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

Abstract

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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.

How to cite

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Kreps, 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

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  7. [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. [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. [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. [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. [11] G. Winkler, Extreme points of moment sets. Math. Oper. Res.13 (1988) 581–587. Zbl0669.60009MR971911

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