Unique Stackelberg equilibrium

For having an Increasing Failure Rate (IFR) distribution, there exists a unique Stackelberg equilibrium solution pair A ) in the single-period... 

Proposition 5. There is a unique Stackelberg equilibrium solution pair in the single-period game with a powerful retailer and without starting inventory that is characterized by the following system of equations ... 

Since the retailer s best response function is single-valued, the Stackelberg equilibrium exists. Further, we will show that the second derivative of the wholesaler s objective function is negative (i.e., the objective function is concave), and so the Stackelberg equilibrium is unique. The first derivative of the wholesaler s objective function is... 

The retailer s objective function is clearly concave, and the uniqueness of the Stackelberg equilibrium follows. Finally, the optimality conditions are found by equating the first derivatives to zero. 

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