The existential part of the definition of weak dominance means that the analogue of Observation 3.3 does not hold for weak dominance: if \(s_i\) is weakly dominated with respect to \(X\) then it need not be the case that \(s_i\) is weakly dominated with respect to some \(X'\subseteq X\).
This dominated condition means weakly dominated (WD), where weak refers to the fact that domination is distributional.
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).
Here it turns out that bidding your value in the first-price auction is weakly dominated.
In this case, regulatory oversight is weakly dominated by one of two alternatives: eliminating oversight or banning regulation.
Strategies were excluded from the cost-effectiveness calculations if they were more costly and less effective (i.e., strongly dominated) or less costly and less cost-effective (i.e., weakly dominated) than an alternative strategy.
This new interpretation permits a simpler solution than those considered in the literature; I derive a mechanism that induces truthful revelation where the equilibrium involves a single round of elimination of weakly dominated strategies, and no monetary transfers.
The MAM implements the Pareto-efficient allocation in multiple solution concepts including backward elimination of weakly dominated strategies (BEWDS), limit logit agent quantal response equilibrium, subgame perfect minimax regret equilibrium, level-k thinking, and diagonalization heuristics.
In the case of a weakly dominated random field, we have the following theorem.
A key issue in epistemic game theory is the epistemic analysis of iterated removal of weakly dominated strategies.
Then, if \(c^*\) is a probabilistic credence function, then \(c^*\) is not weakly dominated relative to \(\mathfrak{D}\).
