Related papers: On Aperiodic Subtraction Games with Bounded Nim Se…
We establish a relation between the Sprague-Grundy function $\text{sg}$ of a $p$-saturation of Welter's game and the degrees of the ordinary irreducible representations of symmetric groups. In this game, a position can be viewed as a…
In this survey we revisit {\sc finite subtraction}, one-heap subtraction games on finite rulesets. The main purpose is to give a general overview of the development, and specifically to draw attention to Flammenkamp's thesis (1997), where…
Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…
Schmidt's game, and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the…
Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…
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…
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…
We study the computational complexity of distance games, a class of combinatorial games played on graphs. A move consists of colouring an uncoloured vertex subject to it not being at certain distances determined by two sets, D and S. D is…
Traces form a coarse notion of semantic equivalence between states of a process, and have been studied coalgebraically for various types of system. We instantiate the finitary coalgebraic trace semantics framework of Hasuo et al. for…
In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…
A binary constraint system game is a two-player one-round non-local game defined by a system of Boolean constraints. The game has a perfect quantum strategy if and only if the constraint system has a quantum satisfying assignment [R. Cleve…
\textsc{cut} is a class of partition games played on a finite number of finite piles of tokens. Each version of \textsc{cut} is specified by a cut-set $\mathcal{C}\subseteq\mathbb{N}$. A legal move consists of selecting one of the piles and…
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
In this paper, we introduce a variant of Francis Su's "Game of Cycles," that we call "Cycles with Sources." The only change to the rules is permitting nodes to be sources, while sinks are still prohibited. Despite this minor change in the…
Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based…
This paper analyses Escard\'o and Oliva's generalisation of selection functions over a strong monad from a game-theoretic perspective. We focus on the case of the nondeterminism (finite nonempty powerset) monad $\mathcal{P}$. We use these…
We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first…
Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in…
Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of…
We introduce Multiplicative Modular Nim (MuM), a variant of Nim in which the traditional nim-sum is replaced by heap-size multiplication modulo m. We establish a complete theory for this game, beginning with a direct, Bouton-style analysis…