Related papers: The three-colour hat guessing game on the cycle gr…
For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the…
Adversarial decision-making in partially observable multi-agent systems requires sophisticated strategies for both deception and counter-deception. This paper presents a sequential hypothesis testing (SHT)-driven framework that captures the…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
Cooperation among self-interested players in a social dilemma is fragile and easily interrupted by mistakes. In this work, we study the repeated $n$-person public-goods game and search for a strategy that forms a cooperative Nash…
In this paper we solve the three-player-game question. A three-player-game consists of a series of rounds. There are altogether three players. Two players participate in each round, at the end of the round the loser quits and the third…
We analyze the version of the deterministic Hats game. In this paper, we present new constructors, i.e. theorems that allow built winning strategies for the sages on different graphs. Using this technique we calculate the hat guessing…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
This paper considers a distributed gossip approach for finding a Nash equilibrium in networked games on graphs. In such games a player's cost function may be affected by the actions of any subset of players. An interference graph is…
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 $K_n$…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is…
The Game of Cycles is a combinatorial game introduced by Francis Su in 2020 in which players take turns marking arrows on the edges of a simple plane graph, avoiding the creation of sinks and sources and seeking to complete a "cycle cell."…
A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players uses a finite set of ad hoc strategies to make their decision, based on the past record. The…
In the concurrent graph sharing game, two players, called First and Second, share the vertices of a connected graph with positive vertex-weights summing up to $1$ as follows. The game begins with First taking any vertex. In each proceeding…
Indicated coloring is a graph coloring game in which two players collectively color the vertices of a graph in the following way. In each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly,…
The 1-2-3 Conjecture, posed by Karo\'{n}ski, {\L}uczak and Thomason, asked whether every connected graph $G$ different from $K_2$ can be 3-edge-weighted so that every two adjacent vertices of $G$ get distinct sums of incident weights. The…
We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the…
This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the…
We study concurrent graph games where n players cooperate against an opponent to reach a set of target states. Unlike traditional settings, we study distributed randomisation: team players do not share a source of randomness, and their…
In this paper we consider a distributed coordination game played by a large number of agents with finite information sets, which characterizes emergence of a single dominant attribute out of a large number of competitors. Formally, $N$…