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

Selling a Single Item with Negative Externalities

We consider the problem of regulating products with negative externalities to a third party that is neither the buyer nor the seller, but where both the buyer and seller can take steps to mitigate the externality. The motivating example to have in mind is the sale of Internet-of-Things (IoT) devices, many of which have historically been compromised for DDoS attacks that disrupted Internet-wide services such as Twitter. Neither the buyer (i.e., consumers) nor seller (i.e., IoT manufacturers) was known to suffer from the attack, but both have the power to expend effort to secure their devices. We consider a regulator who regulates payments (via fines if the device is compromised, or market prices directly), or the product directly via mandatory security requirements. Both regulations come at a cost---implementing security requirements increases production costs, and the existence of fines decreases consumers' values---thereby reducing the seller's profits. The focus of this paper is to understand the \emph{efficiency} of various regulatory policies. That is, policy A is more efficient than policy B if A more successfully minimizes negatives externalities, while both A and B reduce seller's profits equally. We develop a simple model to capture the impact of regulatory policies on a buyer's behavior. {In this model, we show that for \textit{homogeneous} markets---where the buyer's ability to follow security practices is always high or always low---the optimal (externality-minimizing for a given profit constraint) regulatory policy need regulate \emph{only} payments \emph{or} production.} In arbitrary markets, by contrast, we show that while the optimal policy may require regulating both aspects, there is always an approximately optimal policy which regulates just one

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

Pricing Public Goods for Private Sale

We consider the pricing problem faced by a seller who assigns a price to a good that confers its benefits not only to its buyers, but also to other individuals around them. For example, a snow-blower is potentially useful not only to the household that buys it, but also to others on the same street. Given that the seller is constrained to selling such a (locally) public good via individual private sales, how should he set his prices given the distribution of values held by the agents? We study this problem as a two-stage game. In the first stage, the seller chooses and announces a price for the product. In the second stage, the agents (each having a private value for the good) decide simultaneously whether or not they will buy the product. In the resulting game, which can exhibit a multiplicity of equilibria, agents must strategize about whether they will themselves purchase the good to receive its benefits. In the case of a fully public good (where all agents benefit whenever any agent purchases), we describe a pricing mechanism that is approximately revenue-optimal (up to a constant factor) when values are drawn from a regular distribution. We then study settings in which the good is only "locally" public: agents are arranged in a network and share benefits only with their neighbors. We describe a pricing method that approximately maximizes revenue, in the worst case over equilibria of agent behavior, for any $d$-regular network. Finally, we show that approximately optimal prices can be found for general networks in the special case that private values are drawn from a uniform distribution. We also discuss some barriers to extending these results to general networks and regular distributions.Comment: accepted to EC'1

Towards Data Auctions with Externalities

The design of data markets has gained importance as firms increasingly use predictions from machine learning models to streamline operations, yet need to externally acquire training data to fit such models. One aspect that has received limited consideration is the externality a firm faces when data is allocated to competing firms. Such externalities couple firms' optimal allocations, despite the inherent free replicability of data. In this paper, we demonstrate that the presence of externalities increases the optimal revenue of a monopolistic data seller by letting firms pay to prevent allocations to other competing firms. This is shown by first reducing the combinatorial problem of allocating and pricing multiple datasets to the auction of a single digital good. We achieve this by modeling utility for data solely through the increase in prediction accuracy it provides. Then, we find the welfare and revenue maximizing mechanisms, highlighting how the forms of firms' private information - whether they know the externalities they exert on others or vice-versa - affects their overall structures. In all cases, the optimal allocation rule is a single threshold (one per firm), where either all data is allocated or none is

Modeling consumer behaviour in the presence of network effects

Consumer choice models are a key component in fields such as Revenue Management and Transport Logistics, where the demands for certain products or services are assumed to follow a particular form, and sellers or market-makers use that information to adjust their strategies accordingly, choosing for example which products to display (assortment problem) or their prices (pricing problem). In the last couple of decades, online markets have taken a lot of relevance, providing a setting where consumers can compare easily different products, before deciding to buy them. More information is now available, and the purchasing decisions not only depend on the quality, prices and availability of the products, but also on what previous consumers think about them (phenomenon commonly known as Network Effects). Hence, in order to create a suitable model for this kind of market, it is relevant to understand how the collective decisions affect the market evolution. In this thesis we consider a particular subset of those online markets, cultural markets, where the products are for example songs, video games or ebooks. This kind of market has the special feature that its products have unlimited supply (since they are just a digital copy), and therefore we can exploit this in our models, to justify assumptions of the asymptotic behaviour of the market. We study some variations of the traditional Multinomial Logit (MNL) model, characterising the behaviour of consumers, where their purchasing decisions are affected by the quality and prices (initially fixed) of the available products, as well as their visibilities in the market interface and the consumption patterns of previous users. We focus particularly on the parameters associated to the network effects, where depending on the strength of the network effects, it is possible to explain: herd behaviours, where an alternative overpowers the rest; as well as more well-distributed settings, where all the alternatives receive enough attention giving a notion of fairness, since higher quality products get a larger market share. Finally, using the model where market shares are distributed according to the quality of the products, we study pricing strategies, where sellers can either collaborate or compete. We analyse the effect of both type of strategies into the choice model