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Most games violate the common priors doctrine
Author(s) -
Nyarko Yaw
Publication year - 2010
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2009.00129.x
Subject(s) - mathematical economics , lebesgue measure , consistency (knowledge bases) , doctrine , prior probability , zero (linguistics) , measure (data warehouse) , dimension (graph theory) , bayesian game , set (abstract data type) , mathematics , type (biology) , economics , game theory , repeated game , computer science , lebesgue integration , discrete mathematics , philosophy , combinatorics , statistics , bayesian probability , linguistics , ecology , database , programming language , biology , theology
The type of a player in a game describes the beliefs of that player about the types of others. We show that the subset of vectors of such player‐type beliefs which obey the consistency condition sometimes called the Harsanyi doctrine is of Lebesgue measure zero. Furthermore, as the number of players becomes large the ratio of the dimension Harsanyi‐consistent beliefs to the set of all beliefs tends to zero.