Optimal Pricing in Networks with Externalities

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers who are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumer's usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolist's optimal pricing strategy may involve offering discounts to certain agents who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive a characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that consists of three components: (i) a nominal term that is independent of the network structure, (ii) a discount term proportional to the influence that this agent exerts over the rest of the social network (quantified by the agent's Bonacich centrality), and (iii) a markup term proportional to the influence that the network exerts on the agent. In the second part of the paper, we discuss the optimal strategy of a monopolist who can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Third, we assume that the monopolist can offer the good in two prices, full and discounted, and we study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard; however, we provide an explicit characterization of the set of agents who should be offered the discounted price. Next, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88% of the optimal profit. Finally, we highlight the value of network information by comparing the profits of a monopolist who does not take into account the network effects when choosing her pricing policy to those of a monopolist who uses this information optimally

Pricing in networks

This paper studies optimal pricing in networks in the presence of local consumption or price externalities. It analyzes the relation between prices and nodal centrality measures. Using an asymptotic approach, it shows that the ranking of optimal prices and strategies can be reduced to the lexicographic ranking of a specific vector of nodal characteristics. In particular, this result shows that with positive consumption externalities, prices are higher at nodes with higher degree, and with relative price externalities, prices are higher at nodes which have more neighbors of smaller degree.Social Networks, Network Externalities, Oligopolies

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

Network Neutrality and the Evolution of the Internet

In order to create incentives for Internet traffic providers not to discriminate with respect to certain applications on the basis of network capacity requirements, the concept of market driven network neutrality is introduced. Its basic characteristics are that all applications are bearing the opportunity costs of the required traffic capacities. An economic framework for market driven network neutrality in broadband Internet is provided, consisting of congestion pricing and quality of service differentiation. However, network neutrality regulation with its reference point of the traditional TCP would result in regulatory micromanagement of traffic network management. --Broadband Internet,network neutrality,quality of service differentiation,congestion pricing,interclass externality pricing,interconnection agreements

Traffic congestion and congestion pricing

For several decades growth of traffic volumes has outstripped investments in road infrastructure. The result has been a relentless increase in traffic congestion. This paper reviews the economic principles behind congestion pricing in static and dynamic settings, which derive from the benefits of charging travellers for the externalities they create. Special attention is paid to various complications that make simple textbook congestion pricing models of limited relevance, and dictate that congestion pricing schemes be studied from the perspective of the theory of the second best. These complications include pricing in networks, heterogeneity of users, stochastic congestion, interactions of the transport sector with the rest of the economy, and tolling on private roads. Also the implications of congestion pricing for optimal road capacity are considered, and finally some explanations for the longstanding social and political resistance to road pricing are offered. * The authors would..

On-Net/Off-Net Price Discrimination and 'Bill-and-Keep' vs. 'Cost-Based' Regulation of Mobile Termination Rates

This paper surveys the recent literature on competition between mobile network operators in the presence of call externalities and network effects. It shows that the regulation of mobile termination rates based on “long-run incremental costs” increases networks’ strategic incentives to inefficiently set high on-net/off-net price differentials, thus harming smaller networks and new entrants. The paper argues in favor of a “bill-and-keep” system for mobile-to-mobile termination, and presents international evidence in support of this conclusion.mobile termination, network effects, call externalities, bill-and-keep

Network neutrality and the evolution of the internet

In order to create incentives for Internet traffic providers not to discriminate with respect to certain applications on the basis of network capacity require-ments, the concept of market driven network neutrality is introduced. Its basic characteristics are that all applications are bearing the opportunity costs of the required traffic capacities. An economic framework for market driven network neutrality in broadband Internet is provided, consisting of congestion pricing and quality of service differentiation. However, network neutrality regulation with its reference point of the traditional TCP would result in regulatory micro-management of traffic network management. --

Multi-objective road pricing: a cooperative and competitive bilevel optimization approach

Costs associated with traffic externalities such as congestion, air pollution, noise, safety, etcetera are becoming unbearable. The Braess paradox shows that combating congestion by adding infrastructure may not improve traffic conditions, and geographical and/or financial constraints may not allow infrastructure expansion. Road pricing presents an alternative to combat traffic externalities. The traditional way of road pricing, namely congestion charging, may create negative benefits for society. In this effect, we develop a flexible pricing scheme internalizing costs arising from all externalities. Using a game theoretical approach, we extend the single authority road pricing scheme to a pricing scheme with multiple authorities/regions (with likely contradicting objectives)

Monopoly pricing of social goods

We analyse the roles of social network topology and size on the monopoly pricing of network goods in a market, where consumers interact with each other and are characterised by their social relations. The size effect is the well-known network externalities phenomenon, while the topological effect has not been previously studied in this context. The topological effect works against, and dominates, the size effect in monopoly pricing by reducing the monopoly's capacity to extract consumer surplus. Under asymmetric information about consumer types, the monopoly prefers symmetric network topologies, but the social optimum is an asymmetric network.social relations; networks; coordination; monopoly