# Journal of Advances in Economics and Finance

### Fixed Points in Grassmannians with Applications to Economic Equilibrium

Download PDF (517.9 KB) PP. 29 - 39 Pub. Date: February 23, 2017

### Author(s)

**Hans Keiding**^{*}

Department of Economics, University of Copenhagen, Denmark

### Abstract

### Keywords

### References

[1] E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” Mathematical Student, vol. 63, pp. 123-145, 1994.

[2] M. Bianchi and S. Schaible, “Generalized monotone bifunctions and equilibrium problems,” Journal of Optimization Theory and Applications, vol. 90, pp. 31-43. 1996.

[3] A. N. Iusem and W. Sosa, “New existence results for equilibrium problems,” Nonlinear Analysis, vol. 52, pp.621-635, 2003.

[4] Q. H. Ansari and F. Flores-Bazán, “Generalized vector quasi-equilibrium problems with applications,” J. Math. Anal. Appl., vol. 277, pp. 246-256, 2003.

[5] Z. Lin and J. Yu, “The existence of solutions for the system of generalized vector quasi-equilibrium problems,”Applied Mathematics Letters, vol. 18, pp. 415-422, 2005.

[6] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, 1978.

[7] E. Michael, “Continuous selections I,” Annals of Mathematics, vol. 63, pp. 361-381, 1956.

[8] D. Gale and A. Mas-Colell, “An equilibrium existence theorem for a general model without ordered preferences,”Journal of Mathematical Economics, vol. 2, pp. 9-17, 1975.

[9] S. Kakutani, “A generalization of Brouwer’s fixed point theorem,” Duke Mathematical Journal, vol. 8, pp.457-459, 1941.

[10] G. Debreu, Theory of value, Wiley, 1959.

[11] V. I. Danilov and A. I. Sotskov, “A generalized economic equilibrium,” Journal of Mathematical Economics,vol. 19, pp. 341-356, 1990.

[12] M. Florig, “Arbitrary small indivisibilities,” Economic Theory, vol. 22, pp. 831-843, 2002.

[13] A. Konovalov and V. Marakulin, “Generalized equilibria in an economy without the survival assumption,” EI Report 2002D49, Erasmus University Rotterdam, 2002.

[14] D. Duffie and W. Shafer, “Equilibrium in incomplete markets: I. A basic model of generic existence,” Journal of Mathematical Economics, vol. 14, pp. 285-300, 1985.

[15] J. Geanakoplos, “An introduction to general equilibrium with incomplete asset markets,” Journal of Mathematical Economics, vol. 19, pp. 1-38, 1990.

[16] M. Magill and W. Shafer, “Incomplete markets,” in: W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, North Holland, 1991.

[17] Y. Zhou, “Genericity Analysis on the Pseudo-Equilibrium Manifold,” Journal of Economic Theory, vol. 73,pp. 79-92, 1997.

[18] T. Momi, “Failure of the index theorem in an incomplete market economy,” Journal of Mathematical Economics,vol. 48, pp. 437-444, 2012.

[19] M. Hoelle, M. Pireddu and A. Villanacci, “Incomplete financial markets with real assets and wealth-dependent credit limits,” Journal of Economics, vol. 117, pp. 1-36, 2016.

[20] O. Hart, “On the optimality of equilibrium when the market structure is incomplete,” Journal of Economic Theory, vol. 11, pp. 418-443, 1975.

[21] Yu. I. Merslyakov, Rational Groups (in Russian), Nauka, 1987.