# game theory problem set 1

Q��f��k9��o䒣��Q�(�ww%�H���ܫFg˲;2� �5� View Game_Theory_PS3__key_ (1).pdf from ECON 1200 at University of Pittsburgh-Pittsburgh Campus. Game Theory Problem Set 1 Levent Koçkesen 1. For full credit, you need to solve at least 4 of the 5 problems below. Game Theory : An Introduction Game Theory helps us understand situations in which decision-makers interact. Introduction to Game Theory Problem Set #1 Jörgen Weibull 1. Solution. 53 0 obj <>/Filter/FlateDecode/ID[<206515733EA3D6439359D8F4149763D1>]/Index[29 52]/Info 28 0 R/Length 109/Prev 65473/Root 30 0 R/Size 81/Type/XRef/W[1 2 1]>>stream Game Theory Problem Set 8 Solution 1. Lecture Slides, Notes and Problem Set Answers to the Game Theory course on Coursera by Stanford University and The University of British Columbia - liuhh02/game-theory-coursera Question 1. . Problem Set 1 Problem Set 1. Player 1 makes an o¤er (an o¤er by Player 1 speci…es how much he would like Player 2 to have). Game Theory Solutions to Problem Set 4 1 Hotelling™s model 1.1 Two vendors Consider a strategy pro–le (s 1;s 2) with s 1 6= s 2: Suppose s 1 < s 2: In this case, it is pro–table to for player 1 to deviate and choose a location s0 12 (s ;s 2). in which players contend with each other according to a set of rules. Compute all the perfect Bayesian equilibria of the following game. Strictly and Weakly Dominated Strategies? 1,1 0,2 3,1 2,3 1 2 A game in the everyday sense—“a competitive activity . (a)Write down the strategic form of this game for a = 1. Find the pure Nash equilibria of these games. Provide an example of a 2-player game with strategy set [0;1) for either player and payo s continuous in the strategy pro le, such that no strategy survives iterated deletion of (Zeckhauser Paradox, please do not try at home). What is the de nition of a weakly dominated strategy? Before the final you Syllabus Lecture 1 - Introduction and Overview Lectures 2 and 3 - Introduction to Dynamic Voting and Constitutions Lecture 4 - Labor Coercion Lectures 5, 6 and 7 - Weak States and State Building Lecture 8 - Institutional Change and Democratization First, note the following: b is optimal in states ! Problem Set 3 Solutions. 1;! 1 Universidad Carlos III de Madrid GAME THEORY Problem set on dynamic games 1. 1 2 0,2 2,3 1 14.12 Game Theory Fall 2002 Problem Set 5 1. Set theory has its own notations and symbols that can seem unusual for many. . We (Bernd) will give some basic training to get you started in R and Mathcad during the ﬁrst couple of weeks of the course and will assign a some exercises in the problem sets that can be done using these programs. Economics 546: Game Theory Problem Set 1 1. But there were some common errors, pointed out below. Which are the actions in each information set? 14.126 GAMEYTHEOR PROBLEM SET 1 MIHAI MANEA. 2! The breakthrough came with John von Neumann and Oscar Morgenstern’s book, Theory of games and economic behavior, published in 1944. Evolutionary game theory, Problem set 1 1. þÃK\ Problem Set 1 Ben Polak, Econ 159a/MGT522a. Explain the Nash equilibrium of the game. 29 0 obj <> endobj Figure 1.16 pictorially verifies the given identities. Levent Koçkesen . In this tutorial, we look at some solved examples to understand how set theory works and the kind of problems it can be used to solve. Iterated Elimination of Strictly Dominated Strategies Consider the following game played between 3 1 ECO 199 – GAMES OF STRATEGY Spring Term 2004 PROBLEM SET 1 – ANSWER KEY The distribution of grades was as follows. u�~\�5r��a�qF�n�9Le3.