulation that
captures some of the existing models as a special case. We then show that the
social welfare maximization problem benefits some nice diminishing or
increasing marginal return properties. That allows us to devise polynomial-time
approximation algorithms using the Lovasz extension and multilinear extension
of the objective functions. Our principled approach recovers or improves some
of the existing algorithms and provides a simple and unifying framework for
maximizing social welfare subject to network externalities
Inequity aversion pricing over social networks: Approximation algorithms and hardness results
We study a revenue maximization problem in the context of social networks. Namely, we generalize a model introduced by Alon, Mansour, and Tennenholtz [2] that captures inequity aversion, i.e., it captures the fact that prices offered to neighboring nodes should not differ significantly. We first provide approximation algorithms for a natural class of instances, where the total revenue is the sum of single-value revenue functions. Our results improve on the current state of the art, especially when the number of distinct prices is small. This applies, for instance, to settings where the seller will only consider a fixed number of discount types or special offers. To complement our positive results, we resolve one of the open questions posed in [2] by establishing APX-hardness for the problem. Surprisingly, we further show that the problem is NP-complete even when the price differences are allowed to be large, or even when the number of allowed distinct prices is as small as three. Finally, we study extensions of the model regarding the demand type of the clients