Submitted By DenEd

Words 2617

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Words 2617

Pages 11

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 of a strategy for each player which is that player’s best response to the strategies of all players. An equilibrium is a stable state which holds because no rational player has an incentive to deviate from that state, where a rational player is one who always attempts to maximise their utility from any situation which requires a choice between alternatives.

In the…...

...Situations economists and mathematicians call games psychologists call social situations. While game theory has applications to "games" such as poker and chess, it is the social situations that are the core of modern research in game theory. Game theory has two main branches: Non-cooperative game theory models a social situation by specifying the options, incentives and information of the "players" and attempts to determine how they will play. Cooperative game theory focuses on the formation of coalitions and studies social situations axiomatically. This article will focus on non-cooperative game theory. Game theory starts from a description of the game. There are two distinct but related ways of describing a game mathematically. The extensive form is the most detailed way of describing a game. It describes play by means of a game tree that explicitly indicates when players move, which moves are available, and what they know about the moves of other players and nature when they move. Most important it specifies the payoffs that players receive at the end of the game. Strategies Fundamental to game theory is the notion of a strategy. A strategy is a set of instructions that a player could give to a friend or program on a computer so that the friend or computer could play the game on her behalf. Generally, strategies are contingent responses: in the game of chess, for example, a strategy should specify how to play for every possible arrangement of pieces on the board. An......

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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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...Is Game Theory the Right Kind of Game? Game theory is an analysis of a conflict of interest to find optimal choices that will lead to desired outcome under given conditions. It’s a study of ways to win in a situation given the conditions of the situation. 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 game theory provide a language to formulate structure, analyze, and understand strategic scenarios. Game theory provides a nice conceptual or theoretical framework for thinking about multi-agent learning. It is most appropriate provided that the game is stationary and fully specified, other agents are also game theorists, it can solve equilibrium coordination problem. Given the said conditions, it is rarely hold in real applications because firms think differently from each other. We can say that game theory is the right kind of game if we are able to make use of it properly to win in a given situation. This game theory can provide insight into the strategic options and likely outcomes available to participants in particular situations. From this insight, decision-makers can better assess the potential effects of their actions, and can make decisions that will more likely produce the desired goals and avoid conflict. Considering the situation as a game would lead you to think that everyone is a participant which in reality not all......

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...Game Theory Themes 1. Introduction to Game Theory 2. Sequential Games 3. Simultaneous Games 4. Conclusion Introduction to Game Theory Game theory is the branch of decision theory concerned with interdependent decisions. The problems of interest involve multiple participants, each of whom has individual objectives related to a common system or shared resources. Because game theory arose from the analysis of competitive scenarios, the problems are called games and the participants are called players. But these techniques apply to more than just sport, and are not even limited to competitive situations. In short, game theory deals with any problem in which each player’s strategy depends on what the other players do. Situations involving interdependent decisions arise frequently, in all walks of life. A few examples in which game theory could come in handy include: ● Friends choosing where to go have dinner ● Parents trying to get children to behave ● Commuters deciding how to go to work ● Businesses competing in a market ● Diplomats negotiating a treaty ● Gamblers betting in a card game All of these situations call for strategic thinking – making use of available information to devise the best plan to achieve one’s objectives. Perhaps you are already familiar with assessing costs and benefits in order to make informed decisions between several options. Game theory simply extends this concept to interdependent decisions, in which the options being evaluated are functions of...

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...form of this game. (b) Is there a strictly dominant strategy equilibrium of this game? Explain. (c) Is there a weakly dominant strategy equilibrium of this game? Explain. (d) What are the action proﬁles that survive Iterated Elimination of Strictly Dominated actions? Explain. (e) What are the action proﬁles that survive Iterated Elimination of Weakly Dominated actions? Explain. (f) Is the game dominance solvable? 2. Two people are engaged in a joint project. If each person i puts in the eﬀort xi , a non-negative number equal to at most 1, which costs her c(xi ), the outcome of the project is worth f (x1 , x2 ). The worth of the project is split equally between the two people, regardless of their eﬀort levels. 1 ECO502/EE698A (a) Formulate this situation as a strategic game. (b) Find its Nash equilibria when i. f (x1 , x2 ) = 3x1 x2 , c(xi ) = x2 , for i = 1,2. i ii. f (x1 , x2 ) = 4x1 x2 , c(xi ) = xi , for i = 1,2. (c) In each case, is there a pair of eﬀort levels that yields both players higher payoﬀs than the Nash equilibrium eﬀort levels? 3. (Hotelling competition) Consumers are uniformly distributed along a boardwalk that is one mile long. Ice-cream prices are regulated, so consumers go to the nearest vendor because they dislike walking (assume that at the regulated prices all consumers will purchase an ice-cream even if they have to walk a full mile). If more than one vendor is at the same location, they split business evenly. (a) Consider a game in which two......

