Related papers: Impartial Chess on Integer Partitions

We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…

We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate…

We introduce a new type of positional games, played on a vertex set of a graph. Given a graph $G$, two players claim vertices of $G$, where the outcome of the game is determined by the subgraphs of $G$ induced by the vertices claimed by…

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for…

We generalize the results and conjectures of Tam\'{a}s Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of…

We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian…

We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…

We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen's result can be…

Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic. In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized. The…

We introduce $p$-adic manifold learning, propose an algorithm to solve it, and propose benchmark tasks from impartial games.

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 game subset take-away begins with a simplicial complex \Delta. Two players take turns removing any element of \Delta as well as all other elements which contain it, and the last player able to move wins. Graph Chomp is a special case of…

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,…

Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study…

The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…

Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms.…

We provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games with general type spaces, using a version of interim correlated rationalizability. We then focus on the case in which…

We consider learning to play multiplayer imperfect-information games with simultaneous moves and large state-action spaces. Previous attempts to tackle such challenging games have largely focused on model-free learning methods, often…

This paper contributes a new class of games called spacetime games with perfect information. In spacetime games, the agents make decisions at various positions in Minkowski spacetime. Spacetime games can be seen as the least common…

The article describes a model of chess based on information theory. A mathematical model of the partial depth scheme is outlined and a formula for the partial depth added for each ply is calculated from the principles of the model. An…