# Repeated games with asymmetric information modeling financial markets with two risky assets

Victoria Kreps; Victor Domansky

RAIRO - Operations Research - Recherche Opérationnelle (2013)

- Volume: 47, Issue: 3, page 251-272
- ISSN: 0399-0559

## Access Full Article

top## Abstract

top## How to cite

topKreps, Victoria, and Domansky, Victor. "Repeated games with asymmetric information modeling financial markets with two risky assets." RAIRO - Operations Research - Recherche Opérationnelle 47.3 (2013): 251-272. <http://eudml.org/doc/275018>.

@article{Kreps2013,

abstract = {We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer values. The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G∞(p). We give the solutions for these games. Optimal strategies of Player 1 generate random walks of transaction prices. But unlike the case of one-type assets, the symmetry of these random walks is broken at the final stages of the game.},

author = {Kreps, Victoria, Domansky, Victor},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {multistage bidding model; repeated game; asymmetric information; random walk},

language = {eng},

number = {3},

pages = {251-272},

publisher = {EDP-Sciences},

title = {Repeated games with asymmetric information modeling financial markets with two risky assets},

url = {http://eudml.org/doc/275018},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Kreps, Victoria

AU - Domansky, Victor

TI - Repeated games with asymmetric information modeling financial markets with two risky assets

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 3

SP - 251

EP - 272

AB - We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer values. The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G∞(p). We give the solutions for these games. Optimal strategies of Player 1 generate random walks of transaction prices. But unlike the case of one-type assets, the symmetry of these random walks is broken at the final stages of the game.

LA - eng

KW - multistage bidding model; repeated game; asymmetric information; random walk

UR - http://eudml.org/doc/275018

ER -

## References

top- [1] R. Aumann and M. Maschler, Repeated Games with Incomplete Information. The MIT Press, Cambridge, Massachusetts, London, England (1995). Zbl0972.91501MR1342074
- [2] B. De Meyer, Price dynamics on a stock market with asymmetric information. Games Econ. Behav.69 (2010) 42–71. Zbl1229.91128MR2663546
- [3] B. De Meyer and A. Marino, Continuous versus discrete market game. Cowles Foundation Discussion Paper (2005) 1535.
- [4] B. De Meyer and H. Saley, On the Strategic Origin of Brownian Motion in Finance. Int. J. of Game Theory31 (2002) 285–319. Zbl1082.91030MR1968993
- [5] V. Domansky, Repeated games with asymmetric information and random price fluctuations at finance markets. Int. J. Game Theory36 (2007) 241–257. Zbl1125.91018MR2342161
- [6] V. Domansky, Symmetric representations of bivariate distributions. Statist. Prob. Lett.83 (2013) 1054–1061. Zbl1266.60012MR3041375
- [7] V. Domansky and V. Kreps, Repeated games with asymmetric information and random price fluctuations at finance markets. Proceedings of Applied and Industrial Mathematics12 (2005) 950–952. Zbl1125.91018
- [8] V. Domansky and V. Kreps, Repeated games with asymmetric information and random price fluctuations at finance markets: the case of countable state space. Centre d’Economie de la Sorbonne. Preprint 2009.40, Univ. Paris 1 (2009). Zbl1125.91018
- [9] F. Gensbittel, 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). http:/tel.archives-ouvertes.fr/tel-00579522/fr/ (2010).
- [10] M.S. Sandomirskaia, On the estimates of the value of repeated game modeling biddings with bid-ask spread. Publications of the 3-d All-Russian Conference “The economic growth, resource-dependence and socio-economic disparity”, St. Petersburg (2012) 173–176.
- [11] G. Winkler, Extreme points of moment sets. Math. Oper. Res.13 (1988) 581–587. Zbl0669.60009MR971911

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.