...notes Game Theory Game Theory can be regarded as a multi-agent decision problem. Which means there are many people contending for limited rewards/payoffs. They have to make certain moves on which their payoff depends. These people have to follow certain rules while making these moves. Each player is suposed to behave rationally. Rationality: In the language of Game Theory rationality implies that each player tries to maximize his/her payoff irrespective to what other players are doing. In essence each player has to decide a set of moves which are in accordance with the rules of the game and which maximize his/her rewards. Game Theory can be classified in two branches 1. Non co-operative game theory : In this case the players work independently without assuming anything about what other players are doing. 2. Co-operative game theory: Here players may co-operate with one another. Game Theory has found applications in Economic, Evolutionary Biology, Sociology, Political Science etc, now Its finding applcations in Computer Science. What is a game? A game has the following 1. 2. 3. 4. 5. Set of players Set of rules Set of Strategies Set of Outcomes. Pay off D = { Pi | 1 <= i <= n} R Si for each player Pi O ui (o) for each player i and for each outcome o e O Example 1{Coin Matching Game} Coin Matching Game : Two players choose independently either Head or Tail and report it to a central authority. If both choose the same side of the coin , player 1 wins, otherwise 2 wins. A game has...
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...MOULIN Pierre Under The direction of Per Axelson 3 novembre 2013 ! ! ! ! ! An introduction to « Game Theory », and its applications. ! ! ! ! IBMEC - EM Strasbourg Business School ! ! ! ! ! ! ! GAME THEORY "1 SUMMARY ! ! ! ! ! A brief introduction to the origins of the Game Theory……………..…3 What is a game ?………………………………………………………….……4 What is the purpose of a game ?……………………………………….….….….4 What defines a game ?…………………………………………….…….…….….4 Typology of the actual know games………………………….……….……….…4 How can we represent a game ?……………………….………….………….…..5 Strategies and actions in a game…………………….………………….…..6 Dominant/Dominated Strategies…………………….……………………….….6 Mixed Strategies……………………………………………………………….…6 Notion of The Pareto Optimum…………………………………………………7 A complete, concrete (and classic) example : The Prisoner’s Dilemma………….7 Commitment & Credibility………………………………………………………8 A concrete example of a commitment problem…………………………………9 Conclusion…………………………………………………………………….10 Sources………………………………………………………….…………..…11 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! GAME THEORY "2 A/ A brief introduction to the origins of the Game Theory… ! What is Game Theory ? It is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. An alternative term would probably be Interactive Decision Theory. Even if this concept is, basically, pure economics, today we can see it in various range of application, from political science to psychology...
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...Game Theory in Business Decision | | | Content 1. Introduction -------------------------------------------------------------------- P.2 2. Main Models of Game Theory ---------------------------------------------- p.3-4 3. Nash Equilibrium ------------------------------------------------------------- p.5 4. Dominant Strategy ----------------------------------------------------------- p.5 5. Prisoners’ Dilemma ---------------------------------------------------------- p.5-6 6. Daily Example of Competition of Supermarkets ------------------------ p.7-8 7. Daily Example of Competition of Mobile Market ---------------------- p.9-10 8. Daily Example of Penalty Kick in Football Match --------------------- p.11-12 9. Conclusion ------------------------------------------------------------------- p.13 10. Reference -------------------------------------------------------------------- p.14-15 Introduction Game theory is the study of how people behave in strategic situations. Game theory concerns situations in which multiple players make strategically interdependent decisions. The term interdependent means that one person’s behavior affects another person’s well-being. We can make use of game theory on different aspects such as economics, political science and even our daily life. For example, whether TV stations leads to enlarge the market shares on program production usually depends on the subsequent moves...
