So far we have been assuming that each player is choosing a strategy once and for all. For Each, State Your Decision And Then Explain Why You Chose What You Did. Question(s) about the Game Theory episode. This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. But if he thinks that the other firm will overproduce, then he too might do it as well. Raquel has to choose whether to pursue training that costs $1;000 to herself or not. How well do you know Game Theory? What is a dominant strategy equilibrium? Discussion. For, here, for each prisoner, his strategy 1 (confess) is a dominant strategy. Ignore fashion 3. Strategic interaction may involve many players and many strategies, but here we shall consider only two-person games with a finite number of strategies. The game is rather easy to handle if we have a dominant strategy for each player, which, however, may not always be the case. Thus, whatever the prisoner B does, prisoner A is better off if he uses his strategy 1 (confess). Please Read The Instructions To Each Experiment Carefully. Mr. Saggie has theories about the game’s appeal, but isn’t sure why it has sold as well as it has. A great question will challenge your students, sparking collaborative thought-provoking class conversations that lead students to communicate with their peers. However, we have noted at the very outset of this section that the Nash equilibrium solution may not necessarily be Pareto-efficient. Content Guidelines 2. %PDF-1.5 %���� For example, if they shift from the cartel equilibrium to Cournot equilibrium, then both of them would have an equal but smaller payoff [payoff combination in row 1, column 1]. A game in the everyday sense—“a competitive activity . It demands that a particular strategy of A (or B) be optimal for all choices of B’s strategy (or A’s strategy). In cases where a student answers more questions than requested by the examination rubric, the policy of the Economics Department is that the stu-dents –rst set of answers up to the required number will be the ones that count (not the best answers). <<7ab4628aa7b131448c8ff48cf4bf78ee>]>> Game Theory: 5 Questions Vincent F. Hendricks and Pelle G. Hansen, editors, Automatic Press, 2007, 233 + vi pp., index, ISBN 87-991013-4-3, US$ 26.00. Discussion question. If the game is not a repeated one, if it is a one-shot game, then the strategy of confessing or defecting from the cartel seems to be reasonable, for whatever the other player does, the confessing or the defecting player is better off, especially when he has no way of influencing the other person’s behaviour. SF2972 { Game Theory { Exam with Solutions { March 15, 2013 3 (c)In the special case when gis linear, g(y) y, we immediately obtain x = 1=nand ^x= 1. In this example, we would expect, therefore, an equilibrium outcome where A plays his strategy 2 receiving an equilibrium payoff of 2, and B plays his strategy 1 receiving an equilibrium payoff of 1. Game Theory Practice Questions Question 1. His optimal choice would depend on what he thinks A will do. The game is rather easy to handle if we have a dominant strategy for each player, which, however, may not always be the case. Game Theory Solutions & Answers to Exercise Set 1 Giuseppe De Feo May 10, 2011 1 Equilibrium concepts Exercise 1 (Training and payment system, By Kim Swales) Two players: The employee (Raquel) and the employer (Vera). x�b```f``����� ������b ���,�! However, instead of demanding so much, we may just require that A’s choice be optimal for the (optimal) choices of B. 0000000784 00000 n 0000002573 00000 n View Notes - 20-Discussion Questions Solutions from ECON 351 at University of Southern California. Archived. Hence, here these choices of strategy, i.e., strategy 2 for A and strategy 1 for B dominate the alternative choices, and we have an equilibrium in dominant strategies. 0000002334 00000 n You and I are driving towards each other at high speed, trying to make each other veer out of the way. Game theorists will apply the principles of game theory to find out how many research labs need to be involved to establish a Nash equilibrium, and compare that to the most efficient number of labs. No, the one on the left is Mario, and the one on the right is his father. Using Discussion Questions Effectively. The breakthrough came with John von Neumann and Oscar Morgenstern’s book, Theory of games and economic behavior, published in 1944. Question(s) about the Game Theory episode. Compiled by Lauren V. Kachorek with help from Kirsten Olds, CRLT, 2009. To understand game theory, we must –rst understand the meaning of a ™game.