Cooperative (co‐op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co‐op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi's stochastic sales‐advertising model. We obtain the condition when offering co‐op advertising is optimal for the manufacturer. We provide in feedback form the optimal advertising and pricing policies for the manufacturer and the retailer. We contrast the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.

R etailers often face a newsvendor problem. Advance selling helps retailers to reduce demand uncertainty. Consumers, however, may prefer not to purchase in advance unless given a discount because they are uncertain about their valuation for the product in advance. It is then unclear whether or when advance selling to pass some uncertainty risk to consumers is optimal for the retailer. This paper examines the advance selling price and inventory decisions in a two-period setting, where the first period is the advance selling period and the second is the selling (and consumption) period. We find that an advance selling strategy is not always optimal, but is contingent on parameters of the market (e.g., market potential and uncertainty) and the consumers (e.g., valuation, risk aversion, and heterogeneity). For example, we find that retailers should sell in advance if the consumers' expected valuation exceeds consumers' expected surplus when not buying early by a certain threshold. This threshold increases with the degree of risk aversion but decreases with stock out risk. If the degree of risk aversion varies across consumers, then a retailer should sell in advance if the probability for a consumer to spot buy is less than a critical fractile.

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To increase the sales of their products through advertising, firms must integrate their brand-advertising strategy for capturing market share from competitors and their generic-advertising strategy for increasing primary demand for the category. This paper examines whether, when, and how much brand advertising versus generic advertising should be done. Using differential game theory, optimal advertising decisions are obtained for a dynamic duopoly with symmetric or asymmetric competitors. We show how advertising depends on the cost and effectiveness of each type of advertising for each firm, the allocation of market expansion benefits, and the profit margins determined endogenously from price competition. We find that generic advertising is proportionally more important in the short term and that there are free-riding effects leading to suboptimal industry expenditure on generic advertising that worsen as firms become more symmetric. Due to free-riding by the weaker firm, its instantaneous profit and market share can actually be higher. The effectiveness of generic advertising and the allocation of its benefits, however, have little effect on the long-run market shares, which are determined by brand-advertising effectiveness. Extensions of the model show that market potential saturation leads to a decline in generic advertising over time.advertising, generic advertising, differential games, dynamic duopoly, optimal control

Companies spend hundreds of millions of dollars annually on advertising to build and maintain awareness for their brands in competitive markets. However, awareness formation models in the marketing literature ignore the role of competition. Consequently, we lack both the empirical knowledge and normative understanding of building brand awareness in dynamic oligopoly markets. To address this gap, we propose an N-brand awareness formation model, design an extended Kalman filter to estimate the proposed model using market data for five car brands over time, and derive the optimal closed-loop Nash equilibrium strategies for every brand. The empirical results furnish strong support for the proposed model in terms of both goodness-of-fit in the estimation sample and cross-validation in the out-of-sample data. In addition, the estimation method offers managers a systematic way to estimate ad effectiveness and forecast awareness levels for their particular brands as well as competitors' brands. Finally, the normative analysis reveals an inverse allocation principle that suggests--contrary to the proportional-to-sales or competitive parity heuristics--that large (small) brands should invest in advertising proportionally less (more) than small (large) brands.marketing, competitive strategy, advertising and media, nonlinear Kalman filter, dynamic games