General Tit-For-Tat Strategy in The Three Players Prisoner’s Dilemma Game

Tit-For-Tat Strategy which introduced by Robert Axelrod is a highly effective strategy in the iterated Prisoner’s Dilemma. Most game theory research on the prisoner's dilemma has focused on two players, but it is possible to create a Prisoner’s Dilemma involving three or even more players. In this Paper, we discuss a prisoner's dilemma game involving three players which is infinitely iterated “iterated three player Prisoner’s Dilemma game (I3PD)”. The all possible strategies which depend on the previous outcomes are represented by finite state of automata. Four different new strategies are presented in order to discuss the general Tit-For-Tat concept in details, and we the compute the all payoff values for these strategies with the strategy ALLC and the strategy ALLD

Spectra of Some Simple Graphs

We consider a finite undirected and connected simple graph  with vertex set  and edge set . The spectra of some special simple graphs and different types of their matrices are discussed to represent a graph. In this discussion we are interested in the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and seidel adjacency matrix. Keywords: Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, seidel adjacency matrix, spectral. Mathematics Subject Classi?cation: 05C5

General Tit-For-Tat Strategy in The Three Players Prisoner’s Dilemma Game

Tit-For-Tat Strategy which introduced by Robert Axelrod is a highly effective strategy in the iterated Prisoner’s Dilemma. Most game theory research on the prisoner's dilemma has focused on two players, but it is possible to create a Prisoner’s Dilemma involving three or even more players. In this Paper, we discuss a prisoner's dilemma game involving three players which is infinitely iterated “iterated three player Prisoner’s Dilemma game (I3PD)”. The all possible strategies which depend on the previous outcomes are represented by finite state of automata. Four different new strategies are presented in order to discuss the general Tit-For-Tat concept in details, and we the compute the all payoff values for these strategies with the strategy ALLC and the strategy ALLD

Domination in Isosceles Triangular Chessboard

In this article, we are interested in the domination problem in isosceles triangular chessboard. In our study we take in account one type of piece of rooks, bishops and kings, and two different types of pieces together, kings with rooks, kings with bishops and rooks with bishops. The chessboard in this work is isosceles triangular with square cells. Also in most cases we determine the possible number of different methods of domination (total solution). Keywords: domination, Isosceles triangle chessboard, Kings, Bishops and Rooks

Review Article: Game Theory with Neutrosophic Application

The number of research papers focusing on applications of game theory, as well as applications on Neutrosophic, has increased significantly in recent years. These applications may fall into different fields such as: economics, politics, social sciences, and others. This paper presents some of the work that has been done on these two topics, starting with a background in game theory, followed by moving on to the concept of fuzzy sets and neutrosophic sets, and then bringing us to some research papers with different applications in these two topics. The final part of the paper uses the two major scientific databases (Web of Science and Scopus) to analyze the work by topic, country, years, etc. The analysis shows that there is a significant gap in the research conducted in the field of game theory with neutrosophic applicatio

The Trembling Hand Approach to Automata in Iterated Games

We consider two state automata playing infinitely iterated two players, two strategies game, where each move can be mis-implemented (or mis-perceived) with a small error probability, and compute the payoff matrix by means of a perturbation approach. Keywords: Alternating Prisoner's Dilemma, Perturbed Payoff, Repeated Games, Simultaneous Prisoner's Dilemma

On Congruences of Principal GK2-Algebras

We investigate some features of principal GK2-algebras (PGK2-algebras). Necessary and sufficient conditions for a principal GK2- algebra to have 2-permutable congruences are obtained. Furthermore, it is established how 2-permutable congruences are characterized using pairs of principal congruences. Also, a generalization of the 2-permutability of the primary congruences of the GK2-algebras concept to the concept of the n-permutable congruences is provided. We round off with strong extensions of principal GK2 -algebras

Monitor Reaction of Win Stay-Lose Shift Strategies in Iterated Three-Player Prisoner’s Dilemma Game

In this paper, we present an extension model of Prisoner’s Dilemma game, but with three players. We are interested in introducing this model and providing an analysis of competitions of some special types of strategies which have properties of Win Stay-Lose Shift. Therefore, we will show the best one among them and the largest one in the payoff through some graphs by using some numerical values. Also, we will discuss the effect of relatedness between players on the behavior of strategies

A Multi-Criteria Model for Sustainable Development Goals Using Fuzzy Goal Programming-Application for Egypt

This article proposes fuzzy goal programming model that combines optimal resource allocation with prospective goals for economic development, electricity consumption, employment, and greenhouse gas emission reduction in Egypt’s primary economic sectors. The presented model analyses the prospects for improvement, the effort required, and the implementation of sustainable development strategies. The model also offers valuable insights to decision makers for both strategic planning and investment allocations towards sustainable development. We validate the model by applying it to Egypt’s important economic sectors to meet the country’s 2030 sustainable development goals

Analyzing Related Strategic Behavior Through Strictly Alternating Interactions with Two-Memory Length

Reciprocal altruism can often be modeled through the iterated Prisoner’s Dilemma game in which players take turns in the roles of donor and recipient. Several late studies were based on memory alteration in the repeated Prisoner’s Dilemma game. This prompted us to study this alteration in a strictly alternating iterated Prisoner’s Dilemma game. In our work, we represented the repeated games played by finite states of automata. Also, we supposed that there is relatedness between the players in this game. A relatedness average degree r considered between players, where 0 ≤ r ≤ 1. The effect of noise on the relatedness degree among players can be examined with regard to the behavior of the strategies in their competitions