TY  - JOUR
A1  - Schlosser, Rainer
T1  - Stochastic dynamic pricing and advertising in isoelastic oligopoly models
JF  - European Journal of Operational Research
N2  - In this paper, we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticity. We consider the sale of perishable as well as durable goods and include adoption effects in the demand. Based on a unique stochastic feedback Nash equilibrium, we derive closed-form solution formulas of the value functions and the optimal feedback policies of all competing firms. Efficient simulation techniques are used to evaluate optimally controlled sales processes over time. This way, the evolution of optimal controls as well as the firms’ profit distributions are analyzed. Moreover, we are able to compare feedback solutions of the stochastic model with its deterministic counterpart. We show that the market power of the competing firms is exactly the same as in the deterministic version of the model. Further, we discover two fundamental effects that determine the relation between both models. First, the volatility in demand results in a decline of expected profits compared to the deterministic model. Second, we find that saturation effects in demand have an opposite character. We show that the second effect can be strong enough to either exactly balance or even overcompensate the first one. As a result we are able to identify cases in which feedback solutions of the deterministic model provide useful approximations of solutions of the stochastic model.
KW  - Pricing
KW  - Advertising
KW  - Stochastic differential games
KW  - Oligopoly competition
KW  - Adoption effects
Y1  - 2017
U6  - https://doi.org/10.1016/j.ejor.2016.11.021
SN  - 0377-2217
SN  - 1872-6860
VL  - 259
SP  - 1144
EP  - 1155
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Schlosser, Rainer
T1  - Joint stochastic dynamic pricing and advertising with time-dependent demand
JF  - Geophysical journal international
N2  - This paper examines the sale of a finite number of items in a class of stochastic dynamic pricing and advertising models with time-dependent demand elasticities. We prove structural properties of the optimal expected profits with respect to time, inventory level, price impact, advertising impact and different model parameters, such as discount rate, marginal unit costs, and holding costs. We find that the value of an additional item (opportunity costs) is decreasing in the unit costs, the discount rate, the holding cost rate and the number of items left to sell. We also derive structural properties of optimal joint pricing and advertising strategies. This way, we obtain general qualitative insights in the complex interplay and the mutual dependence of optimal pricing and advertising decisions. Among other properties, we show that a higher advertising impact leads to higher optimal prices and lower advertising rates, which in turn implies a lower speed of sale. The results obtained help practitioners to respond to changes in market conditions by adjusting price and advertising accordingly. Our results allow speeding up numerical computations of decisions as the set of possible actions can be reduced significantly. Our analysis implies general results for pure pricing as well as pure advertising models with time-dependent demand elasticities. (C) 2016 Elsevier B.V. All rights reserved.
KW  - Dynamic pricing and advertising
KW  - Optimal stochastic control
KW  - Time-dependent demand elasticities
KW  - Structural properties
Y1  - 2016
U6  - https://doi.org/10.1016/j.jedc.2016.10.006
SN  - 0165-1889
SN  - 1879-1743
VL  - 73
SP  - 439
EP  - 452
PB  - Elsevier
CY  - Amsterdam
ER  -