2014- Working Papers: Operations Research and Decisions

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Weak dominance: A mystery cracked, 9 pp.
J. Hillas and D. Samet
(Working Paper No. 5/2014)
Research no.: 06540100

What strategy profiles can be played when it is common knowledge that weakly dominated strategies are not played? A comparison to the case of strongly dominated strategy is in order. A common informal argument shows that if it is common knowledge that players do not play strongly dominated strategies then players can play only profiles that survive the iterative elimination of strongly dominated strategies. We formalize and prove this claim. However, the analogous claim for the case of weak dominance does not hold. We show that common knowledge that players do not play weakly dominated strategies implies that they must play profiles that survive an iterative elimination of profiles, called flaws of weakly dominated strategies, a process described by Stalnaker (1994). The iterative elimination of flaws of strongly dominated strategies results in the same set of profiles as the iterative elimination of strongly dominated strategies. Thus, the case of weak dominance and strong dominance are completely analogous: Common knowledge that players do not play weakly, or strongly dominated strategies implies iterative elimination of flaws of weakly, or strongly dominated strategies, correspondingly. These processes,  for both weak and strong dominance, are independent of the order of elimination.

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On the dispensable role of time in games of perfect information, 9 pp.
D. Samet
(Working Paper No. 6/2014) 
Research no.: 06530100

In Aumann (1995) and Aumann (1998), time is assumed implicitly in the description of games of perfect information, and it is part of the epistemic distinction between ex-ante and ex-post knowledge. We show that ex-post knowledge in these papers can be expressed by ex-ante knowledge and therefore epistemically, time is irrelevant to the analysis. Furthermore, we show that material rationality by weak dominance and by expectation can be expressed in terms of the timeless strategic form of the game.

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