  The Perfectly Transparent Equilibrium is algorithmically defined, for any
game in normal form with perfect information and no ties, as the iterated
deletion of non-individually-rational strategy profiles until at most one
remains. In this paper, we characterize the Perfectly Transparent Equilibrium
with adapted Kripke models having necessary rationality, necessary knowledge of
strategies as well as eventual logical omniscience.
  Eventual logical omniscience is introduced as a weaker version of perfect
logical omniscience, with logical omniscience being quantized and fading away
counterfactually. It is the price to pay for necessary factual omniscience and
necessary rationality: we conjecture that epistemic omniscience, logical
omniscience and necessary rationality form an impossibility triangle.
  We consider multimodal classes of Kripke structures, with respect to agents,
but also in the sense that we have both epistemic and logical accessibility
relations. Knowledge is defined in terms of the former, while necessity is
defined in terms of the latter. Lewisian closest-state functions, which are not
restricted to unilateral deviations, model counterfactuals.
  We use impossible possible worlds \`a la Rantala to model that some strategy
profiles cannot possibly be reached in some situations. Eventual logical
omniscience is then bootstrapped with the agents' considering that, at
logically possible, but non-normal worlds \`a la Kripke, any world is logically
accessible and thus any deviation of strategy is possible. As in known in
literature, under rationality and knowledge of strategies, these worlds
characterize individual rationality. Then, in normal worlds, higher levels of
logical omniscience characterize higher levels of individual rationality, and a
high-enough level of logical omniscience characterizes, when it exists, the
Perfectly Transparent Equilibrium.
