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E-grāmata: Game Theory and Exercises [Taylor & Francis e-book]

(University of Strasbourg, France)
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Game Theory and Exercises introduces the main concepts of game theory, along with interactive exercises to aid readers learning and understanding. Game theory is used to help players understand decision-making, risk-taking and strategy and the impact that the choices they make have on other players; and how the choices of those players, in turn, influence their own behaviour. So, it is not surprising that game theory is used in politics, economics, law and management.

This book covers classic topics of game theory including dominance, Nash equilibrium, backward induction, repeated games, perturbed strategie s, beliefs, perfect equilibrium, Perfect Bayesian equilibrium and replicator dynamics. It also covers recent topics in game theory such as level-k reasoning, best reply matching, regret minimization and quantal responses. This textbook provides many economic applications, namely on auctions and negotiations. It studies original games that are not usually found in other textbooks, including Nim games and travellers dilemma. The many exercises and the inserts for students throughout the chapters aid the readers understanding of the concepts.

With more than 20 years teaching experience, Umbhauers expertise and classroom experience helps students understand what game theory is and how it can be applied to real life examples. This textbook is suitable for both undergraduate and postgraduate students who study game theory, behavioural economics and microeconomics.
Acknowledgements xix
Introduction 1(4)
1 How To Build A Game 5(57)
Introduction
5(1)
1 Strategic Or Extensive Form Games?
5(23)
1.1 Strategic/normal form games
6(12)
1.1.1 Definition
6(1)
1.1.2 Story strategic/normal form games and behavioural comments
6(6)
1.1.3 All pay auction
12(6)
1.2 Extensive form games
18(10)
1.2.1 Definition
18(2)
1.2.2 Story extensive form games and behavioural comments
20(7)
1.2.3 Subgames
27(1)
2 Strategies
28(12)
2.1 Strategies in strategic/normal form games
28(2)
2.1.1 Pure strategies
28(1)
2.1.2 Mixed strategies
28(2)
2.2 Strategies in extensive form games
30(6)
2.2.1 Pure strategies: a complete description of the behaviour
30(1)
2.2.2 The Fort Boyard Sticks game and the Envelope game
31(4)
2.2.3 Behavioural strategies
35(1)
2.3 Strategic/normal form games and extensive form games: is there a difference?
36(4)
3 Information And Utilities
40(14)
3.1 Perfect/imperfect information
40(3)
3.1.1 A concept linked to the information sets
40(1)
3.1.2 The prisoners' disks game
41(2)
3.2 Complete/incomplete information
43(4)
3.2.1 Common knowledge: does it make sense?
43(2)
3.2.2 Signalling games and screening games
45(2)
3.3 Utilities
47(7)
3.3.1 Taking risks into account
47(2)
3.3.2 Which is the game you have in mind?
49(1)
3.3.3 Fairness and reciprocity
49(2)
3.3.4 Strategic feelings and paranoia
51(1)
3.3.5 How to bypass utilities
52(2)
Conclusion
54(8)
Exercise 1 Easy strategy sets
56(1)
Exercise 2 Children game, how to share a pie equally
57(1)
Exercise 3 Children game, the bazooka game, an endless game
57(1)
Exercise 4 Syndicate game: who will be the free rider?
57(1)
Exercise 5 Rosenthal's centipede (pre-emption) game, reduced normal form game
58(1)
Exercise 6 Duel guessing game, a zero sum game
58(1)
Exercise 7 Akerlof's lemon car, experience good model, switching from an extensive form signalling game to its normal form
59(1)
Exercise 8 Behavioural strategies and mixed strategies, how to switch from the first to the second and vice versa?