™A ™game™ has a speci–c de–nition given by economists. Privacy Policy3. Here the choice of the output level of each firm is the choice of its strategy and the amount of profit obtained by each firm is its payoff. Your Goal Is To Make As Many Coyote Bucks As Possible. This situation has dramatically changed, in wayswe will examine as we go along, over the past seven decades, as theframework has been deepened and generalized. Each firm chooses its output level taking the other firm’s choice as being fixed. Game theory is a topic of discussion that applies to macroeconomic theory. One such field is cartel instability. Tracy knows Amy's payoffs to each choice, and Amy knows Tracy's payoffs. Is a player’s best response in a game the same as his dominant strategy? Worked for Game Theory? Thus, in this game, the unique Nash equilibrium would occur when both prisoners decide to use their strategy 1, i.e., when both decide to confess, because if prisoner A chooses strategy 1, then B would optimize by choosing his strategy 1, and if prisoner B chooses his strategy 1, then A would optimize by using his strategy 1. In other words, there is no dominant strategy for A in this case. 0000002649 00000 n But if player B plays strategy 1, player A will want to play strategy 2 (not strategy 1). In the Cournot equilibrium, the choices are of the output levels of the two duopoly firms. What, if any, conspiracies do you believe to be true? For example, the game given in Table 14.2 does not have dominant strategies. What do you think about Twitter? Close. Add Review Add Salary Add Interview Add Photos Add Benefits. And so, we come to the concept of what is known as the Nash equilibrium. If you are excited by the subject in question, the other person will pick up on this. Welcome! 1.A two-person zero-sum game which is unstable has at least two mixed-strategy equilibria. 2. Here the Nash equilibrium does not exist. We have a dominant strategy, i.e., one optimal choice of strategy for each player irrespective of what the other player does. 0000000016 00000 n It first came about in the 1900s, and has been expounded on and progressed since then. Question: To Help Introduce The Topic Of Game Theory, We Are Going To Do Three Experiments In The Discussion Post This Week. We may verify this by the kind of argument given above, or, we may just note that the structure of the game is symmetric. Refer to the figure above. Thus, A’s optimal choice depends on what he thinks B will do. It is applied to evaluate the situations where individuals and organizations have contradictory objectives. Microeconomics, Product Markets, Oligopolistic Market, Game Theory. Techniques > Conversation techniques > Encouragement signals. Refinement… Learn for its own sake, not for the grade. Questions tagged [game-theory] Ask Question The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. This game is known as the prisoner’s dilemma. So, here, we have a Nash equilibrium. Let us now see what the outcome will be of this sort of game. ESL Conversation Questions: Beside physical differences, what is different between men and women? What kind of music do you like? in which players contend with each other according to a set of rules. This will enable us to […] u/Giggity-Gooo. Game Theory : An Introduction Game Theory helps us understand situations in which decision-makers interact. » Discussion 10 » Follow author » Share . A Cournot equilibrium is obtained when each firm is maximising profits given the other firm’s behaviour. Do you think most conspiracy theories are true or false? Again, if player A plays strategy 2, player B will want to play his strategy 2 (not strategy 1). Warm-up Task: Explain why the following words seem more masculine or more feminine: water, speed, power, love, kindness, loyalty. This will enable us to present the game easily in a payoff matrix. While used in a number of disciplines, game theory … If we both veer, then nothing in particular happens (say we each get 0 utility from this outcome). Game theory True or False Questions. These are some conversation questions about Twitter. Do you follow live events on Twitter? startxref Discussion. 2. Share Your PDF File In this article, we will look at some basic examples of game theory and its application to real-world situations. Game Theory Through Examples, Erich Prisner Geometry From Africa: MathematicalandEducational Explorations,Paulus Gerdes Historical Modules for the Teaching and Learning of Mathematics (CD), edited by Victor Katz and Karen Dee Michalowicz IdentificationNumbers and Check … In the above decision tree, Tracy picks first, and Amy picks second. It is applied to evaluate the situations where individuals and organizations have contradictory objectives. 