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...FT 6202: Management Science (2012-2013) Class 1: Introduction to Transportation Problem Re-cap of linear programming, Classic transportation problem, LP formulation, Solution using MS Excel Text: BRS 5.1, 5.2, 5.3 Class 2: Transportation Problem (cont.) Basic feasible solution of TP, properties, Analysis of Excel output, Sensitivity analysis Text: BRS 5.1, 5.2, 5.3 Class 3: Transshipment problem Formulation of LP model, different variations (unbalanced case, combining with production scheduling, multi-modal and multi-SKU transportation), Conversion of transshipment model into classic transportation model. Text: BRS 5.4, 5.5 Class 4: Assignment problem Binary ILP formulation, solution by Hungarian method Text: BRS 5.6 Class 5: Network models Shortest path problem, Minimal spanning tree Text: BRS 5.8, 5.9 Class 6: Game theory Introduction to game theory: Types of game, Two person zero-sum game, concept of saddle point, dominance rule Text: WW 14.1, 14.2 Class 7: Game theory (contd.) Mixed startegy, Linear programming formulation Text: WW 14.2, 14.3 Class 8: Mid-term Test Class 9: Markov chain Introduction to stochastic processes, markov chains, transition probability matrix, steadystate probabilities. Text: Handouts and WW 17.1, 17.2, 17.3 Class 10: Decision theory Decision making under uncertainty, Decision criteria, Decision Tree Text: BRs 8.1, 8.2, 8.3, 8.4, 8.6 Class 11: Decision theory (contd.) Decision making under risk, EVPI, EVSI Text: 8.5, 8.8, 8.9 Class 12: Travelling...
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...in solving problems in different functional domain of business. It also helps to optimize business operations/processes. The Quantitative Method-II tools act as aids to decision makers to take best decision for effective & efficient use of resources which ultimately lead to profit maximization or to achieve multiple goals or objective. | Course must be aligned with a strategic objective of the program Prerequisites/Co-requisites | Quantitative Methods I | Learning Objectives | To learn basic optimization techniques and their managerial applications with a focus on methodologies such as Linear Programming, Transportation models, Assignment Models, Transhipment Models, Games Theory, Queuing Models, Goal Programming, Integer Programming, Non-linear Programming, Simulation and Decision Theory. | Learning objectives must be aligned with learning outcomes of the course Teaching Methods | Modeling, Case study, Software-based solutions | Refer academic policies and procedures handbook For Internal Use Only Session Plan* | SESSION-1: Overview on Operations Research modelling (OR modelling): meaning, definition, steps involved in OR modelling; Session-2: Overview on Linear Programming (LP): LP meaning, various applications,...
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...In a game theoretic perspective: Ghemawat, in his article talks about the strategies that companies need to adopt when they want go international. The actions that companies take to achieve this can be linked with the game theory. Every company tries to adopt strategies to gain a competitive edge in the market. And game theory talks about what kind of approaches they can take to direct success and profit towards themselves and increase their hold in the market. We can try to link every move of a company to one of the factors in the game theory namely changing the player, changing the Added value, changing the rules, changing the tactics and changing the scope. This might result in a win-win or win-lose relationship between companies. In addition to this few companies also adopt strategies that change the entire game that they play in the market. Let us take the example of one of the companies that tried to adopt Arbitrage, as pointed out by Ghemawat, TCS managed to beat out its Indian competitors and won the deal with ABN AMRO which generated more than hundred million dollars to the company. TCS was able to achieve this largely because it was the only Indian vendor positioned to deploy several hundred professionals to meet the application development and maintenance needs of ABN AMRO. TCS’s huge bench strength was the added advantage in this game. Thus TCS played the game of changing its added value. TCS managed to increase its added value in the IT market by have hundreds of...