60(1)
Exercise 9 Dutch auction and first price sealed bid auction, strategic equivalence of different games
60(2)
2 Dominance 62(36)
Introduction
62(1)
1 Non Iterated Dominance
63(9)
1.1 Definitions, strict and weak dominance
63(1)
1.2 Dominance in normal form games
63(4)
1.2.1 Existence of dominated strategies
63(1)
1.2.2 Normal form games with dominated strategies
64(3)
1.3 Dominance in extensive form games
67(5)
1.3.1 Strict and weak dominance in the ascending all pay auction/war of attrition game
67(1)
1.3.2 Weak dominance and the Fort Boyard sticks game
68(4)
2 Iterated Dominance
72(3)
2.1 Iterated dominance, the order matters
72(1)
2.2 Iterated dominance and first doubts
73(2)
3 Crossed Rationality And Limits Of Iterated Dominance
75(4)
3.1 Envelope game: K-1 iterations for a strange result
75(2)
3.2 Levels of crossed rationality in theory and reality
77(1)
3.3 Crossed rationality in extensive form games, a logical inconsistency
78(1)
4 Dominance And Structure Of A Game, A Come Back To The Prisoner's Disks Game
79(8)
4.1 Solving the game by iterative elimination of strictly dominated strategies
79(5)
4.2 Dominance and easy rule of behaviour
84(3)
Conclusion
87(11)
Exercise 1 Dominance in a game in normal form
89(1)
Exercise 2 Dominance by a mixed strategy
89(1)
Exercise 3 Iterated dominance, the order matters
90(1)
Exercise 4 Iterated dominance in asymmetric all pay auctions
90(1)
Exercise 5 Dominance and value of information
91(1)
Exercise 6 Stackelberg first price all pay auction
92(1)
Exercise 7 Burning money
93(1)
Exercise 8 Pre-emption game in extensive form and normal form, and crossed rationality
93(1)
Exercise 9 Guessing game and crossed rationality
94(1)
Exercise 10 Bertrand duopoly
94(1)
Exercise 11 Traveller's dilemma (Basu's version)
95(1)
Exercise 12 Traveller's dilemma, the students' version
95(1)
Exercise 13 Duel guessing game, the cowboy story
95(1)
Exercise 14 Second price sealed bid auction
96(1)
Exercise 15 Almost common value auction, Bikhchandani and Klemperer's result
97(1)
3 Nash Equilibrium 98(52)
Introduction
98(1)
1 Nash Equilibrium, A First Approach
99(7)
1.1 Definition and existence of Nash equilibrium
99(1)
1.2 Pure strategy Nash equilibria in normal form games and dominated strategies
100(2)
1.3 Mixed strategy Nash equilibria in normal form games
102(4)
2 Nash Equilibria In Extensive Form Games
106(7)
2.1 Nash equilibria in the ascending all pay auction/war of attrition game
107(3)
2.2 Same Nash equilibria in normal form games and extensive form games
110(3)
3 Nash Equilibria Do A Good Job
113(9)
3.1 Nash equilibrium, a good concept in many games
113(5)
3.1.1 All pay auctions with incomplete information
113(2)
3.1.2 First price sealed bid auctions
115(1)
3.1.3 Second price sealed bid auctions, Nash equilibria and the marginal approach
116(2)
3.2 Nash equilibrium and simple rules of behaviour
118(4)
4 Multiplicity Of Nash Equilibria
122(5)
4.1 Multiplicity in normal form games, focal point and talking
122(1)
4.2 Talking in extensive form games
123(1)
4.3 Strange out of equilibrium behaviour, a game with a reduced field of vision
124(3)
5 To Play Or Not To Play A Nash Equilibrium, Cautious Behaviour And Risk Dominance
127(9)
5.1 A logical concept, but not always helpful
127(3)
5.2 Cautious behaviour and risk dominance
130(6)
5.2.1 Cautious behaviour
130(3)
5.2.2 Ordinal differences, risk dominance
133(3)
Conclusion
136(14)
Exercise 1 Nash equilibria in a normal form game
138(1)
Exercise 2 Story normal form games
138(1)
Exercise 3 Burning money
138(1)
Exercise 4 Mixed Nash equilibria and weak dominance
139(1)
Exercise 5 A unique mixed Nash equilibrium
139(1)
Exercise 6 French variant of the rock paper scissors game
139(1)
Exercise 7 Bazooka game
140(1)
Exercise 8 Pure strategy Nash equilibria in an extensive form game
141(1)
Exercise 9 Gift exchange game
141(1)
Exercise 10 Behavioural Nash equilibria in an extensive form game
142(1)
Exercise 11 Duel guessing game
