相关论文: Ordinal Sums with Substitution of Impartial Games

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…

A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…

In this paper we consider ordinal sums of combinatorial games where each summand is a number, not necessarily in canonical form. In doing so we give formulas for the value of an ordinal sum of numbers where the literal form of the base has…

The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include, as subclasses, the scoring games considered by Milnor…

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 present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of…

This paper considers a natural ruleset for playing a partisan combinatorial game on a directed graph, which we call Digraph Placement. Given a digraph $G$ with a not necessarily proper $2$-coloring of $V(G)$, the Digraph Placement game…

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…

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…

Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no chance devices. Also the games have the finite descent property…

Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…

Combinatorial Game Theory(CGT)is a branch of Game Theory that has developed largely independently of Economic Game Theory (EGT), and is concerned with deep mathematical properties of two-player zero-sum games recursively defined over…

Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…

We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…

In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If…

We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by first applying a reduction, then decomposing the position…

A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…

Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…

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…

Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. These arise from simultaneous-play combinatorial games where one…