Related papers: Impartial games with entailing moves

The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games,…

In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we…

Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…

We present and study a variant of the mean payoff games introduced by A. Ehrenfeucht and J. Mycielski. In this version, the second player makes an infinite sequence of moves only after the first player's sequence of moves has been decided…

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…

Traditional game theory assumes that the players in the game are aware of the rules of the game. However, in practice, often the players are unaware or have only partial knowledge about the game they are playing. They may also have…

Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by…

We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which…

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…

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…

We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected…

We define an all-small ruleset, Bipass, within the framework of normal-play combinatorial games. A game is played on finite strips of black and white stones. Stones of different colors are swapped provided they do not bypass one of their…

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…

Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…

Given two finite sets of integers $S\subseteq\NNN\setminus\{0\}$ and $D\subseteq\NNN\setminus\{0,1\}$,the impartial combinatorial game $\IMARK(S,D)$ is played on a heap of tokens. From a heap of $n$ tokens, each player can moveeither to a…

Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by…

Due to their complex dynamics, combinatorial games are a key test case and application for algorithms that train game playing agents. Among those algorithms that train using self-play are coevolutionary algorithms (CoEAs). However, the…

Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…

Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and…