142(1)
Exercise 12 Pre-emption game (in extensive and normal forms)
142(1)
Exercise 13 Bertrand duopoly
143(1)
Exercise 14 Guessing game
143(1)
Exercise 15 Traveller's dilemma (Basu)
143(1)
Exercise 16 Traveller's dilemma, students'version, P<49
143(1)
Exercise 17 Traveller's dilemma, students' version, P>49, and cautious behaviour
144(1)
Exercise 18 Focal point in the traveller's dilemma
145(1)
Exercise 19 Asymmetric all pay auctions
145(1)
Exercise 20 Wallet game, first price auction, winner's curse and a robust equilibrium
146(1)
Exercise 21 Wallet game, first price auction, Nash equilibrium and new stories
146(1)
Exercise 22 Two player wallet game, second price auction, a robust symmetric equilibrium
147(1)
Exercise 23 Two player wallet game, second price auction, asymmetric equilibria
147(1)
Exercise 24 N player wallet game, second price auction, marginal approach
147(1)
Exercise 25 Second price all pay auctions
148(1)
Exercise 26 Single crossing in a first price sealed bid auction
148(1)
Exercise 27 Single crossing and Akerlof's lemon car
148(1)
Exercise 28 Dutch auction and first price sealed bid auction
149(1)
4 Backward Induction And Repeated Games 150(57)
Introduction
150(1)
1 Subgame Perfect Nash Equilibrium And Backward Induction
151(3)
1.1 Subgame Perfect Nash equilibrium and Nash equilibrium
151(2)
1.2 Backward induction
153(1)
2 Backward Induction, Dominance And The Good Job Of Backward Induction/Subgame Perfection
154(6)
2.1 Backward induction and dominance
154(2)
2.2 The good job of backward induction/subgame perfection
156(4)
2.2.1 Backward induction and the Fort Boyard sticks game
156(2)
2.2.2 Backward induction and negotiation games
158(2)
3 When The Job Of Backward Induction/ Subgame Perfection Becomes Less Good
160(9)
3.1 Backward induction, forward induction or thresholds?
160(3)
3.2 Inconsistency of backward induction, forward induction or momentary insanity?
163(2)
3.3 When backward induction leads to very strange results
165(4)
4 Finitely Repeated Games
169(10)
4.1 Subgame Perfection in finitely repeated normal form games
169(6)
4.1.1 New behaviour in finitely repeated normal form games
169(4)
4.1.2 New behaviour, which links with the facts?
173(1)
4.1.3 Repetition and backward induction's inconsistency
174(1)
4.2 Subgame perfection in finitely repeated extensive form games
175(4)
4.2.1 A forbidden transformation
176(1)
4.2.2 New behaviour in repeated extensive form games
177(2)
5 Infinitely Repeated Games
179(16)
5.1 Adapted backward induction
179(1)
5.2 Infinitely repeated normal form games
180(13)
5.2.1 New behaviour in infinitely repeated normal form games, a first approach
180(2)
5.2.2 Minmax values, individually rational payoffs, folk theorem
182(2)
5.2.3 Building new behaviour with the folk theorem
184(5)
5.2.4 Punishing and rewarding in practice
189(4)
5.3 Infinitely repeated extensive form games
193(2)
Conclusion
195(12)
Exercise 1 Stackelberg all pay auction, backward induction and dominance
198(1)
Exercise 2 Duel guessing game
198(1)
Exercise 3 Centipede pre-emption game, backward induction and the students' way of playing
199(1)
Exercise 4 How to share a shrinking pie
200(1)
Exercise 5 English all pay auction
201(1)
Exercise 6 General sequential all pay auction, invest a max if you can
201(1)
Exercise 7 Gift exchange game
202(1)
Exercise 8 Repeated games and strict dominance
203(1)
Exercise 9 Three repetitions are better than two
203(1)
Exercise 10 Alternate rewards in repeated games
204(1)
Exercise 11 Subgame perfection in Rubinstein's finite bargaining game
204(1)
Exercise 12 Subgame perfection in Rubinstein's infinite bargaining game
204(1)
Exercise 13 Gradualism and endogenous offers in a bargaining game, Li's insights
205(1)
Exercise 14 Infinite repetition of the traveller's dilemma game
205(1)
Exercise 15 Infinite repetition of the gift exchange game
205(2)
5 Trembles In A Game 207(43)
Introduction
207(1)
1 Selten's Perfect Equilibrium
208(8)
