| This is a file in the archives of the Stanford Encyclopedia of Philosophy. |
Proof.
Suppose first that common knowledge of Bayesian rationality is
satisfied. Since it is common knowledge that agent i knows that agent k
is Bayesian rational, it is also common knowledge that if
μi(skj)
> 0, then skj must be
optimal for k given some belief over S-k,
so (3.i) is
common knowledge.
Suppose now that (3.i) is common knowledge. Then, by (3.i), agent
i knows that agent k is Bayesian rational. Since
(3.i) is common knowledge, all statements of the form ‘For
i, j, … , k ∈ N, i
knows that j knows that … is Bayesian rational’
follow by induction.
| Peter Vanderschraaf peterv@cyrus.andrew.cmu.edu | Giacomo Sillari Carnegie Mellon University gsillari@andrew.cmu.edu |