1) A person's decision is rational when he does what he believes in his best interest, given the information provided to him, and; 2) A person's decision is rational when it is consistent with other decisions she makes, in accordance with some pre-established preferences over sorts of outcomes in general. We would expect, therefore, that the equilibrium strategy for A is his strategy 2 and that for B is his strategy 1, and so, the equilibrium payoff combination here would be (2, 1). If not, who are they? Let us now see what is the correct way to play the game in prisoner’s dilemma. Nau: Game Theory 3 The Prisoner’s Dilemma Scenario: the police have arrested two suspects for a crime. Veer: Drive: ME: Veer: 0 , 0-2 , 5: Drive: 5 , -2-200 , -200: The payoff matrix above represents the game of chicken. Share Your Word File Here, when B adopts his strategy 1, A gets a payoff of 2 (from strategy 1) or 0 (from strategy 2), and when B chooses strategy 2, the payoff to A is 0 (from strategy 1) or 1 (from strategy 2). Therefore, that dominant strategy equilibrium, although easy to arrive at, does not happen always. That is, here the cartel instability arises from the dilemma that if a member of the cartel thinks that the other member will stick to his quota, then it will pay him to produce more than his own quota. Do you like music or musicians from other countries as well? Game Theory is one of the most fascinating branches of mathematics with tons of applications to fields ranging from the social sciences to the biological sciences. Start with Open-Ended Questions – these types of questions help begin a discussion because they encourage multiple viewpoints. . Outline of two peoples' heads. However, alternatively, we may allow the players to play their choice at random according to some assigned probabilities. Do you like to watch TV? Game theory in the form known to economists, social scientists, andbiologists, was given its first general mathematical formulation byJohn von Neuman and Oskar Morgenstern (1944). For here, if player A plays his strategy 1, then player B will also play his strategy 1. A good course in non-cooperative game theory will most likely deal with these areas: Would you describe yourself as a conspiracy theorist? 0000001235 00000 n Game theory is a topic of discussion that applies to macroeconomic theory. Similarly, if A adopts strategy 1 and B adopts strategy 2, then the payoff combination will be (0, 1). However, the Nash equilibrium has its problems too. The first entry in each combination represents the payoff to player A and the second entry gives the payoff to player B. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. Do you think that governments sometimes cover up events? Source: Other. 0000006301 00000 n Based solely on the information in this decision tree, we can predict that: A. Tracy will always make the decision to give Amy the choice at Y, and Amy will then choose the lower branch. But most of the coverage was wrong. Similarly, if prisoner B uses strategy 1 (confess), then prisoner A would be better off if he also uses his strategy 1 (confess), because if he does otherwise, i.e., uses his strategy 2 (deny), then he would get a sentence of 6 months. This theory aims at providing a systematic approach to business decision making of organizations. 23 14 This theory aims at providing a systematic approach to business decision making of organizations. What are some common conspiracy theories? Who do you follow on Twitter? ( ) 2. This kind of strategy is called a mixed strategy. First, a game may have more than one Nash equilibrium. Close. This recent game theory question got me thinking (this is a tangent, of course): Is it possible to efficiently optimize a personal strategy for choosing research questions to work on using game theory?. This game, of course, has a very simple solution. In this section, we have argued that it is possible to induce a "social norm' in a society if we allow patience and time. The same thing is obtained for prisoner B also, i.e., he is better off using his strategy 1 (con­fess) whatever prisoner A does. GAME THEORY – G. Bonanno 1 Introduction he discipline of game theory was pioneered in the early 20th century by mathematicians Ernst Zermelo (1913) and John von Neumann (1928). Guide to Getting Your First Job. Vocabulary List. Welcome to EconomicsDiscussion.net! 4 years ago. All questions carry equal weight. Change how the game is played 1. . Thus, here when B adopts strategy 1, A will also play his strategy 1; on the other hand, when B plays his strategy 2, A would change his strategy from 1 to 2. Repeated games. For reasons to be discussed later, limitations in their formalframework initially made the theory applicable only under special andlimited conditions. Who are your favorite performers or bands? The payoff combination now would be (-1, -1) whereas the Nash equilibrium payoff combination has been (-3, -3). If the members of a cartel stick to their respective quotas, then there is no danger to cartel stability. We may illustrate cartel instability if, in the game of prisoner’s dilemma, we replace the strategies of “confess” and “deny”, respectively, by “produce more than the quota” and “stick to the original quota” and assume the respective payoff combinations to be those given in Table 4.5. It encompasses a wide … Study for a specific amount of time then have fun. What do you think about this theoretical assessment in terms of real-life experiences? How often do you use Twitter? If A and B follow the mixed strategies given above of playing each of their choices half the time, then we have: One problem with the Nash equilibrium of a game is that it does not necessarily lead to Pareto- efficient outcomes. Conversation Questions. Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. Do you like movies? This is one of over 2,200 courses on OCW. Again, if B chooses his strategy 1, then the best thing for A to do is to choose his strategy 1, for then his payoff would be 2, whereas from strategy 2 his payoff would be 0. 0000001633 00000 n Find the pure-strategy subgame perfect equilibria of the game below: 1 2 3 a 1;0;0 b d f 0;1;1 c 2;1;0 e 0;2;0 [2 pts] Solution In the nal decision node, 3’s payo from eis 0 and from fis 1, so pl. ADVERTISEMENTS: Game theory was introduced by a mathematician, John Von Neumann and an economist, Oskar Morgenstern, in 1950s. }P4$��V�g{�Cr�[�g``��ta`6qq��^�D;�`J. They tell each prisoner they’ll reduce his/her prison sentence if he/she betrays the other prisoner. 23 0 obj <> endobj Solution for Game theory is "the study of mathematical methods of conflict and cooperation between intelligent rational decision-makers". Of course, what is optimal for B will depend again on A’s choice. 0000006449 00000 n Therefore, here Nash equilibrium never occurs. On the other hand, whatever choice A makes, B will get a higher payoff if he adopts his strategy 1. ADVERTISEMENTS: Game theory was introduced by a mathematician, John Von Neumann and an economist, Oskar Morgenstern, in 1950s. For, as we see in the payoff matrix, when A chooses strategy 1, B will choose his strategy 1 and when A chooses strategy 2, B will change from his strategy 1 to strategy 2. %%EOF Get a free employer account. On the other hand, if one of the duopolists stick to the quota but the other duopolist produces more then the latter would be rewarded handsomely but the former would be at a disadvantage [payoff combination in row 1, column 2 or row 2, column 1]. trailer Lecture 20: Game Theory (I) Suggested questions and exercises (Pindyck and Rubinfeld, But if one or both of them produce more than the allotted quota of output, then the cartel faces grave instability, and it breaks down. This is called a pure strategy. That is, B also has no dominant strategy here. To prove this, let us note that if A chooses his strategy 1, then the best thing for B to do is to choose also his strategy 1, for then his payoff would be 1, whereas from strategy 2, his payoff would be 0. Before publishing your Articles on this site, please read the following pages: 1. 3. Game Theory Through Examples, Erich Prisner Geometry From Africa: MathematicalandEducational Explorations,Paulus Gerdes Historical Modules for the Teaching and Learning of Mathematics (CD), edited by Victor Katz and Karen Dee Michalowicz IdentificationNumbers and Check Digit Schemes, Joseph Kirtland InterdisciplinaryLively ApplicationProjects, edited byChris Arney Inverse Problems: … For example, in the game given in Table 14.4, the Nash equilibrium combination (confess, confess) of the two prisoners is Pareto-inefficient, for if they adopt their respective second strategies, i.e., if they choose the combination (deny, deny), then both of them would have larger payoffs. Rεxтεя . For the sake of simplicity, the payoffs are quantified by putting a negative sign before the various prison terms mentioned above, and accordingly, the payoff matrix is given in Table 14.4. Are these two the same people? Some applications of… As such, a Nash equilibrium can be expected as a pair of expectations about each person’s choice such that neither individual wants to change his behaviour when the other person’s choice is revealed.]. 4. Do you think the media is sometimes involved in conspiracies? What Should You Do? View Notes - 20-Discussion Questions Solutions from ECON 351 at University of Southern California. 3. 0000001008 00000 n Each prisoner had two op­tions—that of confessing to the crime, and thereby implicating the other, or, that of denying that he had any role in the crime. For example, if both players adopt their respective first strategies the payoff combination will be (1, 2). YOU. Are men and women mostly similar, or do you sometimes feel like they are totally different? Like the prisoner’s dilemma illustrated in Table 14.4, Table 14.5 illustrates the dilemma of the two member-firms of the cartel. Did you know that the bad weather in the English Channel is to some extend responsible for Ken Binmore being a game theorist? Everything else follows from there. 0000002911 00000 n What is meant by the prisoners’ dilemma? The total number of possible outcomes is, therefore, 2 x 2 = 4. It also signals that you are ready to talk more about the subject. Gender Conversation Questions. Wait for movie to be less popular or wait for home release 2. Table 14.1 is the payoff matrix of the game. Sample Game Theory Questions 1. 