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Antoinette Monteiro

Grand Canyon University

DBA 815

January 13, 2016

The Definition of Game Theory The game is the object of game theory, which is an interactive situation. There are several players involved in the situation; a game with only one person is a decision problem. According to game theory, the players, their preferences, their information, the strategic actions available to them, affects the outcome. Game theory is conflict and cooperation; the agents are interdependent on the actions of others. These agents are individuals, groups, firms or a combination of these combined. Game theory provides a language to formulate, structure, analyze and understand different circumstances (Turocy and Stengel, 2001 p.4).

History and Effects of Game Theory An example of game analysis is the idea of two players dominating the marketplace which was introduced by Antoine Cournot in 1838. Emile Borel, a mathematician proposed a game theory in 1921 and this research was expanded by Neumann in 1928 called the “theory of parlor games.” This theory was solidified in the publication, “The Theory of Games and Economic Behavior by Neumann and Morgenstern. This book pioneers the basic terms and problems that are still in use to this day (Turocy and Stengel, 2001, p.4).

The mathematician, John Nash showed that finite games have an equilibrium point in which players choose actions which give the best outcome for themselves due to their oppositions choices. This is a main point in non-cooperative game theory since his analysis; then game theory expanded and applied to war and politics. Game theory has driven a revolution in economic theory. Game theory has been applied in sociology, psychology, and with evolution and biology. Game theory has been prominent since the 1970s and has been applied to

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...Your Name 07/07/14 –Economics Unit 3 Prisoner’s Dilemma/ Part 1 1. What is a prisoner’s dilemma game? The Prisoner’s Dilemma is the best-known game of strategy in Social Science. It help us understand what governs the balance between cooperation and competition in business. 2. What is a dominant strategy? If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibrium. If both players have a strictly dominant strategy, the game has only one unique Nash equilibrium. 3. What is a cartel? A cartel is a collection of businesses or countries that act together as a single producer and agree to influence prices for certain goods and services by controlling production and marketing. 4. What is Nash equilibrium? (In economics and game theory) a stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged Part 2 – Standard Example | Clyde confesses | Clyde is silent | Bonnie confesses | Both get 10 years. | Bonnie-6 months/Clyde gets 20 years. | Bonnie is silent | Clyde gets 6 months, Bonnie is charged 20 years. | Both get a year. | 1. What is the equilibrium in this game? The equilibrium in this game would be the participation on an agreement between both of the participants, but due to a case of dishonesty, one participant can...

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...Prisoner's Dilemma (Stanford Encyclopedia of Philosophy) 4/3/12 9:58 AM Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia Free Prisoner's Dilemma First published Thu Sep 4, 1997; substantive revision Mon Oct 22, 2007 Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. “You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I'll see to it that you both get early parole. If you both remain silent, I'll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.” The “dilemma” faced by the prisoners here is that, whatever the other does, each is better off confessing than remaining silent. But the outcome obtained when both confess is worse for each than the outcome they would have obtained had both remained silent. A common view is that the puzzle illustrates a conflict between individual and...

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...An introduction to game theory by Martin J. Osborne. Version: 2002/7/23. Martin.Osborne@utoronto.ca http://www.economics.utoronto.ca/osborne Copyright © 1995–2002 by Martin J. Osborne. All rights reserved. No part of this book may be reproduced by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from Oxford University Press, except that one copy of up to six chapters may be made by any individual for private study. 2 Nash Equilibrium: Theory 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Strategic games 11 Example: the Prisoner’s Dilemma 12 Example: Bach or Stravinsky? 16 Example: Matching Pennies 17 Example: the Stag Hunt 18 Nash equilibrium 19 Examples of Nash equilibrium 24 Best response functions 33 Dominated actions 43 Equilibrium in a single population: symmetric games and symmetric equilibria 49 Prerequisite: Chapter 1. 2.1 Strategic games is a model of interacting decision-makers. In recognition of the interaction, we refer to the decision-makers as players. Each player has a set of possible actions. The model captures interaction between the players by allowing each player to be affected by the actions of all players, not only her own action. Speciﬁcally, each player has preferences about the action proﬁle—the list of all the players’ actions. (See Section 17.4, in the mathematical appendix, for a discussion of proﬁles.) More precisely, a strategic game is deﬁned as follows...

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...The Prisoners' Dilemma Cooperation is usually analysed in game theory by means of a non-zero-sum game called the "Prisoner's Dilemma" (Axelrod, 1984). The two players in the game can choose between two moves, either "cooperate" or "defect". The idea is that each player gains when both cooperate, but if only one of them cooperates, the other one, who defects, will gain more. If both defect, both lose (or gain very little) but not as much as the "cheated" cooperator whose cooperation is not returned. The whole game situation and its different outcomes can be summarized by table 1, where hypothetical "points" are given as an example of how the differences in result might be quantified. Action of A\Action of B Cooperate Defect Cooperate Fairly good [+ 5] Bad [ - 10] Defect Good [+ 10] Mediocre [0] Table 1: outcomes for actor A (in words, and in hypothetical "points") depending on the combination of A's action and B's action, in the "prisoner's dilemma" game situation. A similar scheme applies to the outcomes for B. The game got its name from the following hypothetical situation: imagine two criminals arrested under the suspicion of having committed a crime together. However, the police does not have sufficient proof in order to have them convicted. The two prisoners are isolated from each other, and the police visit each of them and offer a deal: the one who offers evidence against the other one will be freed. If none of them accepts the offer, they are in fact cooperating...