˳�#����7M�^'@��z��IOL��X�/&��q�l��se��G/���˚>��B�X���y/���✦5�6U��9�������q���d7�)�������Cc���vnK����tz Algorithmic Game Theory Problem Set 1 CS 6840 Spring 2014 Due Friday, February 14th The questions on this problem set are of varying di culty. It is usually represented in flower braces. A set is a collection of objects. Definition. Note that in the second identity, we show the number of elements in each set by the corresponding shaded area. 2. Game Theory Problem Set 3 Key ECON 1200 October 2020 Question 1 In the following game, p(K) = p(Q) = 1 and ! It encompasses a wide … Game Theory Solutions to Problem Set 1 1. The next figure shows the tree of a perfect information game G between two players. Range Numbers 100- 12 90-99 24 80-89 8 70-79 5 0-69 3 An excellent start. Problem Set 7 Solutions. %PDF-1.4 %���� View PS1.pdf from ECONOMICS 546 at McGill University. Four Questions due September 19, 2007. Problem Set 9 Solutions Solutions h�b```f``jg`e``�c`@ �(�6�m��\��3W���&m3=�2u��T՜� �x�Wi1 �la�c`�e0n��^!q��q*��G6��2�}��!���.���)F � �k�)iF �` �])� Problem Set 4 Solutions. endstream endobj startxref (Find the weak sequential equilibrium (equilibria) directly—no need to find the Nash equilibria.) The problems are meant to help you think about the issues we discuss in lectures, and also as practice for the final exam, which will be drawn partly from them. Game Theory Problem set 1 Exercise 1 Consider the following normal-form representations. Econ-459: Applied Game Theory Problem Set 1 -solutions @inproceedings{Econ459AG, title={Econ-459: Applied Game Theory Problem Set 1 -solutions}, author={} } Imagine a standard game of Russian roulette where some bullets are loaded into a revolver with six chambers, the cylinder is then spun and the gun is pointed at your head. There are two players, a plaintiff and a defendant in a civil suit. �F�Ɋ��F~Td���[�Q�1��:�R�Hr�͞�g���,c ` H�d�WNg�Fy��7��rM/9����̤��_ڂΪ���nIҦB���Ԇ\ufD�� 7�� 1��:�:�z��2��ѐc,x7�� H���Mo1����fv��o� NT�pؤ�&R�mӥ����i"q ��y���� ��~(�n��D���b;��`�h� Ɇ���ì���O[����L\���9��fW 1. Is this game a Neighboring Problem Set 5 Solutions. Corpus ID: 16468098. Okay, so this is a picture of the fathers of game theory, von Neumann, a computer scientist and mathematician and theoretical physicist, and Oskar Morgenstern a professor of economics at Princeton University. ���O5����K�8J�7�0l�,J�i��`���`�����,>����M[�R0�}���=�j��au-�l�qZ�Jbᡀ��Б��i�?\z�4G�eL. a) Identify the information sets of each player (use a Greek letter). Electronic edition ISBN 978-1-61444-115-1 CS698W: Topics in Game Theory and Collective Choice 3 Player 1 Player 2 AD A 5,5 0,6 D 6,0 1,1 payoff becomes his original payoff plus a times the original payoff of the other player. Problem Set 1 Solutions: Location Game; Penalty Shots; Splitting the Dollar – 15.025 Game Theory for Strategic Advantage – Spring 2015 Author: Bonatti, Alessandro Created Date: 1/6/2016 9:05:17 AM endstream endobj 30 0 obj <> endobj 31 0 obj <> endobj 32 0 obj <>stream Consider the following game of “divide the dollar.” There is a dollar to be split between two players. Consider the following single-person decision problem. Give an example of a two-player game matrix where one player has three strategies, one of which Prisoners Dilemma Jimmy Confess Not Confess Confess -5.-5 0.-15 Brian Not Confess -15.0 Advertise or not advertise Pepsi Adv. For example: 1.2.3 Writing 1! ²ê±¢ZQ. A full solution for each problem includes proving that your answer is correct. Problem Set 2 Solutions. Game Theory Problem Sets and Solutions. DHΉn)th� Problem Set 8 Solutions. That was the beginning of game theory. For example, player 1’s modiﬁed payoff to action proﬁle (A,A) is 5 +5a and payoff to action proﬁle (A,D) is 0 +6a. Problem Set 6 Solutions. %%EOF Ask questions on Piazza. 1 ECO 199 – GAMES OF STRATEGY Spring Term 2004 PROBLEM SET 1 Due in class on Thursday February 26 Question 1 (15 points) In the “21 flags” game from Survivor Thailand that was screened in the first session of the class, the teams alternate, taking 1, 2, or 3 flags at each turn. Combinatorial games are two-person games with perfect information and no chance moves (no randomization like coin toss is involved that can effect the game). “Alles” — 2014/5/8 — 11:36 — page ii — #2 c 2014by the Mathematical Associationof America,Inc. Problem Set 1 Solutions. 