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On repeated zero-sum games with incomplete information and asymptotically bounded values
Cornell university, arXiv.org
,
2015.
Sandomirskiy F.
We consider repeated zero-sum games with incomplete information on the side of Player2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value of such N-stage game is of the order of N or square root of N as N tends to infinity. Our aim is to present a general framework for another asymptotic behavior of the value observed for the discrete version of the financial market model introduced by De Meyer and Saley. For this game Domansky and independently De Meyer with Marino found that the value remains bounded as N tends to infinity and converges to the limiting value. This game is almost-fair, i.e. if Player1 forgets his private information the value becomes zero. We describe a class of almost-fair games having bounded values in terms of an easy-checkable property of the auxiliary non-revealing game. We call this property the trigger property and it says that there exists an optimal strategy of Player2 that is piecewise-constant as a function of a prior distribution. Discrete market models have the trigger property. We show that for non-trigger almost-fair games with additional non-degeneracy condition the value is of the order of square root of N.
Language:
English
Sandomirskiy F., Dynamic Games and Applications 2018 Vol. 8 No. 1 P. 180-198
We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value of such an N-stage game is of the order of N or of square root of N, as N tends to infinity. Our aim is to find ...
Added: March 13, 2017
Sandomirskiy F., / Высшая школа экономики. Series EC "Economics". 2016. No. 148.
We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value of such an N-stage game is of the order of N or of square root of N, as N tends to infinity. Our ...
Added: September 1, 2016
Sandomirskaia M., 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 $O(1)$. ...
Added: November 24, 2015
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The famous theorem of R.Aumann and M.Maschler states that the sequence of values of an N-stage zero-sum game G_N with incomplete information on one side converges as N tends to infinity, and the error term is bounded by a constant divided by square root of N if the set of states K is finite. The ...
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