Common Belief Revisited

Romeo Matthew Balanquit

No 201608, UP School of Economics Discussion Papers from University of the Philippines School of Economics

Abstract: This 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, 1996a) can also be given a generalized form, parameterized by the number of players.

Keywords: common p-belief; common knowledge assumption; global games (search for similar items in EconPapers)
JEL-codes: C70 D83 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2016-08
New Economics Papers: this item is included in nep-gth, nep-hpe, nep-mic and nep-sea
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Published as UPSE Discussion Paper No. 2016-08, August 2016

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Persistent link: https://EconPapers.repec.org/RePEc:phs:dpaper:201608

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