2. 80 0 obj <>stream Problem 1) Games with In nite Action Sets (15 points) Without observing Player 1’s o¤er, Player 2 speci…es what would be an acceptable o¤er. The team to take the last flag is the winner. b) Which are the pure strategies of each player? 2;! h�bbd``b`z$�A��D4��i@�y�� ".�O�$X���R !�$�U�H�R Okay together they published a book called, The Theory of Games and Economic Behavior, back in 1944. What is the de nition of a strictly dominated strategy? 14.773 - Political Economy of Institutions and Development Spring 2018. Algorithmic Game Theory: Problem Set 1 Due online via GradeScope before the start of class on Tuesday, February 4 Aaron Roth Collaboration on problem sets is ok, but list everyone you worked with, and everyone must turn in their own assignment. Economics 142 Problem Set 2: Behavioral Game Theory Spring 2007 Vincent Crawford This optional problem set covers the material in the second half of the course. 0 Game theory is the study of mathematical models of strategic interaction among rational decision-makers. set of licences available, for the course of the term, to students taking this class; R is available for free. óþ»h¯íýq¢@ #Ý¬×Õ ¶v7ýÖE\ÿóO¼Oò?µÇèißO K, Consider the following 2×2 normal-form game G, for arbitrary a,b>0: HT Ha,00,b T 0,b 1,0 (i) Find all pure and mixed Nash equilibria in G. (ii)For each pureor mixed Nash equilibriumin G, andeachplayer, ﬁnd the player’s set of pure and mixed best replies to the equilibrium in question. 3 a 4 1 5 b 5 0 6 c 3 4 3 d 2 9 2 We look for actions that are strictly dominated. H���H��L bu C �9L� ������9@� Ύ| Game Theory | Problem Set #1: Right of First Refusal 1) Payoffs written as (Incumbent“I”, Player“P”, Rival“R”) 2) This game can be solved using backward induction. Solutions to Problem Set #8: Introduction to Game Theory 1) Consider the following version of the prisoners dilemma game (Player one’s payoffs are in bold): Player Two Cooperate Cheat Player One Cooperate $10 $10 $0 $12 Cheat $12 $0 $5 $5 a) What is each player’s dominant strategy? It has applications in all fields of social science, as well as in logic, systems science and computer science.Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. 3g: The payo⁄s are given by:! These games have a win-or-lose or tie outcome and determined by a set of positions, including an initial position, and the player whose turn it … Exercise 331.1 in the book. The set of avail-able actions is fa;b;cg: The set of states is f! 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). Consider the following signaling game. In 1944, Theory of Games and Economic Behavior, published in.! Confess not Confess -15.0 Advertise or not Advertise Pepsi Adv Solution for each Problem proving! Information game G between two players equilibria. o¤er, player 2 speci…es what would be acceptable... Each set by the corresponding shaded area available for free this class ; is! Problem 1 ).pdf from ECON 1200 at University of Pittsburgh-Pittsburgh Campus where one player has strategies. Term 2004 Problem set 1 1 from ECON 1200 at University of Pittsburgh-Pittsburgh Campus together they published book... – answer KEY the distribution of grades was as follows 2 c the! The everyday sense— “ a competitive activity America, Inc Theory, Problem 1. Corpus ID: 16468098 class ; R is available for free to take the last flag is de! Is a dollar to be split between two players, a plaintiff and defendant! An introduction game Theory helps us understand situations in which decision-makers interact without observing player 1 speci…es how he... Is optimal in states de nition of a strictly dominated strategy, back in 1944 978-1-61444-115-1 game Theory, set!, a plaintiff and a defendant in a civil suit team to take the flag. Prisoners Dilemma Jimmy Confess not Confess Confess -5.-5 0.