1.1 Selten's horse, what's the impact of perturbing strategies?
208(1)
1.2 Selten's perfect/trembling hand equilibrium
209(1)
1.3 Applications and properties of the perfect equilibrium
210(6)
1.3.1 Selten's horse, trembles and strictly dominated strategies
210(3)
1.3.2 Trembles and completely mixed behavioural strategies
213(1)
1.3.3 Trembles and weakly dominated strategies
214(2)
2 Selten's Closest Relatives, Kreps, Wilson, Harsany And Myerson: Sequential Equilibrium, Perfect Bayesian Equilibrium And Proper Equilibrium
216(11)
2.1 Kreps and Wilson's sequential equilibrium: the introduction of beliefs
216(5)
2.1.1 Beliefs and strategies: consistency and sequential rationality
216(2)
2.1.2 Applications of the sequential equilibrium
218(3)
2.2 Harsanyi's perfect Bayesian equilibrium
221(4)
2.2.1 Definition, first application and links with the sequential equilibrium
221(3)
2.2.2 French plea-bargaining and perfect Bayesian equilibria
224(1)
2.3 Any perturbations or only a selection of some of them? Myerson's proper equilibrium
225(2)
3 Shaking Of The Game Structure
227(8)
3.1 When only a strong structural change matters, Myerson's carrier pigeon game
227(2)
3.2 Small change, a lack of upper hemicontinuity in equilibrium strategies
229(1)
3.3 Large changes, a lack of upper hemicontinuity in equilibrium payoffs
229(3)
3.4 Very large changes, a lack of lower hemicontinuity in equilibrium behaviours and payoffs, Rubinstein's e-mail game
232(3)
4 Perturbing Payoffs And Best Responses In A Given Way
235(6)
4.1 Trembling-hand perfection
236(2)
4.2 Quantal responses
238(2)
4.3 Replicator equations
240(1)
Conclusion
241(9)
Exercise 1 Perfect and proper equilibrium
243(1)
Exercise 2 Perfect equilibrium with weakly dominated strategies
243(1)
Exercise 3 Perfect equilibrium and incompatible perturbations
244(1)
Exercise 4 Strict sequential equiliubrium
245(1)
Exercise 5 Sequential equilibrium, inertia in the players' beliefs
245(1)
Exercise 6 Construct the set of sequential equilibria
246(1)
Exercise 7 Perfect equilibrium, why the normal form is inadequate, a link to the trembling-hand equilibrium
246(1)
Exercise 8 Perfect Bayesian equilibrium
247(1)
Exercise 9 Perfect Bayesian equilibrium, a complex semi separating equilibrium
247(1)
Exercise 10 Lemon cars, experience good market with two qualities
248(1)
Exercise 11 Lemon cars, experience good market with n qualities
248(1)
Exercise 12 Perfect Bayesian equilibria in alternate negotiation with incomplete information
249(1)
6 Solving A Game Differently 250(49)
Introduction
250(1)
1 Best Reply Matching
250(10)
1.1 Definitions and links with correlation and the Nash equilibrium
251(3)
1.1.1 Best reply matching, a new way to work with mixed strategies
251(2)
1.1.2 Link between best reply matching equilibria and Nash equilibria
253(1)
1.1.3 Link between best reply matching equilibria and correlated equilibria
253(1)
1.2 Auction games, best reply matching fits with intuition
254(3)
1.3 Best reply matching in ascending all pay auctions
257(2)
1.4 Limits of best reply matching
259(1)
2 Halpern And Pass's Regret Minimization
260(11)
2.1 A new story game, the traveller's dilemma
260(3)
2.2 Regret minimization
263(3)
2.2.1 Definition
263(1)
2.2.2 Regret minimization and the traveller's dilemma
264(1)
2.2.3 Regret minimization and the envelope game
265(1)
2.3 Regret minimization in the ascending all pay auction/war of attrition: a switch from normal form to extensive form
266(2)
2.4 The limits of regret minimization
268(3)
2.4.1 A deeper look into all pay auctions/wars of attrition
268(2)
2.4.2 Regret minimization: a too limited rationality in easy games
270(1)
3 Level-K Reasoning
271(7)
3.1 Basic level-k reasoning in guessing games and other games
271(3)
3.1.1 Basic level-k reasoning in guessing games
271(2)
3.1.2 Basic level-k reasoning in the envelope game and in the traveller's dilemma game
273(1)
3.2 A more sophisticated level-k reasoning in guessing games
274(2)
3.3 Level-k reasoning versus iterated dominance, some limits of level-k reasoning
276(2)
3.3.1 Risky behaviour and decreasing wins
276(1)
3.3.2 Level-k reasoning is riskier than iterated dominance
277(1)
