Sharif Digital Repository

We consider a special class of Congestion Games enhanced with a notion of time.Network Routing problems, such as road traffic networks, computer neworks, and evacuation problems are some applications of this class of games. Two subclasses of these games, namely atomic and non-atomic is considered in this article, both of them introduced in 2009. Some of the existing results are Nash equilibria existence proof for “single-source single-sink” case, and a mechanism for improving price of anarchy in the non-atomic subclass. There are also some results in the atomic subclass of this game.We extend both models of atomic and non-atomic subclasses to “multi-source,multi-sink” configurations. We call... 

In electrical energy market, an economic game is running in which, power generating companies compete with each other in order to determine their suitable strategies and gain the highest possible profit. The literature shows the researchers actually use different algorithms to determine their suitable strategies but not Nash equilibrium method. These algorithms can not guarantee that the strategic equilibrium points can be found. In this research, the classic Nash method is used to determine GENCOs appropriate strategies and is simulated on some well known models (Cournot, Supply function equilibrium (SFE) and Bertrand), combined energy and reserve markets will be studied. The results of... 

The problem of developing optimal pricing and inventory allocation strategies has been extensively studied over the past two decades. However, most of the literature in this area assumes that customers are myopic price-takers, and do not respond to firm pricing strategically. In this study, we present review on a class of problems that consider a firm selling a finite number of items over a finite time horizon facing stochastic demand and a group of customers who act strategically by timing their purchases. We first review the optimal purchasing policy for the customers, and pricing policy for the firm that is the best response policy to the customer’s strategic behavior. Then we present a... 

In literature, substantial works have been done on supply chain coordination. The majority of these works looking for a mechanism that enforces the supply chain members to follow strategies that produce the equilibria of an integrated supply chain, and most of this literature ignores competition between supply chains. In this thesis, we consider two distinct supply chains which compete to each other on the price. We present a method to calculate the equilibria for three structural forms. In the first form, two supply chains are integrated and in the second form, one of the supply chains is integrated and the other one is decentralized. Finally in the third form, both supply chains are... 

Groups are important elements in social networks. First of all, because in real life human beings are members of different groups from the begining of their life till their death and even more. Moreover, groups’ influence on people and on other groups are undeniable. Thus studying groups in the context of social networks is of a great importance. In this Thesis, we are trying to make an effort in proposing a model for group membership. We discuss two models here: in the first model we consider a set of groups and a set of people, each of which want to gain membership of a subset of the groups’ set in order to maximize their payoff. We neglect the relationships between people and their... 

In this thesis, we consider a network creation game in which, each player (vertex) has a limited budget to establish links to other players. In our model, each link has a unit cost and each agent tries to minimize its cost which is its local diameter or its total distance to other players in the (undirected) underlying graph of the created network. Two variants of the game are studied: in the MAX version, the cost incurred to a vertex is the maximum distance between that vertex and other vertices, and in the SUM version, the cost incurred to a vertex is the sum of distances between that vertex and other vertices. We prove that in both versions pure Nash equilibria exist, but the problem of... 

We consider a network creation game in which, each player(vertex) has bounded budget to draw edges to other vertices. Each player wants to minimize its local diameter in MAX version, and its sum of distances to other vertices in SUM version.
In this thesis, we first prove that the problem of finding the best response for each player in this network creation game, is NP-Hard. But we show that always there exists a Pure Nash Equilibria for each of the versions. Then we focus on the diameter of equilibrium graphs. In Unit Budget case (when each player’s budget is one) we show that the diameter of each equilibrium graph in O(1), and always there exists a Mixed Nash Equilibirum. For each n,... 

In this thesis, first we will have a thorough review on problems and models presented in the field of contagion in networks (spread of diseases, spread of computer viruses,etc.). Then we will investigate the basic model of virus inoculation game with purely selfish players and the modified version of it which takes into account a factor of friendship. We will discuss the results of these models including computing and comparing Nash Equilibria  

Game theory is widely used to model diverse phenomena in the real world such as people’s behavior in elections and auctions. It also has natural applications to some other areas such as computer networks, cryptography, and security. In this thesis, we present a general approach to model two important classes of optimization problems, namely, covering and packing problems, using game theory concepts. This model provides an integrated language to explain the problems, and enables us to use game-theoretic tools to further explore and analyze the problems. In our proposed model, the optimum solutions of the modeled problem are always one of the equilibria of the game. Therefore, one can find... 

Nowadays economical issues are greatly taken into consideration. In this project we aim to study a problem of this area, which focuses on the subject of location allocation and pricing strategy for a good supplier. Solution evaluation is done by taking costumer demand into account. This problem has a sequential characteristic. That is players do not take their decisions at the same time. Suppliers should first decide about where and how they plan to provide their goods. On the other hand almost every economical problem have multiple players who play with or against each other. Therefore modeling this problem using Stackelberg leadership model is a natural choice. Since this problem is in the... 

With the daily increase in the volume of information and due to the growth and pervasiveness of wireless networks, the structures and the way of connection of intermediate nodes have become very important in terms of energy, communication speed and communication overhead. In this thesis, we examine the structure of directionless wireless networks assuming nodes are selfish. In these networks, nodes seek to minimize their costs while being required to access all nodes with limited path length. Due to the selfishness of nodes, we used game theory to analyze the structure and behavior of nodes by calculating the Nash equilibrium state and to compare these networks with networks that are managed... 

Conflict-free coloring problem is one of the computational geometry problems that has been studied in the last two decades. The root of this problem comes from the frequency assignment to cellular networks problem. In that research, we have a cellular network containing several regions in two-dimensional plane and we want to assign a frequency to each of the regions so that if we look at any intersection of them, there is a region with a unique color compared to other regions of that intersection. In other words, a person’s cellular phone in the range of some regions (in the intersection of them) would be able to connect to one antenna with a unique frequency and function properly. This...