Repeated games with asymmetric information and random price fluctuations at finance markets

Abstract

This paper is concerned with multistage bidding models introduced in De Meyer and Moussa Saley (Int J Game Theory 31:285–319, 2002) to analyze the evolution of the price system at finance markets with asymmetric information. The repeated games are considered modelling the biddings with the admissible bids k/m, unlike the above mentioned paper, where arbitrary bids are allowed. It is shown that the sequence of values of n-step games is bounded from above and converges to the value of the game with infinite number of steps. The optimal strategies of infinite game generate a symmetric random walk of transaction prices over admissible bids with absorbing extreme points. The value of infinite game is equal to the expected duration of this random walk multiplied by the constant one-step gain of informed Player 1.