Related papers: Backgammon is Hard
The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…
We consider the following modification of annihilation game called node blocking. Given a directed graph, each vertex can be occupied by at most one token. There are two types of tokens, each player can move his type of tokens. The players…
We consider the computational complexity of Hearthstone which is a popular online CCG (collectible card game). We reduce a PSPACE-complete problem, the partition game, to perfect information Hearthstone in which there is no hidden…
The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game…
The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
Poker is a large complex game of imperfect information, which has been singled out as a major AI challenge problem. Recently there has been a series of breakthroughs culminating in agents that have successfully defeated the strongest human…
In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…
In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…
Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…
We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval…
In his list of open problems, Martin Erickson described a certain game: "Two players alternately put queens on an n x n chess board so that each new queen is not in range of any queen already on the board (the color of the queens is…
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…
We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…
The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…
Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in…
We present a Monte Carlo simulation study of the Bhikar-Sawkar card game, a non-deterministic game structurally similar to the classic Beggar-My-Neighbour, which is fully deterministic. Although both games share a common setup, key…
Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…