Using randomization to break the curse of dimensionality
Article Abstract:
Random versions of consecutive approximations and multigrid algorithms for determining approximate solutions to Markovian decision processes (MDPs) are presented. The upper bounds of randomized complexity of finite and infinite horizon discrete decision process problems (DDPs) were also determined. It was proven that the algorithms were able to overcome the 'curse of dimensionality' for DDPs assuming that the Lipschitz bounds are constants which are not reliant on the problem dimension.
Publication Name: Econometrica
Subject: Mathematics
ISSN: 0012-9682
Year: 1997
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"Beliefs about beliefs" without probabilities
Article Abstract:
The model of a space of states of the world is derived to illustrate the uncertainty faced by decision makers in a strategic situation. The model is based on a hierarchy of preferences to accommodate uncertainty averse preferences and allow the definition of common knowledge of expected utility. The model can also be applied to the foundations for a Harsanyi-style game of incomplete information and the axiomatization of solution concepts for complete information normal form games.
Publication Name: Econometrica
Subject: Mathematics
ISSN: 0012-9682
Year: 1996
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Efficiency of an information system in an agency model
Article Abstract:
A study was conducted to compare the relative efficiencies of various information systems in an agency model. The results showed that the mean preserving spread relation between the likelihood ratio distributions obtained from the original information systems may be used to rank information systems. Moreover, the mean preserving spread relation is applicable to a larger set of information systems than either Blackwell's theorem or Holmstrom's informativeness criterion.
Publication Name: Econometrica
Subject: Mathematics
ISSN: 0012-9682
Year: 1995
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