Geodesic
Bidding models and repeated games with incomplete information: a survey
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 3, pp. 3-35.

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

With the help of a simplified model of multistage bidding with asymmetrically informed agents De Meyer and Saley [17] demonstrate an idea of endogenous origin of Brownian component in the evolution of prices on stock markets: random price fluctuations may originate from strategic randomization of “insiders”. The model is reduced to a repeated game with incomplete information. The present paper contains a survey of multiple researches inspired by this pioneering paper.
Keywords: bidding, repeated games, asymmetric information, optimal strategies, random walk, asymptotic behavior. 
@article{MGTA_2017_9_3_a0,
     author = {Victoria L. Kreps},
     title = {Bidding models and repeated games with incomplete information: a survey},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {3--35},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2017_9_3_a0/}
}
TY  - JOUR
AU  - Victoria L. Kreps
TI  - Bidding models and repeated games with incomplete information: a survey
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2017
SP  - 3
EP  - 35
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2017_9_3_a0/
LA  - ru
ID  - MGTA_2017_9_3_a0
ER  - 
%0 Journal Article
%A Victoria L. Kreps
%T Bidding models and repeated games with incomplete information: a survey
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2017
%P 3-35
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2017_9_3_a0/
%G ru
%F MGTA_2017_9_3_a0
Victoria L. Kreps. Bidding models and repeated games with incomplete information: a survey. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 3, pp. 3-35. http://geodesic.mathdoc.fr/item/MGTA_2017_9_3_a0/

[1] Vershik A. M. , “Metrika Kantorovicha: nachalnaya istoriya i maloizvestnye primeneniya”, Teoriya predstavlenii, dinamicheskie sistemy. XI, Zap. nauchn. sem. POMI, 312, 2004, 69–85

[2] Domanskii V. K., Kreps V. L., “Povtoryayuschiesya igry s asimmetrichnoi informatsiei i sluchainye bluzhdaniya tsen na finansovykh rynkakh”, Obozrenie prikl. i promyshl. matem., 12:4 (2005), 950–952

[3] Domanskii V. K., Kreps V. L., “Mnogoshagovye torgi aktsii v zakrytom aktsionernom obschestve i povtoryayuschiesya igry $n$ lits s nepolnoi informatsiei”, Ekonomicheskaya nauka sovremennoi Rossii, 2008, no. S1, 100–102

[4] Domanskii V. K., Kreps V. L., “Teoretiko-igrovaya model birzhevykh torgov: strategicheskie aspekty formirovaniya tsen na fondovykh rynkakh”, Zhurnal Novoi ekonomicheskoi assotsiatsii, 2011, no. 11, 39–62

[5] Domanskii V. K., Kreps V. L., “Igry torgov neskolkimi aktivami”, Matematicheskaya teoriya igr i ee prilozheniya, 6:3 (2014), 32–53 | Zbl

[6] Kreps V. L., “Povtoryayuschiesya igry, modeliruyuschie birzhevye torgi, i vozvratnye posledovatelnosti”, Izv. RAN, Teoriya i sistemy upravleniya, 2009, no. 4, 109–120

[7] Petrosyan L. A., Zenkevich N. A., Shevkoplyas E. V., Teoriya igr, Izd-vo «BKhV-Peterburg», 2012

[8] Pyanykh A., “Ob odnoi modifikatsii modeli birzhevykh torgov s insaiderom”, Matematicheskaya teoriya igr i ee prilozheniya, 6:4 (2014), 68–84 | Zbl

[9] Pyanykh A., “Mnogoshagovaya model birzhevykh torgov s elementami peregovorov i schetnym mnozhestvom sostoyanii”, Upravlenie bolshimi sistemami, 64 (2016), 6–26

[10] Pyanykh A., “O modifikatsii mnogoshagovoi modeli birzhevykh torgov s nepreryvnymi stavkami i asimmetrichnoi informatsiei”, Matematicheskaya teoriya igr i ee prilozheniya, 8:2 (2016), 91–113 | Zbl

[11] Sandomirskaya M. S., “Teoretiko-igrovaya dinamicheskaya model insaiderskikh torgov s nenulevym spredom”, Upravlenie bolshimi sistemami, 40 (2014), 207–234

[12] Sandomirskaya M. S., Domanskii V. K., “Reshenie odnoshagovoi igry birzhevykh torgov s nepolnoi informatsiei”, Matematicheskaya teoriya igr i ee prilozheniya, 4:1 (2012), 32–54 | Zbl

[13] Aumann R. J., Maschler M., Repeated Games with Incomplete Information, The MIT Press, Cambridge–Massachusetts–London, England, 1995 | MR

[14] Bachelier L., “Theorie de speculation”, Ann. Ecole Norm. Sup., 17 (1900), 21–86 | DOI | MR | Zbl

[15] Chatterjee K., Samuelson W., “Bargaining under Incomplete Information”, Operations Research, 31:5 (1983), 835–851 | DOI | Zbl

[16] De Meyer B., “Price dynamics on a stock market with asymmetric information”, Games and economic behavior, 69 (2010), 42–71 | DOI | MR | Zbl

[17] De Meyer B., Moussa Saley H., “On the Strategic Origin of Brownian Motion in Finance”, Int. Journal of Game Theory, 31 (2003), 285–319 | DOI | MR

[18] De Meyer B., Marino A., Continuous versus discrete market game, Cowles Foundation Discussion Paper No 1535, 2005

[19] Domansky V., “Repeated games with asymmetric information and random price fluctuations at finance markets”, Int. Journal of Game Theory, 36:2 (2007), 241–257 | DOI | MR | Zbl

[20] Domansky V., “Symmetric representations of bivariate distributions”, Statistics and Probability Letters, 83 (2013), 1054–1061 | DOI | MR | Zbl

[21] Domansky V., Kreps V., “Repeated games with asymmetric information modeling financial markets with two risky assets”, RAIRO Operations Research, 47 (2013), 251–272 | DOI | MR | Zbl

[22] Domansky V., Kreps V., Sandomirskaia M., “A Survey on Discrete Bidding Games with Asymmetric Information”, Contributions to Game Theory and Management, 6 (2013), 89–114 | MR

[23] Gensbittel F., Asymptotic analysis of repeated games with incomplete information, Thèse de doctorat de l'Université Paris 1, Panthéon-Sorbonne-Paris (10/12/2010), Bernard De Meyer (Dir), 2010 http://tel.archives-ouvertes.fr/tel-00579522/fr/

[24] Kyle A. S., “Continuous Auctions and Insider Trading”, Econometrica, 53 (1985), 1315–1335 | DOI | Zbl

[25] Sandomirskaia M., “Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence”, Int. Game Theory Rev, 19:1 (2017) | DOI | MR | Zbl

[26] Sandomirskiy F., “On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values”, Dynamic Games and Applications 21 | DOI