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.
Mots-clés : multistage bidding model, repeated game, asymmetric information, random walk
@article{RO_2013__47_3_251_0,
author = {Kreps, Victoria and Domansky, Victor},
title = {Repeated games with asymmetric information modeling financial markets with two risky assets},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {251--272},
publisher = {EDP-Sciences},
volume = {47},
number = {3},
year = {2013},
doi = {10.1051/ro/2013037},
mrnumber = {3143751},
zbl = {1282.91132},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2013037/}
}
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 SP - 251 EP - 272 VL - 47 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2013037/ DO - 10.1051/ro/2013037 LA - en ID - RO_2013__47_3_251_0 ER -
%0 Journal Article %A Kreps, Victoria %A Domansky, Victor %T Repeated games with asymmetric information modeling financial markets with two risky assets %J RAIRO - Operations Research - Recherche Opérationnelle %D 2013 %P 251-272 %V 47 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2013037/ %R 10.1051/ro/2013037 %G en %F RO_2013__47_3_251_0
Kreps, Victoria; Domansky, Victor. Repeated games with asymmetric information modeling financial markets with two risky assets. RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 3, pp. 251-272. doi : 10.1051/ro/2013037. http://www.numdam.org/articles/10.1051/ro/2013037/
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