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We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…

The main result of this paper is that computing the value of a one-clock priced timed game (OCPTG) is PSPACE-hard. Along the way, we provide a family of OCPTGs that have an exponential number of event points. Both results hold even in very…

Crucial to an Evolutionary Algorithm's performance is its selection scheme. We mathematically investigate the relation between polynomial rank and probabilistic tournament methods which are (respectively) generalisations of the popular…

Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and solve two combinatorial games, and we demonstrate some…

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…

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…

We introduce a large family of combinatorial objects, called standard puzzles, defined by very simple rules. We focus on the standard puzzles for which the enumeration problems can be solved by explicit formulas or by classical numbers,…

So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…

Fractional hedonic games are coalition formation games where a player's utility is determined by the average value they assign to the members of their coalition. These games are a variation of graph hedonic games, which are a class of…

In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning…

This paper develops and analyses a novel quantum combinatorial game: quantum checkers (codenamed Cheqqers). The concepts of superposition, entanglement, measurements and interference from quantum mechanics are integrated into the game of…

The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. This article presents a third, independent approach to solving parity games in…

Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…

Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…

In this paper, we will be proving mathematically that scoring play combinatorial game theory covers all combinatorial games. That is, there is a sub-set of scoring play games that are identical to the set of normal play games, and a…

The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call…