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...Game Theory∗ Theodore L. Turocy Texas A&M University Bernhard von Stengel London School of Economics CDAM Research Report LSE-CDAM-2001-09 October 8, 2001 Contents 1 What is game theory? 2 Deﬁnitions of games 3 Dominance 4 Nash equilibrium 5 Mixed strategies 6 Extensive games with perfect information 7 Extensive games with imperfect information 8 Zero-sum games and computation 9 Bidding in auctions 10 Further reading 4 6 8 12 17 22 29 33 34 38 This is the draft of an introductory survey of game theory, prepared for the Encyclopedia of Information Systems, Academic Press, to appear in 2002. ∗ 1 Glossary Backward induction Backward induction is a technique to solve a game of perfect information. It ﬁrst considers the moves that are the last in the game, and determines the best move for the player in each case. Then, taking these as given future actions, it proceeds backwards in time, again determining the best move for the respective player, until the beginning of the game is reached. Common knowledge A fact is common knowledge if all players know it, and know that they all know it, and so on. The structure of the game is often assumed to be common knowledge among the players. Dominating strategy A strategy dominates another strategy of a player if it always gives a better payoff to that player, regardless of what the other players are doing. It weakly dominates the other strategy if it is always at least as good. Extensive game An extensive game (or......

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...Rachel Dillie SOS-360 Final Project March 25, 2014 Game Theory “Game theory is the study of strategic interaction among rational players in an interactive setting” (Stevens, Lecture 1). Elements of a game consist of common knowledge, the players, strategies and payoffs. Every other Friday night my wife and I play cards at our friend’s house and it generally gets more intense as the game and the drinks progress. We mainly play a card game called spades and we play as partners. Common knowledge in this game is every player knows that in order to win you have to bid the correct number of books, meaning you have to guess how many rounds you and your partner can win based off what cards you are holding and what you think the other players are holding in their hands. Each player also is assumed to be an experienced player unless otherwise stated and even if they are it’s easier to guess how the hand will play out. In this card game there is not strictly a pure strategy at play, meaning it doesn’t not involve an act of randomness but a game of mixed strategy. Mixed strategy means using a pure strategy with acts of randomness. I have an idea what the other players will do when it is their turn in the card game but sometimes to force their hand, it is necessary to randomly sacrifice one of your cards to make them display their higher ranked cards. The payoff to a player reflects what that player cares about, not what another player thinks they should care about. Being......

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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......

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...“Planning and Playing a Game” Objectives: * Learn how individuals contribute to teamwork. * Experience some of the features of group work and teamwork. * Understand what managers and organizational developers do to transform groups into teams. * Articulate the tangible benefits (both quantitative and qualitative) of high-performing teams. * Finish with an interest in learning more about these concepts and techniques to apply what you learn. Background: In game theory, there are non-cooperative and cooperative games. A non-cooperative zero-sum game has a definite winner and loser. For one to win, one must lose. A cooperative game is where everyone who plays is better off for having played than not having played the game. That is not to say that everyone is equally well off, but simply better off than they were before playing. Hence, even in a cooperative game, some people will likely benefit more than others. To understand why individuals make the decisions they do in a game it is important to consider the personality of the player. Personality is a term used to describe a great many feelings and behaviors. Literally hundreds of personality dimensions or traits have been identified by psychologist over the last 100 years. However, within the past 25 years or so, a consensus has emerged that, for the most part, the human personality can be described by five dimensions or factors. The Big Five personality dimensions include: extroversion,......

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...independent. For affiliated signals, the result holds under certain restrictions on the seller's choice of negotiating mechanism. The result suggests that the value of negotiating skill is small relative to the value of additional competition. The paper also shows how the analogies between monopoly theory and auction theory can help derive new results in auction theory. (JEL D44, G34) There are close analogies between standard price theory and the theory of auctions. In an absolute English auction, in which the price rises continuously until only one bidder remains and the seller is required to accept the final bid, the sale price equals the lowest competitive price at which supply equals demand. In the theory of optimal auctions the seller is treated as a monopolist who can choose any mechanism, such as establishing a minimum sale (or reserve) price, to maximize expected profit.As in monopoly theory, optimal auction theory assigns all bargaining power to the seller, subject to the constraint that she does not have access to buyers' private information about an asset's value. This paper shows how the analogies between monopoly theory and auction theory can help derive new results in auction theory. Specifically, we are able to put a fairly tight bound on the value of any seller's bargaining power: a seller with no bargainingpower who can only run an English auction with no reserve price among N + 1 symmetric bidders will earn more in expectation than a seller with all the......

