Profitability of price and quantity strategies in an oligopoly

A review of multi-product pricing models

“…Note that p i is the only decision variable for seller i and there may be restrictions on it, like upper and lower bound constraints, as mentioned in Milgrom and Roberts [62], and Topkis [87]. In Garcia-Gallego and Georgantzis [41], Mizuno [63], Oxenstierna [64] and Tanaka [85], a Bertrand game is also discussed, but with variations of the above model. The sellers offer multiple products each, and a multiple-period pricing scheme is considered in [41].…”

“…The focus in their paper is on experimental results, e.g., corresponding to different demand parameters or number of products offered per seller. Mizuno [63], Oxenstierna [64] and Tanaka [85] allowed the cost c i to be a function dependent on demand D i ðpÞ ð¼ D i ðp i ; p Ài ÞÞ, thus the total cost for seller i was c i ðD i ðpÞÞ instead. Four different types of equilibrium configurations were discussed in [85] and the corresponding optimal strategies were compared.…”

“…A list of common assumptions made about demand functions in Bertrand-Nash games was discussed in Tanaka [85]. Given that there are n firms (n products), the demand for product i; d i ðpÞ is assumed to be (i) continuous on R n þ and symmetric for all firms; (ii) positive in X i , a non-empty bounded region of R n þ (let X ¼ \ n i¼1 X i ); and (iii) continuously twice differentiable in intðXÞ (the interior of X), with ð@d i =@p i Þ < 0 and ð@d i =@p j Þ > 0.…”

Coordination of Pricing and Inventory Decisions: A Survey and Classification

“…To study the impacts of choosing pricing strategy or quantity strategy in different business competition environment, Tanaka [146] considers a two stage game of an oligopoly in which n(n ≥ 2) firms produce substitutable goods. The two sequential stages of the game are as follows:…”

Price vs. quantity in oligopoly games

“…Since these two types of models lead to extremely different outcomes in the market, one would like to consider an intermediate model in which some firms quote prices while others 'dump' quantities. Such kinds of models have been formulated in the homogeneous good framework by Allen (1992) and by Qin and Stuart (1997), and in the heterogeneous good framework by Singh and Vives (1984), Klemperer and Meyer (1986), Szidarovszky and Molnár (1992) and Tanaka (2001aTanaka ( , 2001b. For economically relevant examples in which the firms are able to choose their decision variables (price or quantity) we refer to Klemperer and Meyer (1986, Section 2).…”