Optimal pricing based on customers perceived values of products

Different customers attach different perceived values to the same products. And a customer chooses a firm based on such a difference in perceived values and his rational expectation of the firms product availability. In a monopoly market, a firms optimal quantity and product availability increase with its optimal price. Due to the non-monotonicity of distribution density from customers perceived values, a firms local optimal price is not necessarily equal to its global optimal price. In a competitive market with n firms, the pure Nash equilibrium result was solved and its uniqueness proved. When n is finite, firms may adopt different optimal prices, and all firms achieve the same optimal profit expect in two special conditions. However, when n is infinite, all firms share a same optimal profit in equilibrium.