Related papers: The complexity of UNO

This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational…

Boolean games are a succinct representation of strategic games wherein a player seeks to satisfy a formula of propositional logic by selecting a truth assignment to a set of propositional variables under his control. The framework has…

This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated…

We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…

Poker is one of the most popular card games, whose rational investigation represents also one of the major challenges in several scientific areas, spanning from information theory and artificial intelligence to game theory and statistical…

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…

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…

Many of the famous single-player games, commonly called puzzles, can be shown to be NP-Complete. Indeed, this class of complexity contains hundreds of puzzles, since people particularly appreciate completing an intractable puzzle, such as…

In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a…

We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…

We investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters…

Unique Sink Orientations (USOs) are an appealing abstraction of several major optimization problems of applied mathematics such as for instance Linear Programming (LP), Markov Decision Processes (MDPs) or 2-player Turn Based Stochastic…

Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…

We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…

We study the combinatorial two-player game Tron. We answer the extremal question on general graphs and also consider smaller graph classes. Bodlaender and Kloks conjectured in [2] PSPACE- completeness. We proof this conjecture.

In this paper we experiment with a 2-player strategy board game where playing models are evolved using reinforcement learning and neural networks. The models are evolved to speed up automatic game development based on human involvement at…

We study the complexity of computing stationary Nash equilibrium (NE) in n-player infinite-horizon general-sum stochastic games. We focus on the problem of computing NE in such stochastic games when each player is restricted to choosing a…

The UNIQUE GAMES problem is a central problem in algorithms and complexity theory. Given an instance of UNIQUE GAMES, the STRONG UNIQUE GAMES problem asks to find the largest subset of vertices, such that the UNIQUE GAMES instance induced…

We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…

We study the complexity of computing a uniform Nash equilibrium on a non-win-lose bimatrix game. It is known that such a problem is NP-complete even if a bimatrix game is win-lose (Bonifaci et al., 2008). Fortunately, if a win-lose bimatrix…