Related papers: Games with finitely generated structures

We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to…

In a single-state repeated game, zero-determinant strategies can unilaterally force functions of the payoffs to take values in particular closed intervals. When the explicit use of a determinant is absent from the analysis, they are instead…

We introduce a new class of population games that we call monotropic; these are games characterized by the presence of a unique globally neutrally stable Nash equilibrium. Monotropic games generalize strictly concave potential games and…

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

Multi-structural (MS) games are combinatorial games that capture the number of quantifiers of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht-Fraisse (EF) games in two ways: first, MS games are…

We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…

We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM…

Spoiler-Duplicator games are used in finite model theory to examine the expressive power of logics. Their strategies have recently been reformulated as coKleisli maps of game comonads over relational structures, providing new results in…

We establish the existence of fixed points for set-valued maps defined on metric spaces and satisfying a pointwise or a local version of Banach's contraction property. As an application, we demonstrate the existence of Nash equilibrium in a…

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.

We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the…

We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker)…

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game.…

All constructive methods employed in modern mathematics produce only countable sets, even when designed to transcend countability. We show that any constructive argument for uncountability -- excluding diagonalization techniques --…

Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…

Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…

We study two impartial games introduced by Anderson and Harary. Both games are played by two players who alternately select previously-unselected elements of a finite group. The first player who builds a generating set from the…

In this work we propose and develop modified quantum games (zero and non-zero sum) in which payoffs and strategies are entangled. For the games studied, Nash and Pareto equilibriums are always obtained indicating that there are some…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…