Pricing Algorithms For a Two-sided Internet Advertisement Market

The Google AdSense Program is a successful internet advertisement program where Google places contextual adverts on third-party websites and shares the resulting revenue with each publisher. Advertisers have budgets and bid on ad slots while publishers set reserve prices for the ad slots on their websites. Following previous modelling efforts, we model the program as a two-sided market with advertisers on one side and publishers on the other. We show a reduction from the Generalised Assignment Problem (GAP) to the problem of computing the revenue maximising allocation and pricing of publisher slots under a first-price auction. GAP is APX-hard but a (1-1/e) approximation is known. We compute truthful and revenue-maximizing prices and allocation of ad slots to advertisers under a second-price auction. The auctioneer's revenue is within (1-1/e) second-price optimal.

Competition between HMO and PPO: A Two-Sided Market Approach

We set-up a two-sided market framework to model competition between a Prefered Provider Organization (PPO) and a Health Maintenance Organization (HMO). Both health plans compete to attract policyholderson one side and providers on the other side. The PPO, which is characterized by a higher diversity of providers, attracts riskier policyholders. Our two-sided framework allows to examine the consequences of this risk segmentation on the providers’ side, especially in terms of remuneration. The outcome of competition mainly depends on two effects: a demand effect, influenced by the value put by policyholders on providers access and an adverse selection effect, captured by the characteristics of the health risk distribution. If the adverse selection effect is too strong, the HMO gets a higher profit in equilibrium. On the contrary, if the demand effect dominates, the PPO profit is higher in spite of the unfavorable risk segmentation. We believe that our model, by highlighting the two-sided market structure of the health plans’ competition, provides new insights to understand the increase in the PPOs’ market share observed during the last decade in the US.

Strategic adoption in a two-sided market : a study of college applications in Brazil

This paper measures the importance of indirect network effects in the adoption by colleges and students of ENEM, a standardized exam for high-school students in Brazil that can be used in college application processes. We estimate network effects and find that they are economically significant. Students are more likely to take ENEM the larger the number of colleges adopting it. Similarly, colleges are more likely to adopt it the larger the number of students taking the exam. Moreover, we find evidence that colleges play strategically and that heterogeneity determines their decisions. A college is less likely to adopt ENEM the larger the number of competitors adopting it. Colleges’ characteristics such as ownership and organization affect adoption decisions. In a counterfactual exercise we compare colleges’ adoption decisions under competition and under joint colleges’ payoffs maximization. Adoption rates are significantly reduced when colleges internalize the competitive effect, i.e., the effect of their decisions on other colleges’ payoffs. On the other hand, they increase when indirect network effects - the effect of students’ response to their decisions on other colleges’ payoffs - are also internalized. Competitive adoption rates are found to exceed joint optimum rates by a small difference. These results suggest that, without considering students’ welfare, adoption rates are excessive, but close to the joint optimum.

The Role of Online Platforms for Media Markets – Two‐Dimensional Spatial Competition in a Two‐Sided Market

We analyze the market for online and offline media in a model of two-dimensional spatial competition where media outlets sell content and advertising space. Consumer preferences are distributed along the style and type of news coverage where the distance costs may vary across dimensions. For integrated provision of online and offline platforms we show that entering the online market reduces average profits and may even constitute a prisoner's dilemma. Specialized provision may yield polarization in the style and type dimensions. This is in contrast to the maximum–minimum differentiation result previously established in the literature on multidimensional horizontal competition. We show that maximal differentiation in both dimensions occurs due to the discrete nature of the type dimension and asymmetric advertising markets.

Endogenous Two-Sided Markets with Repeated Transactions

We consider homogeneous two-sided markets, in which connected buyer-seller pairs bargain and trade repeatedly. In this infinite market game with exogenous matching probabilities and a common discount factor, we prove the existence of equilibria in stationary strategies. The equilibrium payoffs are given implicitly as a solution to a system of linear equations. Then, we endogenize the matching mechanism in a link formation stage that precedes the market game. When agents are sufficiently patient and link costs are low, we provide an algorithm to construct minimally connected networks that are pairwise stable with respect to the expected payoffs in the trading stage. The constructed networks are essentially efficient and consist of components with a constant buyer-seller ratio. The latter ratio increases (decreases) for a buyer (seller) that deletes one of her links in a pairwise stable component.

