Related papers: Positional Games

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…

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…

Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…

Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential…

The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…

The interactive game theoretical approach to tactics and behavioral self-organization is developed. Though it uses the interactive game theoretical formalization of dialogues as psycholinguistic phenomena, the crucial role is played by the…

The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…

We consider a class of coalition formation games called hedonic games, i.e., games in which the utility of a player is completely determined by the coalition that the player belongs to. We first define the class of subset-additive hedonic…

Maker-Breaker games are played on a hypergraph $(X,\mathcal{F})$, where $\mathcal{F} \subseteq 2^X$ denotes the family of winning sets. Both players alternately claim a predefined amount of edges (called bias) from the board $X$, and Maker…

Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a…

We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…

By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well…

A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…

The legal positions of a strong placement game, such as Domineering, form a simplicial complex called the legal complex. In this paper, we use the legal complex to study the game values taken on by the class of strong placement games using…

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…

Hierarchical simple games - both disjunctive and conjunctive - are natural generalizations of simple majority games. They take their origin in the theory of secret sharing. Another important generalization of simple majority games with…

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium…

We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…