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...Nuclear Weapons: Then and Now Politics, especially on an international level, is a complex and messy subject. One simply has to open up a newspaper or tune into the evening news for evidence. While many problems can be resolved peacefully through negotiations, there are problems in international relations that manage to escalate quickly and result in a war between two or more countries. From revolutionary wars to World Wars, violence has always been part of international relations. However, with recent technological advancements, wars have taken an especially deadly turn. Advanced weaponry has allowed soldiers to become more “efficient” when fighting a battle allowing them to kill many more enemy combatants and innocent bystanders. The most devastating of these newly created weapons are nuclear weapons such as the atomic and hydrogen bombs. These weapons have the capacity to eliminate hundreds of thousands of people, obliterate cities, and possibly end life on earth, as we know it. The most destructive of these weapons was tested by the Soviets in 1961 during the Cold War. The hydrogen bomb that was being tested had a destructive power of approximately 60 megatons. The Soviets formally named the bomb Ivan, but nicknamed it the “King of Bombs.” Originally, Ivan was going to be constructed with a power of 100 megatons, but the Soviets decided it was too risky and dangerous. To put this in perspective, a single megaton can create temperatures that are five times as intense as the...

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... 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 is a general...

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...Prisoner’s dilemma is as standard example of game theory that shows that two rational indicidual might not cooperate even if cooperation will fit their best interest. (wiki) Let me explain the prisoner’s dilemma first. In prisoner’s dilemma, each individual act rationally. That means each individual should do anything that benefit her/him. Let’s imagine Jack and Rose has committed a crime and are arrested. During the interrogating, they are separated in two interrogate room, the game is shown below. - - Rose stays silent ( cooperates) - Rose betrays (defects) - Jack stays silent (cooperates) - Each serves 1 year - Jack: 3 years - Rose: goes free - Jack betrays (defects) - Jack: goes free - Rose: 3 years - Each serves 2 years In this dilemma,...

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...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 alternative...

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...An interpretation of function of leadership using game theory. This paper seek to provide a generalisation of the function of leadership using game theory. Assuming there are 2 ends of spectrum of people- extreme rational and extreme irrational people. Most people will lies within the spectrum with only a handful of them representing extreme rational or extreme irrational. Dixit (2004) define rationality as having 'two essential ingredient: complete knowledge of one's own interests, and flawless calculation of what actions will best serve those interest.' Game theory interpretation of the function leadership assumes the follower lies towards the rational end of the spectrum. Given the follower are mostly rational, we can assume that there are 2 ends of spectrum of people- altruistic people and home economicus. Most people will lies within the 2 ends of spectrum with only a handful of them representing totally altruistic people or homo economicus. The proposed interpretation of the function of leadership assumes the followers lies towards the home economicus end of the spectrum. A brief treatment of the altruistic followers are given at the end of the paper. When followers are given the choice of doing a particular action A. There are two possibilities, either the action result in a positive payoff to the followers or a negative payoff. 1)If action A result in a positive payoff and the assumption that the follower are rational, we can assume that rational followers...

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...Assignment 2 Planning and Playing a Game https://homeworklance.com/downloads/assignment-2-planning-and-playing-a-game/ • 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: For this assignment, you will plan and play a game with your family or friends, or at work based on the idea of the classic prisoner’s dilemma. If you have had a class on game theory, you will be well aware of this concept. It forms the basis of many TV game shows. The prisoner’s dilemma was illustrated in Truman Capote’s book, “In Cold Blood” concerning the 1959 robbery of a Kansas farmhouse by Perry Smith and Dick Hickock, who murdered their victims in order to eliminate the witnesses. After the men were captured, the police interrogated them separately. To get a confession, the police offered the men a reduced sentence for cooperating. Failure to cooperate would result in a death penalty charge for both. In the prisoner’s dilemma, if both parties cooperate they are mildly punished; if one betrays another, one is severely punished while the other goes free; and if both betray one-another, both are moderately punished. Can you think of...

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...Management Science Summary Definitions by Subject Game theory * Nash equilibrium * In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. * Stated simply, Amy and Wili are in Nash equilibrium if Amy is making the best decision she can, taking into account Wili's decision, and Wili is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others. * Pareto efficiency * Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off. The term is named after Vilfredo Pareto (1848–1923), an Italian economist who used the concept in his studies of economic efficiency and income distribution.The concept has applications in academic fields such as economics and engineering. * Given an initial allocation of goods among...

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...Monopoly and Duopoly Models In class, we played a monopoly game. There were 14 students, and 14 cards were distributed to assign roles. A King, Queen and a 2, 4, 6, 8 and 10 (one set of hearts, one of spades) was shuffled and distributed. The King became the recorder, the Queen the monopolist. The numbered cards represented redemption values. Each student individually negotiated a price with the relevant monopolist. Two strategies were evident. One monopolist reduced the price as the round proceeded and negotiated a deal with every buyer. The other monopolist chose not to strike a deal with two potential consumer and instead kept the price uniformly higher than the other monopolist. The second strategy generated the higher profit. If we had repeated the game (randomize on redemption values and renegotiate) then the strategy of lower prices as the round proceeded would break down. Students would learn to wait until the end of the round to negotiate and all would claim to have low redemption values. This is the process presumed by traditional theory. The monopolist sets one price because he or she can not predict the reservation values of consumers and can not successfully negotiate individually. Instead, a single profit maximizing price is set. With linear demand and constant marginal cost, the theory is simple, the profit maximizing rectangle connects the midpoints of the triangle formed by demand and marginal cost. (See diagram,) The height of the rectangle is...

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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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