Related papers: Computational bounds for the 2048 game

Lottery is a game in which multiple players take chances in the hope of getting some rewards in cash or kind. In addition, from the time of the early civilizations, lottery has also been considered as an apposite method to allocate scarce…

We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…

We investigate an algorithm that assigns to any game in normal form an approximating game that admits an ordinal potential function. Due to the properties of potential games, the algorithm equips every game with a surrogate reward structure…

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…

A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

Weighted timed games are played by two players on a timed automaton equipped with weights: one player wants to minimise the accumulated weight while reaching a target, while the other has an opposite objective. Used in a reactive synthesis…

We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant…

Tetravex is a widely played one person computer game in which you are given $n^2$ unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a $n$ by $n$ square such that all neighbouring edges are…

An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

Policy-based methods with function approximation are widely used for solving two-player zero-sum games with large state and/or action spaces. However, it remains elusive how to obtain optimization and statistical guarantees for such…

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…

We investigate zero-sum turn-based two-player stochastic games in which the objective of one player is to maximize the amount of rewards obtained during a play, while the other aims at minimizing it. We focus on games in which the minimizer…

Probabilistic timed automata are a suitable formalism to model systems with real-time, nondeterministic and probabilistic behaviour. We study two-player zero-sum games on such automata where the objective of the game is specified as the…

We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…

We study the problem of optimal games for the solo and coop modes of the board game Room 25 (season 1). We show that the game cannot be won in a single turn for any starting configuration, but that it can be done in two for some…

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…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…