On the Modelling of Price Effects in the Diffusion of Optional Contingent Products

In this chapter, we study the pricing strategies of firms in a multi-product diffusion model where we use a new formalization of the price effects. More particularly, we introduce the impact of prices on one of the factors that affect the diffusion of new products: the innovation coefficient. By doing so, we relax one of the hypotheses in the existing literature stating that this rate is constant. In order to assess the impact of this functional form on the pricing policies of firms selling optional contingent products, we use our model to study two scenarios already investigated in the multiplicative form model suggested by Mahajan and Muller (1991) (M&M). We follow a ‘logical experimentation’ perspective by computing and com- paring the results of three models: (i) The M&M model, (ii) a modified version of M&M where the planning horizon is infinite, and (iii) our model, where the new formalization of the innovation effect is introduced. This perspective allows us to attribute the differences in results to either the length of the planning horizon, or to our model’s formalization. Besides its contribution to the literature on pricing and diffusion, this paper highlights the sensitiv- ity of results to the hypothesis used in product diffusion modelling and could explain the mixed results obtained in the empirical validations of diffusion models (Mesak, 1996).MINECO under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU)

Offensive and Defensive Marketing in Spatial Competition

While it is well-established that travel costs impact on customer preference toward local service providers, research about how this situation affects competitive marketing strategies remains sparse. This paper investigates, in a local market with two competing service providers, whether service providers should undertake defensive marketing, targeted at the nearest customers who typically prefer their offering for convenience and/or offensive marketing, directed to relatively remote customers who favor the rival as the closest alternative. We find that the service providers can exclusively undertake either defensive marketing or offensive marketing or combine the two in a full differentiated strategy at the equilibrium. We compare the outcomes of these three strategic options to identify the conditions under which they are worth implementing. Main findings suggest that service providers are better off undertaking offensive marketing alone when their rival’s retaliatory offensive capacity is weak and customers incur small travel costs. Otherwise, service providers may exclusively undertake defensive marketing or combine it with offensive marketing when travel costs become significant. Also, service providers should not invest in any marketing activity when they have no market power, like in the case of two adjacent outlets in a mall. Finally, the implications of these findings are discussed.MEC under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León under projects VA024P17 and VA105G18, co-financed by FEDER fund

Non-linear incentive equilibrium strategies for a transboundary pollution differential game

Producción CientíficaIn this paper we apply non-linear incentive strategies to sustain over time an agreement. We illustrate the use of these strategies in a linear-quadratic transboundary pollution differential game. The incentive strategies are constructed in such a way that in the long run the pollution stock (the state variable) is close to the steady state of the pollution stock under the cooperative mode of play. The non-linear incentive functions depend on the emission rates (control variables) of both players and on the current value of the pollution stock. The credibility of the incentive equilibrium strategies is analyzed and the performance of open-loop and feedback incentive strategies is compared in their role of helping to sustain an agreement over time. We present numerical experiments to illustrate the results.This research is partially supported by MINECO under projects MTM2016-78995-P (AEI) and ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU

Price Coordination in Distribution Channels: A Dynamic Perspective

Producción CientíficaIn this study, we investigate two important questions related to dynamic pricing in distribution channels: (i) Are coordinated pricing decisions efficient in a context where prices have carry-over effects on demand? (ii) Should fi rms practice a skimming or a penetration strategy if they choose to coordinate or to decentralize their activities? To answer these questions, we consider a differential game that takes place in a bilateral monopoly where the past retail prices paid by consumers contribute to the building of a reference price. The latter is used by consumers as a benchmark to evaluate the value of the product, and by fi rms to decide whether to adopt a skimming or a penetration strategy. We then compute and compare strategies, total channel profi ts and individual profits under vertical integration and decentralization at steady state and along the optimal time-paths. One of our main fi ndings states that, for some values of the initial reference price, there is a time interval where channel decentralization performs better than coordination. During this transition period, at least one of the channel members could be tempted to end his cooperation, especially if he is not farsighted and if there are no binding agreements with the other channel partners.The rst author's research is partially supported by MICINN under projects ECO2008-01551/ECON, ECO2011-24352, co- nanced by FEDER funds and the COST Action IS1104 \The EU in the new economic complex geography: models, tools and policy evaluation". The second author's research is supported by NSERC, Canada

