Related papers: Guaranteed Scoring Games

We consider the abstract structure of the monoid M of mis\`ere impartial game values. Several new results are presented, including a proof that the group of fractions of M is almost torsion-free; a method of calculating the number of…

We propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic…

In many situations, both in human and artificial societies, cooperating agents have different status with respect to the activity and it is not uncommon that certain actions are only allowed to coalitions that satisfy certain criteria,…

We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient…

This paper presents a monoidal category whose morphisms are games (in the sense of game theory, not game semantics) and an associated diagrammatic language. The two basic operations of a monoidal category, namely categorical composition and…

Games such as go, chess and checkers have multiple equivalent game states, i.e. multiple board positions where symmetrical and opposite moves should be made. These equivalences are not exploited by current state of the art neural agents…

Domination game [SIAM J.\ Discrete Math.\ 24 (2010) 979--991] and total domination game [Graphs Combin.\ 31 (2015) 1453--1462] are by now well established games played on graphs by two players, named Dominator and Staller. In this paper,…

First-order (FO) transition systems have recently attracted attention for the verification of parametric systems such as network protocols, software-defined networks or multi-agent workflows like conference management systems. Desirable…

We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…

Subtraction games have a rich literature as normal-play combinatorial games (e.g., Berlekamp, Conway, and Guy, 1982). Recently, the theory has been extended to zero-sum scoring play (Cohensius et al. 2019). Here, we take the approach of…

In everyday life, we frequently make coarse-grained judgments. When we say that Olivia and Noah excel in mathematics, we disregard the specific differences in their mathematical abilities. Similarly, when we claim that a particular…

We introduce and study Minkowski games. These are two player games, where the players take turns to chose positions in $\mathbb{R}^d$ based on some rules. Variants include boundedness games, where one player wants to keep the positions…

It is known that if two players achieve a superclassical score at a nonlocal game $G$, then their outputs are certifiably random - that is, regardless of the strategy used by the players, a third party will not be able to perfectly predict…

We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show…

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

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),…

The paper [Ras15a] introduced distribution-valued games. This game-theoretic model uses probability distributions as payoffs for games in order to express uncertainty about the payoffs. The player's preferences for different payoffs are…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

The balanced chromatic number of a signed graph G is the minimum number of balanced sets that cover all vertices of G. Studying structural conditions which imply bounds on the balanced chromatic number of signed graphs is among the most…

Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…