Related papers: Games with finitely generated structures
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
The Banach-Mazur game, Schmidt's game and McMullen's absolute winning game are three quintessential intersection games. We investigate their determinacy on the real line when the target set for either player is a Bernstein set, a…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
We obtain game-theoretic characterizations for meagerness and rareness of filters on a countable set.
This is a short introduction to the subject of strategic games. We focus on the concepts of best response, Nash equilibrium, strict and weak dominance, and mixed strategies, and study the relation between these concepts in the context of…
We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite $N$-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We consider infinite-state Attacker-Defender games with reachability objectives. The results of the paper are twofold. Firstly we prove a new language-theoretic result for weighted automata on infinite words and show its encoding into the…
In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…
We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…
We consider the abstract structure of the monoid M of mis\`ere impartial game values. Several new results are presented, including a proof that the group of fractions of M is almost torsion-free; a method of calculating the number of…
We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized B\"uchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and…
We begin the systematic study of decision problems for finitely generated groups given by a solution to their word problem. We relate this to the study of computable analysis on the space of marked groups. We point out that several distinct…
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state…
We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant…
We show a simple method for constructing an infinite family of graph formation games with link bias so that the resulting games admits, as a \textit{pairwise stable} solution, a graph with an arbitrarily specified degree distribution.…
We characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorics or structural properties of the given filter. These generalize several ultrafilter games of Galvin.
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…