Related papers: Computational Hardness of Multidimensional Subtrac…

We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…

One-clock priced timed games is a class of two-player, zero-sum, continuous-time games that was defined and thoroughly studied in previous works. We show that one-clock priced timed games can be solved in time m 12^n n^(O(1)), where n is…

We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…

Additive Cost Register Automata (ACRA) map strings to integers using a finite set of registers that are updated using assignments of the form "x := y + c" at every step. The corresponding class of additive regular functions has multiple…

We define the class of "simple recursive games". A simple recursive game is defined as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity…

We study the computational complexity of the Buttons \& Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for $C = 2$ colors but polytime solvable for $C = 1$.…

This paper studies a class of approach-evasion differential games, in which one player aims to steer the state of a dynamic system to the given target set in minimum time, while avoiding some set of disallowed states, and the other player…

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.

We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an…

In a recent arXiv-manuscript Fox studies infinite subtraction games with a finite (ternary) and aperiodic Sprague-Grundy function. Here we provide an elementary example of a game with the given properties, namely the game given by the…

Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…

Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…

Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many…

The exact complexity of solving parity games is a major open problem. Several authors have searched for efficient algorithms over specific classes of graphs. In particular, Obdr\v{z}\'{a}lek showed that for graphs of bounded tree-width or…

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…

A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm…

Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…

Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we…

We study the problem of solving matrix games of the form $\min_{\mathbf{p}\in\Delta}\max_{\mathbf{w}\in\mathcal{W}}\mathbf{p}^{\top}A\mathbf{w}$, where $A$ is a matrix and $\Delta$ is the probability simplex. This problem encapsulates…