On Bayesian-Nash Equilibria Satisfying the Condorcet Jury Theorem: The Dependent Case
AbstractWe investigate sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem ( CJT ). In the Bayesian game G n among n jurors, we allow for arbitrary distribution on the types of jurors. In particular, any kind of dependency is possible. If each juror i has a Ã¢â¬Åconstant strategyÃ¢â¬, s i (that is, a strategy that is independent of the size n ≥ i of the jury), such that s =( s 1, s 2, . . . , s n . . . ) satisfies the CJT , then byMcLennan (1998) there exists a Bayesian-Nash equilibrium that also satisfies the CJT . We translate the CJT condition on sequences of constant strategies into the following problem: (**) For a given sequence of binary random variables X = ( X1 , X 2, ..., X n, ... ) with joint distribution P , does the distribution P satisfy the asymptotic part of the CJT ? We provide sufficient conditions and two general (distinct) necessary conditions for (**). We give a complete solution to this problem when X is a sequence of exchangeable binary random variables. Length: 30 pages
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp527.
Date of creation: Dec 2009
Date of revision:
Publication status: Published in Social Choice and Welfare, 39 (2012) 91-125 as "Extending the Condorcet Jury Theorem to a generalized jury".
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-13 (All new papers)
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