Related papers: Translation Results for Some Star-Selection Games
We study the $\star$-operator (Larsson et al. 2011) of impartial vector subtraction games (Golomb 1965). Here we extend the notion to the mis\`ere-play convention, and prove convergence and other properties; notably more structure is…
A computation in the continuation monad returns a final result given a continuation, ie. it is a function with type $(X \to R) \to R$. If we instead return the intermediate result at $X$ then our computation is called a selection function.…
Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…
Open-textured terms in written rules are typically settled through interpretive argumentation. Ongoing work has attempted to catalogue the schemes used in such interpretive argumentation. But how can the use of these schemes affect the way…
We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to…
We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…
In [8] the authors initiate the study of selective versions of the notion of $\theta$-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising…
This article is a continuation of our investigations in the function space $C(X)$ with respect to the topology $\tau^s_\mathfrak{B}$ of strong uniform convergence on $\mathfrak{B}$ in line of (Chandra et al. 2020 \cite{dcpdsd} and Das et…
We continue the study of topologies of strong uniform convergence on bornologies initiated in [G. Beer and S. Levi, Strong uniform continuity, J. Math Anal. Appl., 350:568-589, 2009] and [G. Beer and S. Levi, Uniform continuity, uniform…
We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
Impartial subtraction games on the nonnegative integers have been studied by many and discussed in detail in for example the remarkable work Winning Ways by Conway, Berlekamp and Guy. We describe how comply variations of these games,…
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
This work presents the selection principle $S_1^*(\tau_x,CD)$ that characterizes $q$-points. We also discuss the induced topological game $G_1^*(\tau_x,CD)$ and its relations with $W$-points and $\widetilde{W}$-points, as well as with the…
Following a newly introduced approach by Rasetti and Merelli we investigate the possibility to extract topological information about the space where interacting systems are modelled. From the statistical datum of their observable…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
In this note, we propose a simple-looking but broad conjecture about star-algebras over the field of real numbers. The conjecture enables many matrix decompositions to be represented by star-algebras and star-ideals. This paper is written…
The main goal of the paper is the full proof of a cardinal inequality for a space with points $G_\delta $, obtained with the help of a long version of the Menger game. This result, which improves a similar one of Scheepers and Tall, was…
We present a general way of defining various reduction games on \omega\ which "represent" corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for…
In this paper we discuss the diffusion of serious games and present reasons for why Rogers traditional approach is limited in this context. We present an alternative overview through the characteristics of relative advantage, compatibility,…