3.3.3 Something odd with basic level-k reasoning?
278(1)
4 Forward Induction
278(11)
4.1 Kohlberg and Mertens' stable equilibrium set concept
279(3)
4.2 The large family of forward induction criteria with starting points
282(5)
4.2.1 Selten's horse and Kohlberg's self-enforcing concept
282(1)
4.2.2 Local versus global interpretations of actions
283(4)
4.3 The power of forward induction through applications
287(2)
4.3.1 French plea-bargaining and forward induction
287(1)
4.3.2 The repeated battle of the sexes or another version of burning money
288(1)
Conclusion
289(10)
Exercise 1 Best reply matching in a normal form game
291(1)
Exercise 2 Best reply matching in the traveller's dilemma
291(1)
Exercise 3 Best reply matching in the pre-emption game
292(1)
Exercise 4 Minimizing regret in a normal form game
293(1)
Exercise 5 Minimizing regret in Bertrand's duopoly
293(1)
Exercise 6 Minimizing regret in the pre-emption game
293(1)
Exercise 7 Minimizing regret in the traveller's dilemma
294(1)
Exercise 8 Level-k reasoning in an asymmetric normal form game
295(1)
Exercise 9 Level-1 and level-k reasoning in Basu's traveller's dilemma
295(1)
Exercise 10 level-1 and level-k reasoning in the students' traveller's dilemma
295(1)
Exercise 11 Stable equilibrium, perfect equilibrium and perturbations
295(1)
Exercise 12 Four different forward induction criteria and some dynamics
296(1)
Exercise 13 Forward induction and the experience good market
296(1)
Exercise 14 Forward induction and alternate negotiation
297(2)
Answers To Exercises 299(138)
1 How To Build A Game
301(15)
Answers 1 Easy strategy sets
301(1)
Answers 2 Children game, how to share a pie equally
301(1)
Answers 3 Children game, the bazooka game, an endless game
301(1)
Answers 4 Syndicate game: who will be the free rider?
302(1)
Answers 5 Rosenthal's centipede (pre-emption) game, reduced normal form game
303(2)
Answers 6 Duel guessing game, a zero sum game
305(2)
Answers 7 Akerlof's lemon car, experience good model, switching from an extensive form signalling game to its normal form
307(2)
Answers 8 Behavioural strategies and mixed strategies, how to switch from the first to the second and vice versa?
309(3)
Answers 9 Dutch auction and first price sealed bid auction, strategic equivalence of different games
312(4)
2 Dominance
316(20)
Answers 1 Dominance in a game in normal form
316(1)
Answers 2 Dominance by a mixed strategy
316(1)
Answers 3 Iterated dominance, the order matters
317(1)
Answers 4 Iterated dominance in asymmetric all pay auctions
317(2)
Answers 5 Dominance and value of information
319(1)
Answers 6 Stackelberg first price all pay auction
320(1)
Answers 7 Burning money
321(1)
Answers 8 Pre-emption game in extensive form and normal form, and crossed rationality
322(1)
Answers 9 Guessing game and crossed rationality
323(1)
Answers 10 Bertrand duopoly
324(1)
Answers 11 Traveller's dilemma (Basu's version)
325(1)
Answers 12 Traveller's dilemma, the students' version
326(1)
Answers 13 Duel guessing game, the cowboy story
327(4)
Answers 14 Second price sealed bid auction
331(2)
Answers 15 Almost common value auction, Bikhchandani and Klemperer's result
333(3)
3 Nash Equilibrium
336(30)
Answers 1 Nash equilibria in a normal form game
336(1)
Answers 2 Story normal form games
337(1)
Answers 3 Burning money
338(1)
Answers 4 Mixed Nash equilibria and weak dominance
339(1)
Answers 5 A unique mixed Nash equilibrium
339(1)
Answers 6 French variant of the rock paper scissors game
340(1)
Answers 7 Bazooka game
341(1)
Answers 8 Pure strategy Nash equilibria in an extensive form game
342(1)
Answers 9 Gift exchange game
342(1)
Answers 10 Behavioural Nash equilibria in an extensive form game
343(1)
Answers 11 Duel guessing game
344(1)
Answers 12 Pre-emption game (in extensive and normal forms)
345(2)
Answers 13 Bertrand duopoly
347(1)
Answers 14 Guessing game
348(1)
Answers 15 Traveller's dilemma (Basu)
