Related papers: Query Complexity of Mastermind Variants

We consider the following Tur\'an-type problem: given a fixed tournament $H$, what is the least integer $t=t(n,H)$ so that adding $t$ edges to any $n$-vertex tournament, results in a digraph containing a copy of $H$. Similarly, what is the…

We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the…

A rank-3 Maker-Breaker game is played on a hypergraph in which all hyperedges are sets of at most 3 vertices. The two players of the game, called Maker and Breaker, move alternately. On his turn, maker chooses a vertex to be withdrawn from…

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…

We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his…

We develop a method that integrates the tree of thoughts and multi-agent framework to enhance the capability of pre-trained language models in solving complex, unfamiliar games. The method decomposes game-solving into four incremental tasks…

Attention is fundamental to cognition, yet it remains a challenge to understand attention in tasks approaching real-world complexity. Here, we approached this problem by modeling gaze patterns of monkeys playing Pac-Man. We first show a…

In the first-order query model for zero-sum $K\times K$ matrix games, players observe the expected pay-offs for all their possible actions under the randomized action played by their opponent. This classical model has received renewed…

We study the problem of online learning in Stackelberg games with side information between a leader and a sequence of followers. In every round the leader observes contextual information and commits to a mixed strategy, after which the…

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…

The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a…

Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…

Hunters and Rabbit game is played on a graph $G$ where the Hunter player shoots at $k$ vertices in every round while the Rabbit player occupies an unknown vertex and, if not shot, must move to a neighbouring vertex after each round. The…

The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…

In an influential paper, Erd\H{o}s and Selfridge introduced the Maker-Breaker game played on a hypergraph, or equivalently, on a monotone CNF. The players take turns assigning values to variables of their choosing, and Breaker's goal is to…

We study the unbiased WalkerMaker-WalkerBreaker games on the edge set of the complete graph on $n$ vertices, $K_n$, a variant of well-known Maker-Breaker positional games, where both players have the restriction on the way of playing.…

The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by…

We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of $j$ given losing coalitions into a set of $j$ winning coalitions.…

Let $H$ be a fixed graph on $n$ vertices. Let $f_H(G) = 1$ iff the input graph $G$ on $n$ vertices contains $H$ as a (not necessarily induced) subgraph. Let $\alpha_H$ denote the cardinality of a maximum independent set of $H$. In this…