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Repeated bidding games with incomplete information and bounded values: on the exponential speed of convergence

International Game Theory Review. 2017. Vol. 19. No. 1. P. 1650017-1-1650017-7.

We consider the repeated zero-sum bidding game with incomplete information on one side with non-normalized total payoff. De Meyer, Marino (2005) and Domansky, Kreps (2005) investigated a game $G_n$ modeling multistage bidding with asymmetrically informed agents and proved that for this game $V_n$ converges to a finite limit $V_\infty$, i.e., the error term is $O(1)$. In this paper we show that for this example $V_n$ converges to the limit exponentially fast. For this purpose we apply the optimal strategy $\sigma_\infty$ of insider in the infinite-stage game obtained by Domansky (2007) to the $n$-stage game and deduce that it is $\varepsilon_n$-optimal with $\varepsilon_n$ exponentially small.