348(2)
Answers 16 Traveller's dilemma, students' version, P<49
350(1)
Answers 17 Traveller's dilemma, students' version, P>49, and cautious behaviour
351(1)
Answers 18 Focal point in the traveller's dilemma
352(1)
Answers 19 Asymmetric all pay auctions
352(2)
Answers 20 Wallet game, first price auction, winner's curse and a robust equilibrium
354(1)
Answers 21 Wallet game, first price auction, Nash equilibrium and new stories
355(1)
Answers 22 Two player wallet game, second price auction, a robust symmetric equilibrium
356(1)
Answers 23 Two player wallet game, second price auction, asymmetric equilibria
357(2)
Answers 24 N player wallet game, second price auction, marginal approach
359(1)
Answers 25 Second price all pay auctions
360(1)
Answers 26 Single crossing in a first price sealed bid auction
361(1)
Answers 27 Single crossing and Akerlof's lemon car
362(1)
Answers 28 Dutch auction and first price sealed bid auction
363(3)
4 Backward Induction And Repeated Games
366(29)
Answers 1 Stackelberg all pay auction, backward induction and dominance
366(1)
Answers 2 Duel guessing game
367(1)
Answers 3 Centipede pre-emption game, backward induction and the students' way of playing
368(2)
Answers 4 How to share a shrinking pie
370(1)
Answers 5 English all pay auction
371(2)
Answers 6 General sequential all pay auction, invest a max if you can
373(2)
Answers 7 Gift exchange game
375(1)
Answers 8 Repeated games and strict dominance
376(2)
Answers 9 Three repetitions are better than two
378(1)
Answers 10 Alternate rewards in repeated games
379(1)
Answers 11 Subgame perfection in Rubinstein's finite bargaining game
380(3)
Answers 12 Subgame perfection in Rubinstein's infinite bargaining game
383(1)
Answers 13 Gradualism and endogenous offers in a bargaining game, Li's insights
384(1)
Answers 14 Infinite repetition of the traveller's dilemma game
385(8)
Answers 15 Infinite repetition of the gift exchange game
393(2)
5 Trembles In A Game
395(19)
Answers 1 Perfect and proper equilibrium
395(1)
Answers 2 Perfect equilibrium with weakly dominated strategies
396(2)
Answers 3 Perfect equilibrium and incompatible perturbations
398(1)
Answers 4 Strict sequential equilibrium
399(1)
Answers 5 Sequential equilibrium, inertia in the players' beliefs
399(2)
Answers 6 Construct the set of sequential equilibria
401(1)
Answers 7 Perfect equilibrium, why the normal form is inadequate, a link to the trembling-hand equilibrium
402(2)
Answers 8 Perfect Bayesian equilibrium
404(2)
Answers 9 Perfect Bayesian equilibrium, a complex semi separating equilibrium
406(1)
Answers 10 Lemon cars, experience good market with two qualities
407(1)
Answers 11 Lemon cars, experience good market with n qualities
408(2)
Answers 12 Perfect Bayesian equlibria in alternate negotiation with incomplete information
410(4)
6 Solving A Game Differently
414(23)
Answers 1 Best reply matching in a normal form game
414(2)
Answers 2 Best-reply matching in the traveller's dilemma
416(3)
Answers 3 Best-reply matching in the pre-emption game
419(2)
Answers 4 Minimizing regret in a normal form game
421(1)
Answers 5 Minimizing regret in Bertrand's duopoly
422(1)
Answers 6 Minimizing regret in the pre-emption game
423(1)
Answers 7 Minimizing regret in the traveller's dilemma
424(2)
Answers 8 Level-k reasoning in an asymmetric normal form game
426(1)
Answers 9 Level-1 and level-k reasoning in Basu's traveller's dilemma
426(3)
Answers 10 Level-1 and level-k reasoning in the students' traveller's dilemma
429(2)
Answers 11 Stable equilibrium, perfect equilibrium and perturbations
431(2)
Answers 12 Four different forward induction criteria and some dynamics
433(1)
Answers 13 Forward induction and the experience good market
434(1)
Answers 14 Forward induction and alternate negotiation
435(2)
Index 437
Gisčle Umbhauer is Associate Professor of economics at the University of Strasbourg, France.