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...Through visionary thought and understanding, a creative strategy increases the outcome of success in a given situation or variable. In many cases, strategy is understood as a plan that chooses an individual’s future possible position. Speaking with respect to Game Theory within the Healthcare field, there are many ways to move forward with creating this ideal insightful approach. Learning through class discussions, it’s clear the topic of the discussion with Game Theory is very evolved, diverse, and dynamic with all different observations. All games share an interdependence meaning the result for each individual is dependent on the option they primarily choose. For myself, this is definitely considered an everyday normalcy working in the Healthcare Industry. Whether Game Theory is applied in all of society is only understood through the participants as all situations are different and unique, but all equally share the mindset of increasing their individual outcome of achievement. The analysis of Game Theory within Healthcare is spread across an increasingly strategy-prone competitive market. Governmental changes alone within healthcare laws create challenges for decision makers to compete within this highly-regulated domain. Creating governmental regulation lessens efficiency for providers who serve society to collaboratively work together, and in addition, diminishes their likelihood of optimal standing within the environment. Turning the hand in reference to my current......

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...A game is any situation of conflict with at least two players (it may be a person, company). Each side chooses some kind of behavior (strategy) to get the best payoff. Game theory is a way to study conflicts and strategies used to get best results. The decision process is made without full knowledge and that’s what drives people engage into game to strategize to get as good output as possible- perfectly to win everything or at least to lose as little as possible. Game theory as a mix of psychology, mathematics, logic and other academics areas can be useful in several ‘real life’ situations, including negotiations and business. It can be observed in an oligopoly market, when two companies offering a very similar product (for example gas) must find a way to win over their competitors. One can notice parallels in a situation of those companies and classical example of the game theory “prisoner dilemma”. Game theory may also be used in auctions, mergers and acquisitions, bargaining, real estate negotiations, salary negotiations and so on. The most common application of game theory in real life is setting price. Each company wants to set price as high as possible to maximize profit but also wants to win market share as big as possible. Companies can all set the same price for their products and split the profit between themselves or one could try and forecast an advantageous set of lower prices and basically win since their higher market share even at their lower prices......

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...Managerial Economics 2010 1. A. Design a simple two-company game that illustrates why it might have been in economic interests of the cigarette companies to support the ban. In designing the game, assume that there is no regulation and that the two firms simultaneously choose between advertising and not advertising. Display your hypothetical payoffs in strategic form (see Figure 9.1) and highlight the Nash equilibrium. Explain the intuition for why the firms in your example would favor regulation to ban advertising. Winston |Advertise |Not Advertise | |fff | | | | | |100/100 |160/60 | | | | | | | | | | |160/60 |150/150 | Profits – Advertising Cost from TV (In millions) Advertise Tareyton Not Advertise During the 1960’s, numerous reports started to surface connecting cancer to smoking...

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...Game theory is the method utilized to understand the behavior of oligopolies or market situations in which each of a few producers affects but does not control the market. Unlike monopolies in which a company has complete control of the entire supply of goods and/or services in a certain market, oligopolies do have competitors with in the market. However, unlike monopolistically competitive firms and perfectly competitive firms, firms within a oligopolistic frame work have so few competitors that marketing and pricing decisions made by one firm has a very unique possibility of affecting all the other firms within that market segment. In essence, competitors must take their competitors' possible reactions and responses into account when making decisions. The table below shows the Coke and Pepsi Payoff Matrix with respect to price competition. Both companies have two fundamental strategies: charge an elevated or above market price or a minimal or below market price for its products. Both companies have the possibility of obtaining a big payoff by charging a minimal price while its competitor charges an elevated price, but both companies know that if one of them cuts it price the other will quickly follow suit, resulting in a smaller payoff for both. The resulting equilibrium is both companies charging a high price and engaging instead in non-price competition. Coke vs. Pepsi Payoff Matrix Pepsi charges high price Pepsi charges low price Coke charges high......

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...Game Theory Game A game is a formal description of a strategic situation. Game Theory Game theory is the formal study of decision-making where several players must make choices that potentially affect the interests of the other players. Mixed Strategy A mixed strategy is an active randomization, with given probabilities, that determines the player’s decision. As a special case, a mixed strategy can be the deterministic choice of one of the given pure strategies. Nash Equilibrium A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for each player, which has the property that no player can unilaterally change his strategy and get a better payoff. Pay-Off A payoff is a number, also called utility, that reflects the desirability of an outcome to a player, for whatever reason. When the outcome is random, payoffs are usually weighted with their probabilities. The expected payoff incorporates the player’s attitude towards risk. Perfect information A game has perfect information when at any point in time only one player makes a move, and knows all the actions that have been made until then. Player A player is an agent who makes decisions in a game. Rationality A player is said to be rational if he seeks to play in a manner which maximizes his own payoff. It is often assumed that the rationality of all players is common knowledge. Strategic form A game in strategic form, also called normal form, is a compact representation of a......

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