Game theory is defined as “the study of the ways in which strategic interactions among economic agents produce outcomeswith respect to thepreferences of those agents, where the outcomes in question might have been intended by none of the agents” by the Stanford Encyclopedia of Philosophy (Ross 1997). The disciplines most involved in game theory “are mathematics, economics and the other social and behavioral sciences” (McCain 1997). Game theory was created to confront the problem and provide a theory of economic and strategic behavior. In game theory, "games" have always been a metaphor for more serious interactions in human society. But game theory addresses the serious interactions using the metaphor of a game: in these serious interactions, as in games, the individual's choice is essentially a choice of a strategy, and the outcome of the interaction depends on the strategies chosen by each of the participants (McCain1997). John von Neumann a great mathematician founded game theory. The legend of John Von Neumann gives a good insight on who John Von Neumann was and his theory. John von Neumann was a child prodigy, born into a banking family in Budapest, Hungary, “when he was only six years old he could divide eightdigit numbers in his head; by 8 he had mastered calculus and by 12 he was at the graduate level in mathematics” (Halmos 1973). In 1926, at 23, he received a degree in chemical engineering in Zurich and a Ph.D. in mathematics in Budapest. From the start, mathematics provided well enough for him he quickly gained a reputation in set theory, algebra, and quantum mechanics (Halmos 1973). The start of World War II greatly changed his area of interest. According to Halmos “during and after the war, he became one of the best applied mathematicians. John von Neumann's furthered his expertise in hydrodynamics, ballistics, meteorology, game theory, and statistics". By the latter years of World War II von Neumann was playing the part of an executive management consultant, serving on several national committees, and applying his amazing ability to rapidly see through problems to their solutions. Through this means he was also a conduit between groups of scientists who were otherwise shielded from each other by the requirements of secrecy (Halmos.P, 1973). Game theory was developed in order. In the article A Chronology of Game Theory by author Paul Walker it is clear to say that in 1928 modern game theory began then was backed up with more research in 1944. In 1928 with the idea regarding the existence of mixedstrategy equilibrium in twoperson zerosum games and its proof by John von Neumann; he proved the minimax theorem in his German article "ZurTheorie der Gesellschaftsspiele" which reads "On the Theory of Parlor Games" in English (Walker 2005). Within the article it stated that “every two person zerosum game with finitely many pure strategies for each player is determined, ie: when mixed strategies are admitted, this variety of game has precisely one individually rational payoff vector” (Walker 2005). The paper also introduced the extensive form of a game. In 1944 the Theory of Games and Economic Behavior was published by John von Neumann and Oskar Morgenstern, the book contained work in areas of game theory such as the notion of a cooperative game, transferable utility, its coalitional form and its von NeumannMorgenstern stable sets (Walker 2005). It was also the account of axiomatic utility theory given that led to its wide spread adoption within economics. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decisionmaking under uncertainty (Hamos 1973). According to McCain “games have been a scientific metaphor for a much wider range of human interactions in which the outcomes depend on the interactive strategies of two or more persons, who have opposed or at best mixed motives” (McCain 1997). Game theory is often...
... 2012 
 Application Of GameTheory to Business: Preliminary Findings for Term paper
Saurabh Mandhanya 11p164Rajat Barve 11p157Shashank Gupta 11p166Deepak Bansal 11P133Padmini Narayan 11p152Lizanne Marie Raphael 11P025 
[ The Kargil War: Analysis and Learning Through GameTheory ] 

Introduction
India and Pakistan have been involved in conflict over Kashmir since Independence. It has led to numerous wars and attacks. The relations and wars over Kashmir can be studied using GameTheory. Tit for Tat policy has been practiced by both nations. The pay of for wars for both countries has been changing depending on the context. This context has been based on many parameters –
1. Ally countries – US and China are widely regarded as Pakistan allies. China has been against India due to border issues. USSR has been traditionally supporting India until recently. The situation keeps on changing with changing stance of allies.
2. International support  International communities like UN tries to solve the conflict through negotiations.
3. Military strength – It keeps on changing depending upon development and purchase of weapons on both sides.
4. Resources including financial and others – India has always been in a relatively better position due to more available resources.
5. Leadership of both countries especially of Pakistan (Army Rule) – Army Rulers might...
...110976
MOSES NGONE 10
PRESENTED TO: Mr. MORIASI MARANGA
DUE DATE: 29TH OCTOBER 2013
DEPARTMENT OF COMMERCE
SCHOOL OF BUSINESS AND ECONOMICS
ATHIRIVER CAMPUS
Table of Contents
GameTheory 3
History and impact of gametheory 5
Gametheory and information systems 6
Definition of key terms 6
Dominance 8
Nash equilibrium 8
Mixed strategies 9
Extensive games with perfect information 9
Extensive games with imperfect information 10
Zerosum games and computation 11
Bidding in auctions 12
GameTheoryGametheory is the formal study of conflict and cooperation. Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals,
groups, firms, or any combination of these. The concepts of gametheory provide a language to formulate structure, analyze, and understand strategic scenarios.
The object of study in gametheory is the game, which is a formal model of an interactive situation. It typically involves several players; a game with only one player is usually called a decision problem. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these influence the...
