相关论文: Mis\`ere canonical forms of partizan games

We consider the class of "well-tempered" integer-valued scoring games, which have the property that the parity of the length of the game is independent of the line of play. We consider disjunctive sums of these games, and develop a theory…

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…

Losing a game is difficult. Recent work of Larsson, Nowakowski, and Santos, as well as that of Siegel, has opened up enticing lines of research into partizan mis\`ere theory. The algebraic structure of mis\`ere monoids is not yet well…

In Combinatorial Game Theory, we study the set of games G, whose elements are mapped from positions of rulesets. In many case, given a ruleset, not all elements of G can be given as a position in the ruleset. It is an intriguing question…

In 2010, Bre\v{s}ar, Klav\v{z}ar and Rall introduced the optimization variant of the graph domination game and the game domination number, which was proved PSPACE-hard by Bre\v{s}ar et al. in 2016. In 2024, Leo Versteegen obtained the…

Recently, Clow and McKay proved that the Digraph Placement ruleset is universal for normal play: for all normal play combinatorial games $X$, there is a Digraph Placement game $G$ with $G=X$. Clow and McKay also showed that the 22 game…

We introduce a new type of game on natural numbers of variable countable length, which can be regarded as a diagonalization of all games of fixed countable length on natural numbers. Building on previous work by Trang and Woodin, we show…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

A Bayesian game is said to have nested information if the players are ordered, and each player knows the types of all players that follow her in that order. We prove that all multiplayer Bayesian games with finite actions spaces, bounded…

We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite natural, but different possibilities arises for the notion of…

Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…

Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…

We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the…

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…

Past efforts to classify impartial three-player combinatorial games (the theories of Li and Straffin) have made various restrictive assumptions about the rationality of one's opponents and the formation and behavior of coalitions. One may…

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…

In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…

The ``losing positions" of certain combinatorial games constitute linear error detecting and correcting codes. We show that a large class of games that can be cast in the form of *annihilation games*, provides a potentially polynomial…

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…

Playing impartial games under the normal and misere conventions may differ a lot. However, there are also many "exceptions" for which the normal and misere plays are very similar. As early as in 1901 Bouton noticed that this is the case…