Related papers: A General Theorem for Non-Simultaneous Hat Guessin…
This paper studies asymmetric Ebert's Hat Problem with five players where the probability of the colors may be unequal. We obtain maximal winning probabilities and optimal winning strategies using the concept of adequate sets.
Prisoner's dilemma has been heavily studied. In classical model, each player chooses to either "Cooperate" or "Defect". In this paper, we generalize the prisoner's dilemma with a new alternative which is neither defect or cooperation. The…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
The Prisoners' Dilemma is perhaps the most famous model in the field of game theory. Consequently, it is natural to investigate its quantum version when one considers to apply quantum strategies to game theory. There are two main results in…
This paper explores the use of Generative Pre-trained Transformers (GPT) in strategic game experiments, specifically the ultimatum game and the prisoner's dilemma. I designed prompts and architectures to enable GPT to understand the game…
In Problem #1542 of Mathematics Magazine, Grossman and Turett define the Cantor game. In his 2007 Mathematics Magazine article about the Cantor game, Matt Baker proves several results and poses three challenging questions about it: Do there…
The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot succeed with probability greater than 1-ln2 \approx 0.31, no matter how many players are…
Synchronization, cooperation, and chaos are ubiquitous phenomena in nature. In a population composed of many distinct groups of individuals playing the prisoner's dilemma game, there exists a migration dilemma: No cooperator would migrate…
We study the Levine hat problem, a cooperative puzzle introduced by Lionel Levine in 2010, in which $n \geq 2$ players must simultaneously identify a black hat on their own infinite stack, each seeing only their teammates' stacks. While the…
I present the results from a spatial model of the prisoner's dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating ($C$) or defecting ($D$). Two strategies were tested, including ``tit-for-tat''…
Gallice and Monzon (2019) present a natural environment that sustains full cooperation in one-shot social dilemmas among a finite number of self-interested agents. They demonstrate that in a sequential public goods game, where agents lack…
We initiate the study of the hat guessing number of a graph where the adversary is only allowed to provide a proper coloring of the graph. This is the largest number $q$ for which there is a guessing strategy on each vertex that only…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
In the context of multiplayer games, the parallel repetition problem can be phrased as follows: given a game $G$ with optimal winning probability $1-\alpha$ and its repeated version $G^n$ (in which $n$ games are played together, in…
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.
We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T),…
In this paper I present a mathematically novel approach to the Prisoner's Dilemma. I do so by first defining recursively a distinct action type, what I call 'universalizing', that I add to the original prisoner's dilemma. Such a modified…
This paper presents research comparing the effects of different environments on the outcome of an extended Prisoner's Dilemma, in which agents have the option to abstain from playing the game. We consider three different pure strategies:…