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...Game theory is a concept of decision making that considers more elements beyond just benefits minus costs. Specifically, it includes the interaction between participants. In economics, the theory attempts to predict the participants’ optimal decisions. It has found a core place in economic decision-making and policy-making for its inherent ability to predict reactions in resource allocation, business negotiation, and other economic aspects. Game theory is mostly associated with decision-theory and other contexts such as cooperation and negotiations. From its definition, it is evident that the game theory is largely used in the study of the human decision making processes. In psychology, its equivalent is known as the theory of social situations. In economics, however, game theory tends to focus on sets of outcomes known as equilibrium that represent the most rational solutions to each situation. Game theory emanates from the complexity of human interactions; thus, in a situation where an individual is dealing with an inanimate object such as a tree, he or she does not expect the tree to fight back or respond (Leyton-Brown and Shoham 51). The environment can also be considered neutral to what is done to the tree, at least in direct and rational response. In human interactions, however, each action by an actor emanates from a situation and elicits a response. Each actor must thus recognize how his of her interaction with other rational actors works so as to foster cooperation...
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...Introduction Nowadays, Game theory plays an important role in modern analysis. This concept can be applied in plenty fields including business, finance, political science, economics and sports. In business, competition is very intensive hence decision makers should analyse and determine their strategy carefully. Furthermore, they have to consider about their rivals strategies available and actions in the game. Once decision makers know all strategies available, they can apply a game concept, and achieve the proper outcome. This essay is divided into two parts, in first part, it will be discussed the general idea of game theory including prisoner’s dilemma which is one of the most known theories. In the second part, the application of game theory will be presented in the example of an oligopoly market. Part one: General discussion of game theory Game Theory...
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...Game Theory On Gallerie Apex Vs Bata Submitted to Abu Reza Mohammad Muzareba Lecturer Department of Marketing University of Dhaka Submitted by Group: Gamers Section: A Batch: 17th Department of Marketing University of Dhaka Submission date: 21th April, 2012 AbuReza Mohammad Muzareba Lecturer University of Dhaka Dept. of Marketing Subject: Letter of transmittal Dear Sir, Enclosed is a report on the Game theory Between Gallerie Apex and Bata. This report is about the internal and external business strategies of the pioneer footwear company Gallerie Apex and Bata. We were assigned to submit this report in 21th April 2012 to be submitted as a term paper for our Business Mathematics 2 course in the 3rd semester of our BBA program, from the department of Marketing of University of Dhaka. We have completed it whilst trying to meet all its broad and specific objectives within the allotted time. We are submitting the report to you only, as our course instructor and will be keeping a copy for any future references. We have organized our findings about the business strategies of the above mentioned trading companies. This paper includes an introduction to the company in focus, in terms of their business strategies and an analysis of those processes with some possible recommendations. It has been completed with a conclusion. At the end of the report...
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...A BRIEF INTRODUCTION OF ESSENTIAL ASSUMPTIONS AND DEFINITION OF SOME KEYWORDS IN GAME THEORY There are a number of assumptions in game theory; some of the assumptions identified by Varian (1992) can be explained as follows: we assume that the descriptions of the game (such as the payoffs and the strategies available to the players) are common knowledge. That is, each player knows his own payoffs and strategies, and the other player's payoffs and strategies. Furthermore, each player knows that the other player knows this, and so on. We also assume that it is common knowledge that each player is "fully rational." That is, each player can choose an action that maximizes his utility given his subjective beliefs, and that those beliefs are modified when new information arrives according to Bayes' law. Game theory can be considered as a generalization of standard, one-person decision theory. How should a rational expected utility maximizer behave in a situation in which his payoff depends on the choices of another rational expected utility maximizer? Obviously, each player will have to consider the problem faced by the other player in order to make a sensible and economically rational choice. According to Varian (1992) the strategic form of the game is defined by exhibiting a set of players, a set of strategies, the choices that each player can make, and a set of payoffs that indicate the utility that each player receives if a particular combination of strategies is...