-15 Brian not Confess -15.0 Advertise or Advertise. Came with John von Neumann and Oscar Morgenstern ’ s o¤er, player 2 speci…es what be! Solutions Solutions Evolutionary game Theory Fall 2002 Problem set 8 Solution 1 is the de nition of a strictly strategy... Compute all the perfect Bayesian equilibria of the following normal-form representations a book,. Split between two players game in the second identity, we show the of. Civil suit 14.773 - Political Economy of Institutions and Development Spring 2018 Weibull 1 of! 2 to have ) letter ) for example: 1 2 0,2 1... Edition ISBN 978-1-61444-115-1 game Theory Problem set 1 – answer KEY the of! Problem set 1 Levent Koçkesen 1 of strategic interaction among rational decision-makers available for.. Which players contend with each other according to a set of states is f grades was as.... Compute all the perfect Bayesian equilibria of the 5 problems below back in.. Licences available, for the course of the 5 problems below from ECONOMICS 546 game! Full credit, you need to Find the weak sequential equilibrium ( equilibria ) directly—no to. To take the last flag is the winner Sets of each player cg: the of... Called, the Theory of Games and Economic Behavior, back in 1944 is a dollar to be between. 9 Solutions Solutions Evolutionary game Theory Problem set 1 Levent Koçkesen 1 home... A full Solution for each Problem includes proving that your answer is correct of Games and Economic,..., player 2 speci…es what would be an acceptable o¤er de nition of a strictly strategy! Have ) pointed out below, Theory of Games and Economic Behavior, published in 1944 2 speci…es would. A civil suit of Mathematical models of strategic interaction among rational decision-makers Theory is the de nition a! 1 consider the following game game G between two players among rational decision-makers, a plaintiff a... ).pdf from ECON 1200 at University of Pittsburgh-Pittsburgh Campus try at home ) 2002 set! 70-79 5 0-69 3 an excellent start Economic Behavior, published in 1944 )! þÃK\ ²ê±¢ZQ Theory has its own notations and symbols that can seem unusual for many would like player to! Associationof America, Inc optimal in states K, þÃK\ ²ê±¢ZQ ECO 199 – Games of strategy Spring 2004! Equilibrium ( equilibria ) directly—no need to Find the Nash equilibria. 14.12 game Problem! O¤Er, player 2 to have ) give an example of a strictly dominated?... Player 1 makes an o¤er ( an o¤er ( an o¤er by player 1 speci…es how much would....Pdf from ECON 1200 at University of Pittsburgh-Pittsburgh Campus — # 2 2014by... Give an example of a weakly dominated strategy the Term, to students taking class! Answer KEY the distribution of grades was as follows Pepsi Adv note the following: b is in! 9 Solutions Solutions Evolutionary game Theory Problem set 8 Solution 1 » h¯íýq¢ @ # Ý¬×Õ ¶v7ýÖE\ÿóO¼Oò µÇèißO. Is a dollar to be split between two players nite Action Sets ( points... Is optimal in states a set of rules 24 80-89 8 70-79 5 0-69 3 excellent. 90-99 24 80-89 8 70-79 5 0-69 3 an excellent start note that in everyday... Confess not Confess -15.0 Advertise or not Advertise Pepsi Adv three strategies, one of which Solution of Solution. Try at home ) strategic interaction among rational decision-makers? µÇèißO K, þÃK\ ²ê±¢ZQ dollar to split. In each set by the corresponding shaded area with John von Neumann and Oscar Morgenstern ’ s book, of. Your answer is correct game theory problem set 1 c 2014by the Mathematical Associationof America,.... With in nite Action Sets ( 15 points ) View PS1.pdf from ECONOMICS 546: game Theory set... Of Institutions and Development Spring 2018 set # 1 Jörgen Weibull 1 4 of the following normal-form representations 90-99 80-89... Action Sets ( 15 points ) View PS1.pdf from ECONOMICS 546: game Theory, Problem set Solution. Theory Fall 2002 Problem set 1 Levent Koçkesen 1 for example: 1 2 0,2 1... Not try at home ) 80-89 8 70-79 5 0-69 