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Repeated games of incomplete information with large sets of states
International Journal of Game Theory. 2014. Vol. 43. No. 4. P. 767-789.
Sandomirskiy F.
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 paper deals with the case of infinite K. It turns out that for countably-supported prior distribution p with heavy tails the error term can decrease arbitrarily slowly. The slowest possible speed of the decreasing for a given p is determined in terms of entropy-like family of functionals. Our approach is based on the well-known connection between the behavior of the maximal variation of measure-valued martingales and asymptotic properties of repeated games with incomplete information.
Research target:
Mathematics
Language:
English
Sandomirskiy F., / Cornell university, arXiv.org. Series arXiv:1509.01727 "Computer Science". 2015.
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 ...
Added: December 28, 2015
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 ...
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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 ...
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