# “脏脸博弈”中的推理（3）

【参考文献】

Aumann RJ (1999) Interactive epistemology I: Knowledge. International Journal of Game Theory 28: 263±300

http://www.ma.huji.ac.il/raumann/pdf/Interactive epistemology1.pdf

Aumann RJ (1999) Interactive epistemology II: Probability. International Journal of Game Theory 28:301±314

http://www.ma.huji.ac.il/raumann/pdf/Interactive epistemology2.pdf

Vanderschraaf, Peter and Sillari, Giacomo, "Common Knowledge", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.),

http://plato.stanford.edu/archives/spr2009/entries/common-knowledge/

【公共知识的一种定义】

We can now define mutual and common knowledge as follows:

Definition
Let a set Ω of possible worlds together with a set of agents N be given.

1. The proposition that A is (first level or first order) mutual knowledge for the agents of N,K1N(A), is the set defined by

K 1 N (A) ≡ ∩ i N K i (A).

2. The proposition that A is mth level (or mth order) mutual knowledge among the agents of N,KmN(A), is defined recursively as the set

K m N (A) ≡ ∩ i N K i (Km−1N(A)).

3. The proposition that A is common knowledgeamong the agents of N,K*N(A), is defined as the set

 K * N (A) ≡ ∞ ∩ m=1 K m N (A).

https://blog.sciencenet.cn/blog-826653-639402.html

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