Related papers: Games with finitely generated structures
Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…
As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there…
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…
We continue the investigation of finite-duration variants of infinite-duration games by extending known results for games played on finite graphs to those played on infinite ones. In particular, we establish an equivalence between pushdown…
We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular…
We explore the generation of diverse environments using the Amorphous Fortress (AF) simulation framework. AF defines a set of Finite State Machine (FSM) nodes and edges that can be recombined to control the behavior of agents in the…
Generalized Tur\'an problems investigate the maximization of the number of certain structures (typically edges) under some constraints in a graph. We study a game version of these problems, the Constructor-Blocker game. We mainly focus on…
In this paper, we study a famous discrete dynamical system, the Chip Firing Game, used as a model in physics, economics and computer science. We use order theory and show that the set of reachable states (i.e. the configuration space) of…
We prove that chess played on the infinite chessboard $\mathbb{Z}^2$ with infinitely many pieces is as powerful as it could possibly be, by showing that every open Gale-Stewart game with draws is strategically equivalent to some infinite…
Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequalities techniques, we prove…
We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman's neat…
Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald's pick-the-larger-integer game. Several authors have provided conditions for the existence of…
We endow projective (resp. direct) limits of Banach tensor structures with Fr\'{e}chet (resp. convenient) structures and study adapted connections to $G$-structures in both frameworks. This situation is illustrated by a lot of examples.
A finite impartial game is a two-player game in which the players take turns making moves and the game ends after finitely many moves. In this paper, we study a class of finite impartial games introduced by H.~Lenstra, which we call coin…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
We provide here an epistemic analysis of arbitrary strategic games based on the possibility correspondences. Such an analysis calls for the use of transfinite iterations of the corresponding operators. Our approach is based on Tarski's…
The Galois lattice is a graphic method of representing knowledge structures. The first basic purpose in this paper is to introduce a new class of Galois lattices, called graded Galois lattices. As a direct result, one can obtain the notion…
We study the existence of uncountable first-order structures that are homogeneous with respect to their finitely generated substructures. In many classical cases this is either well-known or follows from general facts, for example, if the…