Repeated games of incomplete information with large sets of states
International Journal of Game Theory(2014)
摘要
The famous theorem of R. Aumann and M. Maschler states that the sequence of values of an N -stage zero-sum game _N(ρ ) with incomplete information on one side and prior distribution ρ converges as N→∞ , and that the error term err[ _N(ρ )]=val[ _N(ρ )]- lim _M→∞val[ _M(ρ )] is bounded by C N^-1/2 if the set of states K is finite. The paper deals with the case of infinite K . It turns out that, if the prior distribution ρ is countably-supported and has heavy tails, then the error term can be of the order of N^α with α∈( -1/2,0) , i.e., the convergence can be anomalously slow. The maximal possible α for a given ρ 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.
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关键词
Repeated games with incomplete information,Error term,Bayesian learning,Maximal variation of martingales,Entropy
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