The problem of the existence of Berge equilibria in the sense of Zhukovskii in normal-form finite games in pure and in mixed strategies is studied. The example of a three-player game that has Berge equilibrium neither in pure, nor in mixed strategies is given.

In this paper, we propose a new interpretation of quantum mechanics according to which Born probabilities are interpreted as many-valued truth values of statements concerning results of not-yet-performed experiments on quantum objects, or equivalently [0,1]-valued degrees to which quantum objects possess all their properties prior to measurements. The interpretation is based on mathematical results already published by the author, according to which any Birkhoff–von Neumann quantum logic can be isomorphically represented as a family of fuzzy sets or, equivalently, many-valued propositional functions.

The long-lasting problem of proper mathematical representation of conjunctions and disjunctions in quantum logics is reviewed and three recent proposals of solutions are described.

The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players’ strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).

Bell-type inequalities on orthomodular lattices, in which conjunctions of propositions are not modeled by meets but by maps for simultaneous measurements ( \(s\) -maps), are studied. It is shown, that the most simple of these inequalities, that involves only two propositions, is always satisfied, contrary to what happens in the case of traditional version of this inequality in which conjunctions of propositions are modeled by meets. Equivalence of various Bell-type inequalities formulated with the aid of bivariate maps on orthomodular lattices is studied. Our investigations shed new light on the interpretation of various multivariate maps defined on orthomodular lattices already studied in the literature. The paper is concluded by showing the possibility of using \(s\) -maps and \(j\) -maps to represent counterfactual conjunctions and disjunctions of non-compatible propositions about quantum systems.