Monday, July 18, 2011

21 July 2011: Common Belief Revisited

Romeo Balanquit
Jawaharlal Nehru University, New Delhi

This brief study presents how selection of equilibrium in a game with
many equilibria can be made possible when the common knowledge
assumption (CKA) is replaced by the notion of common belief.
Essentially, this idea of pinning down an equilibrium by weakening the
CKA is the central feature of the global game approach which
introduces a natural perturbation on games with complete information.
We argue that since common belief is another form of departure from
the CKA, it can also obtain the results attained by the global game
framework in terms of selecting an equilibrium. We provide here
necessary and sufficient conditions. Following the program of
weakening the CKA, we weaken the notion of common belief further to
provide a less stringent and a more natural way of believing an event.
We call this belief process as iterated quasi-common p-belief which is
a generalization to many players of a two-person iterated p-belief. It
is shown that this converges with the standard notion of common
p-belief at a sufficiently large number of players. Moreover, the
agreeing to disagree result in the case of beliefs (Monderer & Samet,
1989 and Neeman, 1996) can also be given a generalized form,
parameterized by the number of players.

Date: July 21, 2011
Time: 03:00 P.M.

AMEX Conference Room (Second Floor),
Department of Economics,
Delhi School of Economics,
New Delhi-110007(INDIA)


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