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Weaker dominance results in a bushy growth form with repeated branching.
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Assuming that the players' beliefs are "cautious" is naturally related to weak dominance (recall the characterization of weak dominance, Section 3.2 in which a strategy is weakly dominated iff it does not maximize expected utility with respect to any full support probability measure).
The event in which \(i\) chooses rationality is then defined as In addition, we have \(\mathsf{Rat^{sd}}\ :=\ \bigcap_{i\in N}\mathsf{Rat_i^{sd}}\). Similarly, we can define the set of states in which player \(i\) is playing a strategy that is not weakly dominated, denoted \(\mathsf{Rat_i^{wd}}\) and \(\mathsf{Rat^{wd}}\) using weak dominance.
It is prevalent that the Pareto-based dominant framework is inefficient in non-dominated sorting because the performance sharply deteriorates when there are numerous weak dominance relations.
The same observation does not hold for weak dominance.
Table 8 Stated ANA with MNL and ≤ 14-day recall Efficient Orthogonal Weak dominance No dominance Weak dominance No dominance Coeff.
There are two main ingredients to the epistemic characterization of iterated weak dominance.
Similar facts hold about weak dominance, though the situation is more subtle.
We can use non-expected-utility considerations like weak dominance as tiebreakers.
Comparing these two Lemmas, we see that strict dominance implies weak dominance, but not necessarily vice versa.
In the epistemic game theory literature the most commonly used choice rules are: (strict) dominance, maximization of expected utility and admissibility (also known as weak dominance).
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