Foundations for iterated admissibility (i.e., the iterated removal of weakly dominated strategies) need to confront a fundamental challenge. On the one hand, admissibility requires that a player consider every strategy of their opponents possible. On the other hand, reasoning that the opponents are rational requires ruling out certain strategies. Brandenburger, Friedenberg and Keisler’s (BFK, E...

We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such Weyl-Heisenberg frames are admissible with regard to the action of a suitably defined type-I discrete group G. This allows to relate the construction of Weyl-Heisenber...

While developing a method for reasoning about programs, Pitts defined the ⊤⊤-closed relations as an alternative to the standard admissible relations. This paper reformulates and studies Pitts’s operational concept of ⊤⊤-closure in a semantic framework. It investigates the nontrivial connection between ⊤⊤-closure and admissibility, showing that ⊤⊤-closure is strictly stronger than admissibility ...

Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator B defined on an infinite-dimensional Hilbert space U is an admissible control operator if for every element u ∈ U the vector Bu defines an admissible control operator. The other conjecture says that B is an admissible control operator if a certain resolvent estimate ...

We investigate the computational complexity of admissibility of inference rules in infinite-valued Lukasiewicz propositional logic ( L). It was shown in [13] that admissibility in L is checkable in PSPACE. We establish that this result is optimal, i.e., admissible rules of L are PSPACE-complete. In contrast, derivable rules of L are known to be coNP-complete.

We compare the properties of several notions of perfectness within classes of compact, metric, and (possibly) discontinuous games, and show that in the presence of payoff discontinuities, standard notions of perfectness may fail a weakening of admissibility termed limit admissibility. We also provide conditions ensuring the existence of a limit admissible perfect equilibrium. These conditions a...

We study the computational complexity of abstract argumentation semantics based on weak admissibility, a recently introduced concept to deal with arguments self-defeating nature. Our results reveal that admissibility are much higher (under typical assumptions) compared all which have been analysed in terms so far. In fact, we show PSPACE-completeness non-trivial standard decision problems for w...

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The Robust No Free Lunch with Vanishing Risk (RNFLVR) condition for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, ...

Although courts in the United States and Canada regularly admit graphic photographs into evidence, little research exists on whether such evidence prejudices the decisions of jurors. Mock jurors (N = 120) read a detailed trial transcript of a murder trial, and were either presented with color, black and white, or no photographs of an actual murder victim. The proportion of guilty verdicts in th...