The paper provides a survey of the literature which utilizes dynamic state-space games to formulate and analyze intertemporal, many decision-maker problems in the economics and management of pollution.

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Most of the cooperative advertising literature has focused on studying the e¤ects of such programs considering marketing variables. This paper integrates production and inventory management with pricing and advertising considerations to assess the e¤ects of cooperative advertising programs in bilateral monopolies. We consider a supply chain where a Vendor Managed Inventory (VMI) along with a consignment contract is implemented to coordinate the chain. We develop and solve a di¤erential model for two games. The …rst one is a benchmark scenario where no cooperative advertising is o¤ered, while the manufacturer o¤ers the cooperative program in the second game. The main results show that cooperative advertising programs, usually considered as successful marketing initiatives, can be very di¢ cult to implement in a supply chain undertaking a VMI policy with a consignment contract, in which operations and marketing interface is taken into account. A cooperative program mainly hurts the manufacturer's pro…ts, and can be pro…t-Pareto-improving only in a few cases. Although the retailer is generally willing to receive a support from the manufacturer, she can opt for a non-cooperative program when the largest part of the supply chain pro…ts goes to the manufacturer. We developed several special cases to strengthen our …ndings.

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This paper investigates whether manufacturers can use the timing (sequence) of their pricing and advertising 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 impacts 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. 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 1 The authors are grateful to three anonymous reviewers for valuable comments and suggestions on an earlier draft of this paper. 2 Corresponding author. The author is grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC) for their financial supports (RGPIN-2015-03880). 3 The author gratefully acknowledges financial support from the Spanish Ministry of Economics and Competitiveness under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and from Junta de Castilla y León under projects VA024P17 and VA105G18 co-financed by FEDER funds (EU).

We analyze a transboundary pollution differential game where pollution control is spatially distributed among a number of agents with predetermined spatial relationships. The analysis emphasizes, first, the effects of the different geographical relationships among decision makers; and second, the strategic behaviour of the agents. The dynamic game considers a pollution stock (the state variable) distributed among one large region divided in subregions which control their own emissions of pollutants. The emissions are also represented as distributed variables. The dynamics of the pollution stock is defined by a parabolic partial differential equation. We numerically characterize the feedback Nash equilibrium of a discrete-space model that still captures the spatial interactions among agents. We evaluate the impact of the strategic and spatially dynamic behaviour of the agents on the design of equilibrium environmental policies.

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