Non-separable, Quasiconcave Utilities are Easy – in a Perfect Price Discrimination Market Model (Extended Abstract)
Recent results, establishing evidence of intractability for such restrictive utility functions as additively separable, piecewise-linear and concave, under both Fisher and Arrow-Debreu market models, have prompted the question of whether we have failed to capture some essential elements of real markets, which seem to do a good job of finding prices that maintain parity between supply and demand.
The main point of this paper is to show that even non-separable, quasiconcave utility functions can be handled efficiently in a suitably chosen, though natural, realistic and useful, market model; our model allows for perfect price discrimination. Our model supports unique equilibrium prices and, for the restriction to concave utilities, satisfies both welfare theorems.
Unable to display preview. Download preview PDF.
- [BT04]Bhaskar, V., To, T.: Is perfect price discrimination really efficient? An analysis of free entry. The RAND journal of economics 35(4), 762–776 (2004)Google Scholar
- [CDDT09]Chen, X., Dai, D., Du, Y., Teng, S.-H.: Settling the complexity of Arrow-Debreu equilibria in markets with additively separable utilities. In: FOCS (2009)Google Scholar
- [CT09]Chen, X., Teng, S.-H.: Spending is not easier than trading: on the computational equivalence of Fisher and Arrow-Debreu equilibria. Journal of the ACM 56(3) (2009)Google Scholar
- [DPSV08]Devanur, N., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibrium via a primal-dual-type algorithm. JACM 55(5) (2008)Google Scholar
- [EEH94]Edlin, A., Epelbaum, M., Heller, W.: Surplus maximization and price discrimination in general equilibrium: Part I. Technical Report 9405, Centro de Investigacion Economica, ITAM (1994)Google Scholar
- [GV10]Goel, G., Vazirani, V.V.: A perfect price discrimination market model with production, and a (rational) convex program for it. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, Springer, Heidelberg (2010)Google Scholar
- [Jai04]Jain, K.: A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. In: FOCS (2004)Google Scholar
- [Uza62]Uzawa, H.: Walras’ existence theorem and brower’s fixpoint theorem. In: Econ. Stud. Quart., pp. 59–62 (1962)Google Scholar
- [Var96]Varian, H.: Differential pricing and efficiency. First Monday 1(2) (1996)Google Scholar
- [Vaz10]Vazirani, V.V.: Spending constraint utilities, with applications to the Adwords market. Mathematics of Operations Research 35(2) (2010)Google Scholar
- [VY10]Vazirani, V.V., Yannakakis, M.: Market equilibria under separable, piecewise-linear, concave utilities. In: Proceedings of The First Symposium on Innovations in Computer Science (2010)Google Scholar