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Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version)


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  • Dow, James
  • Werlang, Sérgio Ribeiro da Costa


We define Nash equilibrium for two-person normal form games in thepresence of uncertainty, in the sense of Knight(1921). We use the fonna1iution ofuncertainty due to Schmeidler and Gilboa. We show tbat there exist Nash equilibriafor any degree of uncertainty, as measured by the uncertainty aversion (Dow anelWer1ang(l992a». We show by example tbat prudent behaviour (maxmin) can beobtained as an outcome even when it is not rationaliuble in the usual sense. Next, webreak down backward industion in the twice repeated prisoner's dilemma. We linkthese results with those on cooperation in the finitely repeated prisoner's dilemmaobtained by Kreps-Milgrom-Roberts-Wdson(1982), and withthe 1iterature onepistemological conditions underlying Nash equilibrium. The knowledge notionimplicit in this mode1 of equilibrium does not display logical omniscience.

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Paper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 213.

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Date of creation: Apr 1993
Date of revision:
Handle: RePEc:fgv:epgewp:213

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