Second-best taxation for a polluting monopoly with abatement investment

This paper characterizes the optimal tax rule to regulate a polluting monopoly when the firm has the possibility of investing in an abatement technology and the environmental damages are caused by a stock pollutant. The optimal policy is given by the stagewise feedback Stackelberg equilibrium of a dynamic policy game between a regulator and a monopolist. The regulator playing as the leader chooses an emission tax to maximize net social welfare, and the monopolist acting as the follower selects the output and the investment in abatement technology to maximize profits. We find that the optimal tax has two components. The first component is negative and equal to the gap between the marginal revenue and the price caused by the firm market power; the second component is given by the difference between the social and private shadow prices of the pollution stock. Considering a linear-quadratic model we show that if marginal environmental damages are constant, the difference between social and private shadow prices is positive and the optimal policy consists of taxing emissions at a constant rate if the marginal damages are large enough. However, if the marginal environmental damages are increasing the numerical exercises carried out show that this difference is negative at the steady state and the optimal policy gives the firm a subsidy when approaching the steady state regardless of the importance of the environmental damages. This result is explained by the negative effect that abatement technology accumulation has on the tax. Finally, it can be pointed out that although both models yield different predictions about the sign of the optimal policy the dynamics is globally stable for both cases.Guiomar Martín-Herrán and Santiago J. Rubio gratefully acknowledge financial support from the Spanish Ministry of Economics and Competitiveness under projects ECO2014-52343-P, ECO2017-82227-P and ECO2016-77589-R. Guiomar Martín-Herrán and Santiago J. Rubio also gratefully acknowledge financial support from Junta de Castilla y León and Valencian Generality under projects VA024P17 and PROMETEO II/2014/054, respectivel

Optimal environmental policy for a polluting monopoly with abatement costs: Taxes versus standards

Producción CientíficaIn this paper, we characterize the optimal environmental policy for a polluting monopoly that devotes resources to abatement activities when damages are caused by a stock pollutant. With this aim, we calculate the stagewise feedback Stackelberg equilibrium of a (differential) policy game where the regulator is the leader and the monopolist is the follower. Our analysis shows that the first-best policy consists of applying a Pigouvian tax and a subsidy on production equal to the difference between the price and the marginal revenue. However, for a stock pollutant, the Pigouvian tax is not equal to the marginal damages but is given by the difference between the social and private valuation of the pollution stock. On the other hand, if a second-best emission tax is used, the tax is lower than the Pigouvian tax and the difference decreases with the price elasticity of the demand. Finally, we find that taxes and standards are equivalent in a second-best setting. In the second part of the paper, we solve a linear-quadratic differential game and we obtain that the first-best tax increases with the pollution stock whereas the subsidy decreases. Moreover, the tax is negative for low values of the pollution stock, i.e., for low values of the pollution stock, we obtain that the social valuation of the stock is lower than the private valuation. Furthermore, when a second-best policy is applied, the steady-state pollution stock is lower than the steady-state pollution stock associated with the efficient outcome

Fighting store brands through the strategic timing of pricing and advertising decisions

Producción CientíficaThis paper investigates whether manufacturers can use the timing (sequence) of their pricing and ad- vertising decisions to benefit from or to deter store brand (SB) introductions. We develop and solve six sequential game-theoretic models for a bilateral channel where different timing of these decisions are considered before and after the retailer introduces a store brand. Comparisons of equilibrium solutions across games show that the sequence of pricing and advertising decisions in the channel significantly im- pacts the profitability of a store brand entry by the retailer. Such impact depends on: (1) whether each channel member decides on pricing and advertising simultaneously or sequentially prior to the SB entry, (2) whether the timing chosen for these decisions changes following the SB introduction , and (3) the intensity of competition between the store and national brands (NB). In particular, the SB entry leads to losses for the manufacturer when the sequence of advertising and pricing decisions is kept unchanged after the SB entry even when it is much differentiated from the NB. These results offer new perspectives on the effects of store brand entry in distribution channels, and suggest that for low levels of competition intensity between the NB and the SB, the manufacturer can either prevent or benefit from the retailer’s brand given an adjustment in the sequence of the manufacturer’s decisions.MEC under projects ECO2014-52343-P and ECO2017-82227-P, co- financed by FEDER fundsJunta de Castilla y León under projects VA024P17 and VA105G18 co-financed by FEDER fund

