Pricing in Social Networks with Negative Externalities

TL;DR

This paper investigates revenue maximization through pricing strategies in social networks with negative externalities, revealing computational hardness and proposing approximation algorithms.

Contribution

It introduces the first hardness results for optimal iterative pricing with negative externalities and offers a 2-approximation algorithm for general networks.

Findings

Optimal iterative pricing is NP-hard even on simple tree networks.

A 2-approximation algorithm is developed for general weighted networks.

Single pricing can perform arbitrarily poorly compared to iterative pricing.

Abstract

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.