Related papers: $\mathcal{L}\mathcal{R}$-Ending partisan rulesets
We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our…
In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless…
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
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)…
A combinatorial game is a two-player game without hidden information or chance elements. The main object of combinatorial game theory is to obtain the outcome, which player has a winning strategy, of a given combinatorial game. Positions of…
We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…
This paper addresses several significant gaps in the theory of restricted mis\`ere play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\mathcal{E}$ (Milley, Renault 2013); if a player run out of moves…
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…
Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss…
Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of…
In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…
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…
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning…
We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.
This article concerns the resolution of impartial combinatorial games, and in particular games that can be split in sums of independent positions. We prove that in order to compute the outcome of a sum of independent positions, it is always…
We study the structure of the set of equilibrium payoffs in finite games, both for Nash equilibrium and correlated equilibrium. A nonempty subset of R^2 is shown to be the set of Nash equilibrium payoffs of a bimatrix game if and only if it…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- mis\`ere- and scoring-play monoids. In this note we show that the class is categorical, by extending Joyal's…
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.
A notion of combinatorial game over a partially ordered set of atomic outcomes was recently introduced by Selinger. These games are appropriate for describing the value of positions in Hex and other monotone set coloring games. It is…