The effects of decision timing for pricing and marketing efforts in a supply chain with competing manufacturers

Producción CientíficaThis paper investigates the impact of decision timing for pricing and marketing efforts in a supply chain led by competing manufacturers. We develop and solve six games to consider the scenarios (games) where prices and marketing efforts (ME) are decided simultaneously, and when they are not (i.e., ME is set either before or after prices). We examine these three scenarios for the benchmark case of a bilateral monopolistic channel, then extend the analysis to a supply chain with competing manufacturers. We identify the optimal decision timing by comparing equilibrium profits and strategies across games in each supply chain setup. We find that a monopolistic manufacturer always prefers that prices and ME be decided simultaneously. However, this result does not hold when product competition is taken into account. The optimal decision timing for competing manufacturers depends on the retailer's and manufacturers' ME effectiveness levels as well as on competition intensity. Specifically, when ME are not very effective, a simultaneous decision scenario is preferred because it provides the advantage of higher profit margins or sales. However, for highly effective ME, manufacturers prefer to decouple ME and pricing decisions. The retailer's optimal scenario is either to make all decisions simultaneously or to choose prices prior to ME. This means that supply chain firms can face conflict due to the decision timing for prices and ME

The Impact of Foresight in a Transboundary Pollution Game

Producción CientíficaWe study the impact of foresight in a transboundary pollution game; i.e. the ability of a country to control its emissions taking into account the relationship between current emissions and future levels of pollution and thus on future damages. We show that when all countries are myopic, i.e., choose the 'laisser-faire' policy, their payo s are smaller than when all countries are farsighted, i.e., non-myopic. However, in the case where one myopic country becomes farsighted we show that the welfare impact of foresight on that country is ambiguous. Foresight may be welfare reducing for the country that acquires it. This is due to the reaction of the other farsighted countries to that country's acquisition of foresight. The country that acquires foresight reduces its emissions while the other farsighted countries extend their emissions. The overall impact on total emissions is ambiguous. Moreover, our results suggest that incentive mechanisms, that involve a very small (possibly zero) present value of transfers, can play an important role in inducing a country to adopt a farsighted behavior and diminishing the number of myopic countries. These incentives would compensate the myopic country for the short-run losses incurred from the acquisition of foresight and can be reimbursed by that country from the gains from foresight that it enjoys in the long run.The rst author research is supported by SSHRC, Canada. The second author research is partially supported by MEC under projects ECO2011-24352 and ECO2014-52343-P, co- nanced by FEDER funds, and by COST Action IS1104. One working paper version has circulated under a di erent title: \Myopia in a Transboundary Pollution Game"

Manufacturer defensive and offensive advertising in competing distribution channels

Producción CientíficaThis paper investigates how two competing manufacturers should invest in defensive and offensive advertising in a two-segment market and whether they should each adopt a decentralized or an integrated channel if \ their goal is to maximize total channel profits. We find \ that, manufacturers in decentralized channels can exclusively undertake either of the two types of advertising or combine the two at the equilibrium. In integrated channels, they can either combine the two or exclusively undertake defensive advertising. When multiple equilibria exist, strategies that combine both types of advertising should be preferred to exclusive defensive advertising strategies, which are better than exclusive offensive advertising strategies. Also, total channel profits are higher in decentralized channels than in integrated channels when the brands are moderately or highly substitutable. Conversely, total channel profits of integrated channels are higher than those of decentralized channels in areas where the brands are relatively differentiated and the offensive advertising retaliatory capacity of the rival is stronger. Theoretical and managerial implications of these findings are discussed