Related papers: Cyclic impartial games with carry-on moves

We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $\mathfrak{s}$ since the corresponding cardinal invariants behave in an interesting way. We introduce three…

We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly…

In this paper we will be examining impartial scoring play games. We first give the basic definitions for what impartial scoring play games are and look at their general structure under the disjunctive sum. We will then examine the game of…

Coalition Logic is an important logic in logical studies of strategic reasoning, whose models are concurrent game models. In this paper, first, we systematically discuss three assumptions of concurrent game models and argue that they are…

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…

We extend the formalism of Conjectural Variations games to Stackelberg games involving multiple leaders and a single follower. To solve these nonconvex games, a common assumption is that the leaders compute their strategies having perfect…

Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…

In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…

Repeated games have a long tradition in the behavioral sciences and evolutionary biology. Recently, strategies were discovered that permit an unprecedented level of control over repeated interactions by enabling a player to unilaterally…

We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity,…

In 1973 Fraenkel discovered interesting sequences which split the positive integers. These sequences became famous, because of a related unsolved conjecture. Here we construct combinatorial games, with `playable' rulesets, with these…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players. Starting from a fixed vertex, players take turns to move a token along…

We study a general $2 \times 2$ symmetric, entangled, quantum game. When one player has access only to classical strategies while the other can use the full range of quantum strategies, there are ``miracle'' moves available to the quantum…

A traditional assumption in game theory is that players are opaque to one another---if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an…

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…

We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…

Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…

We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…