...Game Theoretic Methods for the Smart Grid
Walid Saad1 , Zhu Han2 , H. Vincent Poor3 , and Tamer Basar4 ¸
1 2
Electrical and Computer Engineering Department, University of Miami, Coral Gables, FL, USA, email: walid@miami.edu Electrical and Computer Engineering Department, University of Houston, Houston, TX, USA, email: zhan2@mail.uh.edu 3 Electrical Engineering Department, Princeton University, Princeton, NJ, USA, email: poor@princeton.edu 4 Coordinated Science Laboratory, University of Illinois at UrbanaChampaign, USA, email: basar1@illinois.edu
arXiv:1202.0452v1 [cs.IT] 2 Feb 2012
Abstract The future smart grid is envisioned as a largescale cyberphysical system encompassing advanced power, communications, control, and computing technologies. In order to accommodate these technologies, it will have to build on solid mathematical tools that can ensure an efﬁcient and robust operation of such heterogeneous and largescale cyberphysical systems. In this context, this paper is an overview on the potential of applying gametheory for addressing relevant and timely open problems in three emerging areas that pertain to the smart grid: microgrid systems, demandside management, and communications. In each area, the stateoftheart contributions are gathered and a systematic treatment, using gametheory, of some of the most relevant problems for future power systems is provided. Future...
...consult the experts of the gametheory at this point. In the 1980’s Axelrod and Hamilton worked on a famous problem in the gametheory, the Prisoner’s Dilemma, exactly because it deals with this problem. The rational pursuit of individual selfinterest drives everybody into an outcome that is not favored by anybody. Imagine two partners in a crime being interrogated at the same time. Each one has two options, cooperate with the other and keep quiet or betray the other and confess. Case C, we can say, is if both cooperate then the police cannot get much out of them and they will both get a light sentence (2 years); if one defects and the other keeps quiet then the traitor will get an even lighter sentence (1 year) – this is case B. If the one who cooperates gets the longest sentence (10 years), this is the worst end of the deal and we can call this case S. In a case when both betray one another they will both get a sentence (6 years) longer than if they had cooperated but lighter than if one had kept quiet and the other spoke, and this is case D.
Out of the four outcomes, B is the best and S is the worst from an individualistic point of view, while the order of preference is B, C, S, D. We should realize that this is a nonzero sum game. In a zerosum game, my loss is your gain; for example, if we are trying to divide a certain amount of money in the bank into two, anything over fifty...
...marksRevision materials on the Economics blog: AS Micro  AS Macro  A2 Micro  AS Macro A2 Markets & Market Systems Oligopoly  GameTheory 

“When I am getting ready to reason with a man I spend onethird of my time thinking about myself and what I am going to say, and twothirds thinking about him and what he is going to say.”
Abraham LincolnA game occurs when there are two or more interacting decisiontakers (players) and each decision or combination of decisions involves a particular outcome (payoff.) The fate (or the payoff) of a player in a game depends not only on the actions of that player but also on the other players!The Monty Hall problem!
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number 3, which has a goat. He says to you, “Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors?
Possible answer to the Monty Hall problemGame theory is mainly concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions. The Prisoners’ DilemmaThe classic example of gametheory...
...Consider a firm that is contemplating entry into a new market. What
contribution, if any, can gametheory make to the analysis of the economic
viability of such a strategy? Refer to the critical time line, reaction functions
and the Nash premise in your reply.
Introduction:
Management decisions lack the full information, so they are bounded rationality decisions.
Companies are players in a game, and the game dimensions are defined in terms of geography and product. So any new entrant will try to enter the market he will play a game in two dimensions geography and product (example Apple entering the smart phone market).
The entrant has to decrease its price from the market price so he can guarantee a portion of the market share (steal market share from the incumbents).
The incumbents have two options: either to compete or to accommodate.
We introduce the principles of the GameTheory as follows:
Critical Timeline:
Management can observe behaviour as signals and as patterns in the signals.
Patterns do emerge in the observed behaviour, patterns in price movements or patterns to do with achieving growth through acquisition. The patterns create a critical timeline (CTL) of observed actions and as the CTL unfolds, it reveals a strategy.
The new entrant has to observe these patterns and management types of the incumbents over a considerable CTL, to...
...GameTheory
International Business Management
Preface
Since GameTheory is a tool used to analyze strategic behavior by taking into consideration how participants expect other to behave I thought about an everyday example in my life. I wanted to analyze my job at the bar and take into account some independent parties that compete with me. Since it’s not my choice who my boss will hire or fire I was interested in how each decisions outcome would be for the corresponding parties. What would be my benefits, considering different situations?
The game begins:
To finance my studies I work as a waitress in a bar. Usually, the bar is very crowded and it is difficult to serve all the guests. It is a tough job and sometimes very exhausting but serving all the guests is still doable. Nevertheless my boss realized that doable doesn’t mean high quality service. Due to the delay in receiving their order, customers sometimes complain to the boss. My boss is now in dilemma what to do. He could either replace me with a new waitress, hoping for better quality service with her, or he could hire a new waitress to support me in serving the customers and therefore have 2 waitresses serving. However, he knows the delay is most probably due to crowded bar and not due to lack of knowledge and skills form my side, he is having in mind to get a second waitress and have two waitresses, which will...
...GameTheory and Economic
Analysis
GameTheory and Economic Analysis presents the wide range of current contributions of gametheory to economics. The chapters fall broadly into two
categories. Some lay out in a jargonfree manner a particular branch of the
theory, the evolution of one of its concepts, or a problem that runs through
its development. Others are original pieces of work that are signiﬁcant to
gametheory as a whole.
After taking the reader through a concise history of gametheory, the
contributors discuss such topics as:
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the connections between Von Neumann’s mathematical gametheory and
the domain assigned to it today since Nash
the strategic use of information by game players
the problem of the coordination of strategic choices between independent players in noncooperative games
cooperative games and their place within the literature of games
incentive and the implementation of a collective decision in gametheoretic modeling
team games and the implications for ﬁrms’ management.
The nature of the subject and the angle from which it is examined will ensure
that GameTheory and Economic Analysis reaches a wide readership. As an
established...