Related papers: Othello is Solved
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then…
Since the advent of AI, games have served as progress benchmarks. Meanwhile, imperfect-information variants of chess have existed for over a century, present extreme challenges, and have been the focus of decades of AI research. Beyond…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for…
Blackwell games are infinite games of imperfect information. The two players simultaneously make their moves, and are then informed of each other's moves. Payoff is determined by a Borel measurable function $f$ on the set of possible…
We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. This enables the solution of known positions so far (up to the 10 x 10 board) much quicker…
Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all…
Hex is a turn-based two-player connection game with a high branching factor, making the game arbitrarily complex with increasing board sizes. As such, top-performing algorithms for playing Hex rely on accurate evaluation of board positions…
We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…
Something is definitely wrong. If the game has a linear winning strategy, then it is tractable. What's going on? Well, we describe a two-person game which has a definite winner, that is, a player who can force a win in a finite number of…
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 improve the complexity of solving parity games (with priorities in vertices) for $d={\omega}(\log n)$ by a factor of ${\theta}(d^2)$: the best complexity known to date was $O(mdn^{1.45+\log_2(d/\log_2(n))})$, while we obtain…
Wordle is a single-player word-based game where the objective is to guess the 5-letter word in a maximum of 6 tries. The game was released to the public in October 2021 and has since gained popularity with people competing against each…
Tasks of different nature and difficulty levels are a part of people's lives. In this context, there is a scientific interest in the relationship between the difficulty of the task and the persistence need to accomplish it. Despite the…
The design of fair voting rules has been addressed quite often in the literature. Still, the so-called inverse problem is not entirely resolved. We summarize some achievements in this direction and formulate explicit open questions and…
The Colonel Blotto game, first introduced by Borel in 1921, is a well-studied game theory classic. Two colonels each have a pool of troops that they divide simultaneously among a set of battlefields. The winner of each battlefield is the…
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…