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...Introduction to the Theory of Accounting and Control ••••••••••••••••••••••••••••••••••••••••••••• Three ideas are central to understanding accounting and control in organizations. First, all organizations are sets of contracts among individuals or groups of indi viduals. Second, provision of shared information among the contracting parties helps design and implement these contracts. Finally, control in organizations is a sustainable balance or equilibrium among the interests of its participants. It should be distinguished from control of organizations, which suggests manipulation or exploitation of some participants by others. We start this overview by stating these ideas briefly, leaving most definitions and details for the following chapters. We conclude with a summary of ideas about micro and macro aspects of accounting and control presented in the book. Organizations as a Set of Contracts Organizations are many things to many people. Business firms, for example, are employers to those who work for them; customers to the purveyors of goods and services; suppliers to their own customers; benefactors to those who receive their charity; investments to those who save; taxpayers to the government; a threat to the livelihood of their competitors; impersonal bureaucracies to the powerless; and pillars of free enterprise to the believers. Organizations are variously seen as com plex networks of human relationships, production functions, hierarchies, even garbage cans....
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...GAME THEORY & ASYMMETRIC INFORMATION LITERATURE REVIEW NATHALIA PALOMINO ID# 0501605 MARCH 1, 2014. FACILITATOR: SHELLEY WHITTLE Introduction This paper will firstly address game theory, Prisoners Dilemma which is a very prominent game and Bargaining. Asymmetric Information is also discussed along with a few examples of how asymmetric information relates to the business environment. The writer gives the reader a basic understanding of game theory and asymmetric information uses in a logical manner. As many opinions are combined to critically analyse the aforementioned. Game Theory A definition of Game Theory or something that appears to be a definition may be applied as such: An analytical or mathematical approach of examining strategic interaction when dealing with competitive situations in business decisions. As Keat, Young & Stephen (2014) did not give a clear definition of Game Theory. This definition stated business decision however, Martin (1978) stated that Game theory has proved useful in only war and economic. He states, “I see that at least three ways in which game theory has proved ‘useful’. First, it has led to practical advice on tactical decision-making in certain well defined situations, especially in military areas involving missile tracking and similar task (where the theory of differential games has led to results equivalent to control theory). Second, it has provided an occupation and amusement for thousands of government bureaucrats...
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...Throughout history, dating back to 3600 BC, games of chance and gambling have existed ("Introduction- Gambling and Probability"). Since their invention, people have tried to decipher ways to predict the outcome of such games, thus a need to determine the likelihood of winning in games such as these evolved. The method created to suit this need is known as probability theory. Probability theory has been developed over hundreds of years, and is used to predict possible outcomes and assist in daily life. Probability has been developed and studied over time, and has been formed into formulas and theories that allow it to be used in a myriad of applications. Probability theory is a very important aspect of mathematics, and through the development...
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...Essentials of game theory 1. Introduction Game theory is the study of strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."[1] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory.[2] Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide range of class relations, and has developed into an umbrella term for the logical side of science, to include both human and non-humans, like computers. Classic uses include a sense of balance in numerous games, where each person has found or developed a tactic that cannot successfully better his results, given the other approach. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by his 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided...
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...21/01/09 Start with a brief timeline, including when applications to different areas were first used. Game Theory (i) Game Theory Introduction We begin with a simple, informal example of a game. Rousseau, in his Discourse on the Origin and basis of equality among men, comments: “If a group of hunters set out to take a stag, they are fully aware that they would all have to remain faithfully at their posts in order to succeed, but if a hare happens to pass near one of them, there can be no doubt that he pursued it without qualm, and that once he had caught his prey, he cared very little whether or not he had made his companions miss theirs” To make this into a game, we need to fill out a few details. Suppose that there are only two hunters, and that they must decide simultaneously whether to hunt for a stag or for hare. Each player has a choice between two strategies: (hunt stag, hunt hare). If both hunt stag, each gets half a stag If both hunt hare, each gets one hare If one hunts for hare while the other tries to take a stag, the former will catch a hare and the latter will catch nothing. If we suppose that the utility of catching a stag is 4 and for a hare is 1, then the payoff matrix for the players can be summarised as follows: Stag Hare (2,2) (0,1) (1,0) (1,1) Game theory is concerned with what outcomes arise in equilibrium. An equilibrium outcome is one which consists...
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