相关论文: The strange algebra of combinatorial games

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study…

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of…

This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and…

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…

The field of Game Theory provides a useful mechanism for modeling many decision-making scenarios. In participating in these scenarios individuals and groups adopt particular strategies, which generally perform with varying levels of…

The framework of graded semantics uses graded monads to capture behavioural equivalences of varying granularity, for example as found on the linear-time/branching-time spectrum, over general system types. We describe a generic…

Collectible card games are challenging, widely played games that have received increasing attention from the AI research community in recent years. Despite important breakthroughs, the field still poses many unresolved challenges. This work…

We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…

This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning…

A comply/constrain game or a game with a Muller twist is a game where the next player is allowed to place constraints on opponent's next move. We develop a closed form formula for the Grundy value of the single-pile subtraction game where…

Arithmetic functions in Number Theory meet the Sprague-Grundy function from Combinatorial Game Theory. We study a variety of 2-player games induced by standard arithmetic functions, such as Euclidian division, divisors, remainders and…

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…

Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of…

Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melli\`es (2018) suggested that such categories of games and strategies may…

The study of combinatorial games is intimately tied to the study of graphs, as any game can be realized as a directed graph in which players take turns traversing the edges until reaching a sink. However, there have heretofore been few…

Game-semantic models usually start from the core model of the prototypical language PCF, which is characterised by a range of combinatorial constraints on the shape of plays. Relaxing each such constraint usually corresponds to the…

Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective…

This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model…

Matching games is a novel matching model introduced by Garrido-Lucero and Laraki, in which agents' utilities are endogenously determined as the outcome of a strategic game they play simultaneously with the matching process. Matching games…