25 0 obj<>stream What kinds of music don't you like? Start studying Chapter 10 - QUESTIONS Monopolistic Competition, Oligopoly, and Game Theory. Do the players in the prisoner’s dilemma game have a dominant strategy? But each person may have some expectations about what the other person’s choice will be. We will say that a pair of strategies form a Nash equilibrium (named after an American mathematician John Nash) if A’s choice is optimal, given B’s choice, and B’s choice is optimal given A’s choice, [Let US remember that player A (or B) does not know what player B (or A) will do when he has to make his own choice of strategy. Here we shall briefly discuss how the game theory can be used to study the economic behaviour in oligopolistic markets. For each possible outcome there is a corresponding payoff to each player. xref For example, the game given in Table 14.2 does not have dominant strategies. Game theory has been one of those disciplines that have reached phenomenal status because it has introduced concepts and methodologies that are deemed by many to be “game-changers” (no pun intended). An examination of this matrix gives us: If prisoner B uses his strategy 2 (deny), then the prisoner A would certainly be better off if he uses his strategy 1 (confess), for then he would be set free. Less popular or wait for home release 2 of strategy 1 of B is a player ’ choice! Can you name some singers or groups that you dislike level taking the other person ’ s as... Gives the payoff matrix of the game in prisoner ’ s dilemma Scenario: the police have two. Dominant strategy here specific example to understand the subject, game theory episode only games... Decision tree, Tracy picks first, a game the same as his dominant equilibrium... In which decision-makers interact is a particular case of Nash equilibrium your articles this! Table, the Nash equilibrium payoff combination has been expounded on and progressed since then the Nash equilibrium its. Choice at random according to a set of rules a simple game be Pareto-efficient makes... ™Game.™A ™game™ has a speci–c de–nition given by economists payoff combination has been (,... To play their choice at random according to a set of rules theory, we have a dominant?! Were being questioned separately the other person ’ s choice as being fixed player irrespective of what is different men... Great question will challenge your students, sparking collaborative thought-provoking class conversations lead... First came about in the Cournot equilibrium under oligopoly is a particular case of equilibrium... At high speed, trying to make as many Coyote Bucks as possible the dilemma the... A discussion because they encourage multiple viewpoints 's payoffs to each player sticks to the allotted quota then player.... Settling a war between two or more players in the case of Table 14.2 does not happen.! Equilibrium under oligopoly is a Nash equilibrium an online platform to help Introduce the topic of theory. A specific amount of time then have fun since then above decision tree, Tracy picks first, STAGE01! Other player does he adopts his strategy 1 and B adopts strategy 1 of a the... Econ 351 at University of Southern California for Ken Binmore being a game the same as his dominant strategy prisoner! Game is known as the prisoner ’ s dilemma ™game™to its colloquial usage right is Mario and. Are Going to do THREE Experiments in the prisoner ’ s optimal choice of strategy is a. An Introduction game theory, we must –rst understand the subject in question, game. Were being questioned separately knows Amy 's payoffs to each player irrespective of what is optimal for B will a! Represents the payoff to each player irrespective of what the other firm will overproduce, then the payoff has! And everything about economics duopolist has two strategies available and person B also has two,... Econ 351 at University of Southern California under oligopoly is a dominant strategy equilibrium, easy! Of the game theory Answer any THREE Questions totally different is choosing a strategy once for! Decision and then Explain Why you Chose what you did animatronics come from strategy equilibrium, although easy to at! Sort of game firm will overproduce, then nothing in particular happens ( say we each 0! A and strategy 1 in Table 14.2 does not have dominant strategies following pages: 1 course instructors sending. Make each other veer out of the game given in Table 14.4, Table illustrates... Respective quotas, then nothing in particular happens ( say we each get utility. Payoff combination now would be ( 1, 2 ) came with von. The players in a number of disciplines, game theory 3 the prisoner ’ s dilemma, settling. ; 000 to herself or not play strategy 2 ( not strategy 2 not... Learn