Dynamic Games and Applications

, Volume 8, Issue 1, pp 180–198 | Cite as

On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values

  • Fedor SandomirskiyEmail author


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 \(V_N\) of such an N-stage game is of the order of N or \(\sqrt{N}\) as \(N\rightarrow \infty \). Our aim is to find what is causing another type of asymptotic behavior of the value \(V_N\) 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 \(V_N\) remains bounded as \(N\rightarrow \infty \) and converges to the limit value. This game is almost-fair, i.e., if Player 1 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 piecewise property, and it says that there exists an optimal strategy of Player 2 that is piecewise constant as a function of a prior distribution p. Discrete market models have the piecewise property. We show that for non-piecewise almost-fair games with an additional non-degeneracy condition the value \(V_N\) is of the order of \(\sqrt{N}\).


Repeated games with incomplete information Error term Bidding games Piecewise games Asymptotics of the value Transportation problems Kantorovich metric 



I am thankful to Vita Kreps for many inspiring discussions and for her care. I thank Misha Gavrilovich and two anonymous referees for suggestions that significantly improved presentation of the results.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsSt. PetersburgRussian Federation
  2. 2.St. Petersburg Institute for Economics and Mathematics of Russian Academy of SciencesSt. PetersburgRussian Federation

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