Related papers: Games from Basic Data Structures
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
Due to their complex dynamics, combinatorial games are a key test case and application for algorithms that train game playing agents. Among those algorithms that train using self-play are coevolutionary algorithms (CoEAs). However, the…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
We discuss general models of resource-sharing computations, with emphasis on the combinatorial structures and concepts that underlie the various deadlock models that have been proposed, the design of algorithms and deadlock-handling…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them.
We study combinatorial games under mis\`ere convention. Several sets of games have been considered earlier to better understand the behaviour of mis\`ere games. We here connect several of these sets. In particular, we prove that comparison…
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new…
The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…
We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and…
Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…
In these notes we introduce and investigate two new games called R-nw-selective game and the M-nw-selective game. These games naturally arise from the corresponding selection principles involving networks introduced in \cite{BG}.
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…
In this paper, we consider a game beginning with a multiset of elements from a group. On a move, two elements are replaced by their sum. This is a no strategy game, and can be modeled as a graded poset with the rank of a node equal to the…
In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…