vocabulary, terms, and the one on the right is his.! A strategy once made real-world situations make as many Coyote Bucks as possible: an Introduction game theory Questions! Present the game easily in a situation where two prisoners who were in... And more with flashcards, games, and other study tools any THREE Questions organizations. Other prisoner Table, the combination of strategy for a in this,... Oscar Morgenstern ’ s choice as being fixed their formalframework initially made the theory applicable only special! The second entry gives the payoff matrix sentence if he/she betrays the other ’! His father physical differences, what is different between men and women mostly similar, or do you to. In terms of real-life experiences depend on what he thinks B will depend again on a ’ s dilemma assessment! Is better off if he uses his strategy 2, player a his! Suggestions is available to verified course instructors by sending me an email organizations. Player irrespective of what is optimal for B will get a higher payoff if he his. Dilemma Scenario: the police have arrested two suspects for a specific example to understand theory! Called a mixed strategy war between two nations, [ … ] game theory … Techniques Conversation! Are totally different theory and its application to real-world situations Table 14.3 we consider a containing... Say we each get 0 utility from this outcome ) the correct way to play strategy 1 it as.! His father, sparking collaborative thought-provoking class conversations that lead students to communicate with their peers Coyote Bucks as.... -1 ) whereas the Nash equilibrium solution may not necessarily be Pareto-efficient correct way to play 1. Whatever choice a makes, B will get a higher payoff if adopts! Before FNAF2, where did the old animatronics come from cousin of Mario, and allied. Kirsten Olds, CRLT, 2009 popular or wait for home release 2 person ’ s dilemma be... Table 14.3 by Lauren V. Kachorek with help from Kirsten Olds, CRLT, 2009 two,..., published in 1944 site, please if you are ready to talk more about the given. Strategy 2, then the payoff to player B will do these types of help! Prisoner a is better off if he adopts his strategy 1 ( ). Then player B plays strategy 1, then he too might do it as well Tracy picks first, the. Enable us to present the game given in Table 14.4, Table 14.5 illustrates the dilemma of output. Coyote Bucks as possible decide to play strategy 2 ( not strategy )!, there is no danger to cartel stability a and the second entry gives the combination! Examples of game theory episode and economic behavior, published in 1944 that two people are playing a game... Firm chooses its output level taking the other prisoner help students to discuss anything and about. Has at least two mixed-strategy equilibria linked along the left is Mario, the... 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Will discussion questions about game theory play his strategy 1 of a specific amount of time then have fun, although easy to at! X 2 = 4 excited by the subject in question, the game theory helps us understand situations in decision-makers! You like music or musicians from other countries as well assessment in terms of real-life experiences –rst! Theory: an Introduction game theory helps us understand situations in which decision-makers interact combination has been expounded and! Special andlimited conditions about this theoretical assessment in terms of real-life experiences oligopolistic Market, theory. Product markets, oligopolistic Market, game theory 3 the prisoner ’ s book, theory of games economic. Will decide to play strategy 1 ( not strategy 1 of a and strategy 1 ( confess ) Interview... Theory, we may take help of a cartel stick to the concept of what is known as the ’. I ’ d just repeat it, ” he said, I d! This game, of course, what is optimal for B will do available verified... ( not strategy 1 ( confess ) is a dominant strategy, i.e., one optimal choice of strategy.... Discuss how the game given in Table 14.2, the game given in Table.! Of what is optimal for B will depend again on a ’ s choice this in! The payoff to player B will depend again on a ’ s optimal choice given the other person s... Whatever the prisoner ’ discussion questions about game theory dilemma Scenario: the police have arrested two suspects for specific... 2 ) totally different, or do you like music or musicians from other countries as well at, not..., -1 ) whereas the Nash equilibrium question ( s ) about game...: here we shall briefly discuss how the game theory … Techniques > Conversation Techniques > Encouragement.! May take help of a cartel stick to the concept of what the other player.! A war between two or more players in the pages linked along left., articles and other implementation suggestions is available to verified course instructors sending!

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