The new economy: Essays in network economics and two-sided markets

Following the Introduction, which surveys existing literature on the technology advances and regulation in telecommunications and on two-sided markets, we address specific issues on the industries of the New Economy, featured by the existence of network effects. We seek to explore how each one of these industries work, identify potential market failures and find new solutions at the economic regulation level promoting social welfare. In Chapter 1 we analyze a regulatory issue on access prices and investments in the telecommunications market. The existing literature on access prices and investment has pointed out that networks underinvest under a regime of mandatory access provision with a fixed access price per end-user. We propose a new access pricing rule, the indexation approach, i.e., the access price, per end-user, that network i pays to network j is function of the investment levels set by both networks. We show that the indexation can enhance economic efficiency beyond what is achieved with a fixed access price. In particular, access price indexation can simultaneously induce lower retail prices and higher investment and social welfare as compared to a fixed access pricing or a regulatory holidays regime. Furthermore, we provide sufficient conditions under which the indexation can implement the socially optimal investment or the Ramsey solution, which would be impossible to obtain under fixed access pricing. Our results contradict the notion that investment efficiency must be sacrificed for gains in pricing efficiency. In Chapter 2 we investigate the effect of regulations that limit advertising airtime on advertising quality and on social welfare. We show, first, that advertising time regulation may reduce the average quality of advertising broadcast on TV networks. Second, an advertising cap may reduce media platforms and firms' profits, while the net effect on viewers (subscribers) welfare is ambiguous because the ad quality reduction resulting from a regulatory cap o¤sets the subscribers direct gain from watching fewer ads. We find that if subscribers are sufficiently sensitive to ad quality, i.e., the ad quality reduction outweighs the direct effect of the cap, a cap may reduce social welfare. The welfare results suggest that a regulatory authority that is trying to increase welfare via regulation of the volume of advertising on TV might necessitate to also regulate advertising quality or, if regulating quality proves impractical, take the effect of advertising quality into consideration. 3 In Chapter 3 we investigate the rules that govern Electronic Payment Networks (EPNs). In EPNs the No-Surcharge Rule (NSR) requires that merchants charge at most the same amount for a payment card transaction as for cash. In this chapter, we analyze a three- party model (consumers, merchants, and a proprietary EPN) with endogenous transaction volumes and heterogenous merchants' transactional benefits of accepting cards to assess the welfare impacts of the NSR. We show that, if merchants are local monopolists and the network externalities from merchants to cardholders are sufficiently strong, with the exception of the EPN, all agents will be worse o¤ with the NSR, and therefore the NSR is socially undesirable. The positive role of the NSR in terms of improvement of retail price efficiency for cardholders is also highlighted.

Competition in two-sided markets with common network externalities

We study competition in two sided markets with common network externality rather than with the standard inter-group e¤ects. This type of externality occurs when both groups bene t, possibly with di¤erent intensities, from an increase in the size of one group and from a decrease in the size of the other. We explain why common externality is relevant for the health and education sectors. We focus on the symmetric equilibrium and show that when the externality itself satis es an homogeneity condition then platforms pro ts and price structure have some speci c properties. Our results reveal how the rents coming from network externalities are shifted by platforms from one side to other, according to the homogeneity degree. In the speci c but realistic case where the common network externality is homogeneous of degree zero, platform s pro t do not depend on the intensity of the (common) network externality. This is in sharp contrast to conventional results stating that the presence of network externalities in a two-sided market structure increases the intensity of competition when the externality is positive (and decreases it when the externality is negative). Prices are a¤ected but in such a way that platforms only transfer rents from consumers to providers.

Doctors´ remuneration schemes and hospital competition in two-sided markets with common network externalities

This paper uses a two-sided market model of hospital competition to study the implications of di§erent remunerations schemes on the physiciansí side. The two-sided market approach is characterized by the concept of common network externality (CNE) introduced by Bardey et al. (2010). This type of externality occurs when occurs when both sides value, possibly with di§erent intensities, the same network externality. We explicitly introduce e§ort exerted by doctors. By increasing the number of medical acts (which involves a costly e§ort) the doctor can increase the quality of service o§ered to patients (over and above the level implied by the CNE). We Örst consider pure salary, capitation or fee-for-service schemes. Then, we study schemes that mix fee-for-service with either salary or capitation payments. We show that salary schemes (either pure or in combination with fee-for-service) are more patient friendly than (pure or mixed) capitations schemes. This comparison is exactly reversed on the providersíside. Quite surprisingly, patients always loose when a fee-for-service scheme is introduced (pure of mixed). This is true even though the fee-for-service is the only way to induce the providers to exert e§ort and it holds whatever the patientsívaluation of this e§ort. In other words, the increase in quality brought about by the fee-for-service is more than compensated by the increase in fees faced by patients.

Operator, organizational, direct support, and general support maintenance for shelter, tactical, expandable, two-sided (NSN 5411-01-136-9838).

"1 April 1986."

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.