Date
2010
Dewey
Probabilités et mathématiques appliquées
Sujet
Optimization; Pricing; Transportation costs
JEL code
C61
Conference name
International Conference on Nonlinear Analysis and Optimization in celebration of Alex Ioffe's 70th and Simeon Reich's 60th birthdays
Conference date
06-2008
Conference city
Haifa
Conference country
Israël
Book title
Nonlinear Analysis and Optimization II: Optimization
Author
Leizarowitz, Arie; Mordukhovich, Boris; Shafrir, Itai; Zalavski, Alexander
Publisher
American Mathematical Society
Publisher city
Providence (R.I.)
Year
2010
Pages number
290
ISBN
0-8218-4835-6
Author
Carlier, Guillaume
Buttazzo, Giuseppe
Type
Communication / Conférence
Item number of pages
105-122
Abstract (EN)
We consider an optimization problem in a given region Q where
an agent has to decide the price p(x) of a product for every x ∈ Q. The
customers know the pricing pattern p and may shop at any place y, paying
the cost p(y) and additionally a transportation cost c(x, y) for a given trans-
portation cost function c. We will study two models: the first one where
the agent operates everywhere on Q and a second one where the agent op-
erates only in a subregion. For both models we discuss the mathematical
framework and we obtain an existence result for a pricing strategy which
maximizes the total profit of the agent. We also present some particular
cases where more detailed computations can be made, as the case of con-
cave costs, the case of quadratic cost, and the onedimensional case. Finally
we discuss possible extensions and developments, as for instance the case of
Nash equilibria when more agents operate on the same market.