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Monotonic Knowledge Models, Cycles, Linear Versions and Auctions with Differential, Finite Information
Author(s) -
RodriguesNeto José A.
Publication year - 2015
Publication title -
economic record
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 42
eISSN - 1475-4932
pISSN - 0013-0249
DOI - 10.1111/1475-4932.12193
Subject(s) - monotonic function , common value auction , social connectedness , mathematics , partition (number theory) , function (biology) , differential (mechanical device) , state space , simple (philosophy) , mathematical economics , mathematical optimization , combinatorics , statistics , mathematical analysis , psychology , philosophy , epistemology , evolutionary biology , engineering , psychotherapist , biology , aerospace engineering
In games of incomplete information where each player's information is represented by a partition of the state space, this paper presents a characterisation of monotonic models in terms of connected partitions and another in terms of versions . A model is monotonic if and only if there is a linear version, and this is true if and only if there is a real‐valued function on the state space such that every partition of the model is connected with respect to this function. These results help us understand the strength of the connectedness assumption on common‐value, second‐price auctions with differential, finite information. We offer a simple sufficient condition for non‐monotonicity to check if models are monotonic.