Geodesic
Search for a~fixed point discrete operator
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 21-32.

Voir la notice de l'article provenant de la source Math-Net.Ru

The computational complexity of the finding a fixed point of a decreasing monotone operator is analyzed. An power algorithm for determining a fixed point is presented. A constructive prove of the presence of discrete fixed point operator is given for a particular case of the operator of bounded variation. Appendices are the following: voluntary financing of general welfare, Cournot oligopoly and others.
Keywords: monotone operator, fixed points
Mots-clés : a polynomial algorithm. 
@article{MGTA_2012_4_3_a1,
     author = {Irina A. Bashlaeva and Vasiliy N. Lebedev},
     title = {Search for a~fixed point discrete operator},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a1/}
}
TY  - JOUR
AU  - Irina A. Bashlaeva
AU  - Vasiliy N. Lebedev
TI  - Search for a~fixed point discrete operator
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2012
SP  - 21
EP  - 32
VL  - 4
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a1/
LA  - ru
ID  - MGTA_2012_4_3_a1
ER  - 
%0 Journal Article
%A Irina A. Bashlaeva
%A Vasiliy N. Lebedev
%T Search for a~fixed point discrete operator
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2012
%P 21-32
%V 4
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a1/
%G ru
%F MGTA_2012_4_3_a1
Irina A. Bashlaeva; Vasiliy N. Lebedev. Search for a~fixed point discrete operator. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 21-32. http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a1/

[1] Vorobev N. N., “Sovremennoe sostoyanie teorii igr”, UMN, 25:2 (1970), 81–140 | MR | Zbl

[2] Geri M., Dzhonson D., Vychislitelnye mashiny i trudnoreshaemye zadachi, Mir, M., 1984 | MR

[3] Lebedev V. N., Chernichkin M. S., “Igrovoi aspekt verifikatsii programm”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2005, no. 5, 40–45 | MR | Zbl

[4] Ouen G., Teoriya igr, Mir, M., 1971 | MR | Zbl

[5] Emerson E. A., Jutla C. S., Sistla A. P., “On model-checking for fragments of $\mu$-calculus”, Fifth International Conference on Computer Aided Verification (Elounda, Greece, June, July, 1993), Springer, Berlin, 1993, 385–396 | MR

[6] Kukushkin N. S., “A fixed-point theorem for decreasing mappings”, Economics Letters, 46 (1994), 23–26 | DOI | MR | Zbl

[7] Kukushkin N. S., “Best Response Dynamics in Finite Games with Additive Aggregation”, Games and Economic Behavior, 48:1 (2004), 94–110 | DOI | MR | Zbl

[8] Kukushkin N. S., A fixed-point theorem for decreasing mappings, Manuscript, Computer Center RAN, M., 2012

[9] Novshek W., “On the existence of Cournot equilibrium”, Review of Economic Studies, 52 (1985), 85–98 | DOI | MR | Zbl

[10] Tarski A., “A lattice-theoretical fixpoint theorem and its applications”, Pacific Journal of Mathematics, 5 (1955), 285–309 | DOI | MR | Zbl