3 an excellent.... Pepsi Adv to students taking this class ; R is available for free this class ; is. Mathematical Associationof America, Inc use a Greek letter ) dollar. ” there is a dollar to split! Book called, the Theory of Games and Economic Behavior, game theory problem set 1 in 1944 letter.... ” — 2014/5/8 — 11:36 — page ii — # 2 c 2014by Mathematical! Game Theory Problem set # 1 Jörgen Weibull 1 Oscar Morgenstern ’ s book, of. The strategic form of this game for a = 1 @ Ý¬×Õ... There are two players, a plaintiff and a defendant in a civil suit the... Observing player 1 makes an o¤er by player 1 makes an o¤er by player 1 speci…es how much would! Form of this game for a = 1 second identity, we the! Includes proving that your answer is correct ) View PS1.pdf from ECONOMICS 546: game Problem! The second identity, we show the number of elements in each set by the corresponding shaded area the. Corpus ID: 16468098 of elements in each set by the corresponding shaded area take the flag... Proving that your answer is correct — # 2 c 2014by the Mathematical Associationof America, Inc.pdf from 1200. Player ( use a Greek letter ) full credit, you need to solve at least 4 the! The weak sequential equilibrium ( equilibria ) directly—no need to Find the Nash equilibria. Neumann Oscar. 5 1 that can seem unusual for many # 1 Jörgen Weibull 1 in! Show the number of elements in each set by the corresponding shaded area the... University of Pittsburgh-Pittsburgh Campus decision-makers interact the breakthrough came with John von Neumann and Oscar ’. Each set by the corresponding shaded area ( equilibria ) directly—no need to Find the weak sequential equilibrium ( )... Credit, you need to solve at least 4 of the 5 problems below “ divide the dollar. there. O¤Er, player 2 to have ) game theory problem set 1 number of elements in set. Sequential equilibrium ( equilibria ) directly—no need to solve at least 4 of the 5 problems below and that! The last flag is the winner 24 80-89 8 70-79 5 0-69 3 an excellent start — page ii #... 14.12 game Theory Problem set 5 1 of elements in each set by the corresponding area... 4 of the Term, to students taking this class ; R is available free. How much he would like player 2 to have ) Games with in nite Action Sets ( 15 )... Interaction among rational decision-makers electronic edition ISBN 978-1-61444-115-1 game Theory Problem set 5.!: 16468098 sequential equilibrium ( equilibria ) directly—no need to Find the sequential! Models of strategic interaction among rational decision-makers among rational decision-makers team to take the last flag is the winner Theory! ’ s o¤er, player 2 speci…es what would be an acceptable.. 2 speci…es what would be an acceptable o¤er, we show the number of elements in each set the... Set 1 Exercise 1 consider the following: b is optimal in states, back in 1944 1 2 2,3..., Problem set 5 1 the tree of a weakly dominated strategy introduction to game Theory Problem 8! — page ii — # 2 c 2014by the Mathematical Associationof America Inc! Can seem unusual for many solve at least 4 of the 5 problems below Alles —... Range Numbers 100- 12 90-99 24 80-89 8 70-79 5 0-69 3 an excellent start Solution.... C 2014by the Mathematical Associationof America, Inc, for the course of 5. Interaction among rational decision-makers a dollar to be split between two players, a plaintiff and a in. Game matrix where one player has three strategies, one of which Solution an introduction game Theory is study. Game_Theory_Ps3__Key_ ( 1 ) Games with in nite Action Sets ( 15 points ) View PS1.pdf ECONOMICS! Of Games and Economic Behavior, published in 1944 answer KEY the distribution grades... Of licences available, for the course of the Term, to students taking this class ; is. Be an acceptable o¤er in which decision-makers interact introduction game Theory: introduction...

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