Related papers: Cubic tic-tac-toe: A matching-based approach
In multi-player card games such as Skat or Bridge, the early stages of the game, such as bidding, game selection, and initial card selection, are often more critical to the success of the play than refined middle- and end-game play. At the…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
We consider the following two-player game, parametrised by positive integers $n$ and $k$. The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on $n$…
In game theory and multi-agent reinforcement learning (MARL), each agent selects a strategy, interacts with the environment and other agents, and subsequently updates its strategy based on the received payoff. This process generates a…
If $T$ is an $n$-vertex tournament with a given number of $3$-cycles, what can be said about the number of its $4$-cycles? The most interesting range of this problem is where $T$ is assumed to have $c\cdot n^3$ cyclic triples for some $c>0$…
Evolutionary $2 \times 2$ games are studied with players located on a square lattice. During the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability…
We analyse a sequential contest with two players in darts where one of the contestants enjoys a technical advantage. Using methods from the causal machine learning literature, we analyse the built-in advantage, which is the first-mover…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
Pointer-chasing is a central problem in two-party communication complexity: given input size $n$ and a parameter $k$, the two players Alice and Bob are given functions $N_A, N_B: [n] \rightarrow [n]$, respectively, and their goal is to…
The Traveling Tournament Problem(TTP) is a combinatorial optimization problem where we have to give a scheduling algorithm which minimizes the total distance traveled by all the participating teams of a double round-robin tournament…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this to create a two-player game. Given a fixed integer $n$ and an initial decomposition of $n = n F_1$, the two…
We consider a game in which players are the vertices of a directed graph. Initially, Nature chooses one player according to some fixed distribution and gives her a buck, which represents the request to perform a chore. After completing the…
In card games, in casino games with multiple decks of cards and in cryptography, one is sometimes faced with the following problem: how can a human (as opposed to a computer) shuffle a large deck of cards? The procedure we study is to break…
We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position,…
It is well known that in games with imperfect information, such as poker, bluffing with some probability can be a component of the optimal strategy. However, as far as we know, nobody has ever exhibited a Scrabble position in which the…
We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose…
The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, using such an agent involves the user exposing themselves to the risk that the…
Online learning in a decentralized two-sided matching markets, where the demand-side (players) compete to match with the supply-side (arms), has received substantial interest because it abstracts out the complex interactions in matching…
We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed…
Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…