عنوان مقاله [English]
This paper considers the problem of optimal advertising and pricing paths of a dual- channel supply chain members through differential games approach. Considered Supply Chain consists of a manufacturer and a retailer. The manufacturer indirectly trades with the final consumer in retail or traditional channel and directly trades with the final consumer in online channel. Retailer trades with the final consumer just in traditional channel. Manufacturer aeffects on chain membersmember's profits with identifying control variables as online price, global advertising effort, and online advertising effort. The global advertising effort of the manufacturer has indirect and long-term effects on sale functions of both members. On the other hand, local advertising efforts of both firms in retail and online channel have direct and short-time effects on sales functions. Retailer's control variables are retail price and
local advertising effort. The state variable of the dynamic system is the goodwill of the manufacturer which means that the accumulated reputation of the manufacturer is increased by the national advertising effort of manufacturer. In this article, competition between chain members are is modeled by evaluating Feedback Nash equilibrium. Also, the model is validated by results of the Stackelberg game model with manufacturer leadership consideration. The comparison between the two models showed that, chain profit in Stackelberg model is higher than chain profit in Nash model. At last, with a numerical example, impact of parameters named as advertising effectiveness of each member on rival member's sale response functions, on optimal decision variable paths of each chain member, is examined in three scenarios. In the first scenario, the effect of Manufacturer's advertising on retailer's strategies was performed. In the second scenario, the effect of retailer's advertising on the manufacturer's strategies was evaluated. Finally, in the third scenario, simultaneous change in Manufacturer and retailer's effect on competitor's profit functions was investigated. In all scenarios, it is observed that theses parameters have a decreasing effect on all channel member's optimal decision variable paths.