Lecture notes

 The course materials are based on the following textbook.

 Steven Tadelis (2012)  Game Theory: An Introduction, Princeton University Press.

 I put the materials on the web.

 Schedule (pdf), Schedule (slide, pdf) (Oct. 5)
 Chapter 3 (pdf) (Oct. 5)

 I will put the slide of Chapter 4 until the end of October 15, 2015 (Oct. 5). 
 Chapter 4 (pdf) (Oct. 15)

 I will put the slide of Chapter 5 until the end of October 25, 2015 (Oct. 19).
 Chapter 5 (pdf) (Oct. 25)

 On October 26, we have learned from the beginning of Chapter 5 to Example (3).
 Please learn the rest of the slide of Chapter 5 by yourself although we learn it 
 on November 9. After finishing the explanation on the slide of Chapter 5,
 I will assign the first short answer question, which is based on the lecture slides.

 I will put the slide of Chapter 6 until the end of November 4, 2015 (Oct. 28).
 Chapter 6 (pdf), Supplement of Chap 6.4 (pdf) (Nov. 4)

 I have assigned the first short answer question (SAQ) (Nov. 9). 
 In the subsequent SAQs, I will give you chances to recover the (bad) outcome
 of the first SAQ by assigning extra bonus questions. Don't be discounraged 
 by today's achievement. (Nov. 9).

 Brief comments on the first SAQ (Nov. 9).
 To prove that a strategy profile is a Nash equilibrium, 
 you need to check that no player has an incentive to change his/her strategy  
 given the opponents' strategies (note that, if the strategy he/she chooses now 
 is the best for him/her, he/she does not have an incentive to change it).
 If no one has an incentive to change his/her strategy,
 the strategy profile is a Nash equilibrium.
 This point still holds even if we allow mixed strategy. 

 At today's SAQ, to prove that pi > pj >= c does not hold in equilibrium,
 you should focus on the incentive of firm j because this inequality allows
 the case, pj = c (given pj = c, firm i does not have an incentive to change
 his/her price). 
 Given the price pair (the strategy profile), firm j has an incentive to increase 
 its price and sets it at pi - ε, ε(> 0) is small enough. 
 So, the strategy profile, pi > pj >= c, does not hold in equilibrium. 

 I will put the slide of Chapter 7 until the end of November 14, 2015 (Nov. 9).
 I found that I eliminated the link to the slide of Chapter 7 (pdf) (Nov. 22)

 On November 16, I did not return your SAQ beuase I need to adjust the scores although
 I have checked all the answer sheets (the last week comments reflect the fact).

 Today (Nov. 16), I receive several questions in/after the class. 
 1. In the 20th slide of Section 6, why do we focus on the pure strategy si′ instead of
 focusing on σi′  ?
 We have picked up σi′ for player i's (mixed) strategy such that vi(σi′,σ-i) > vi(σi,σ-i).
 Under σi′, player i ramdomizes at least one pure strategy. When Si+(σi′) includes
 only one pure strategy, this pure strategy is equivalent with σi′, then we directly go
 to the last inequality in the 20th slide. When Si+(σi′) includes more than one pure
 strategy, we must find at least one pure strategy, si′, in Si+(σi′) such that
  vi(si′,σ-i) > vi(σi,σ-i). To understand this fact, remember that the expected payoff is
 given as the equation in the 13th slide. If there is no pure strategy si in Si+(σi′) such
 that vi(si,σ-i) > vi(σi,σ-i), for all the strategies in Si+(σi′), vi(si,σ-i) <= vi(σi,σ-i), which
 contradicts the fact that we have picked up σi′ such that vi(σi′,σ-i) > vi(σi,σ-i) (note
 that, in the 13th slide, σi(si) is the probability of playing si under σi).

 2. The 3rd item in the 18th slide of Chapter 7. 
 If the actions in the action set Ai(x′) are different from those in the action set Ai(x),  
 player i can find the node he stays from the difference between the available actions
 in the two action sets. So, Ai(x′) = Ai(x) must hold if x and x′ are in the same
 information set.

 Thank you very much for asking me the questions, which clarifies
 how my explanation is not good. 

 I will put the slide of Chapter 8 by the end of November 22, 2015 although the class
 is closed on November 23, 2015. (Nov. 16) 

 I put the slide of Chapters 8 and 9 (pdf) and Supplement of Chap 8.1 (pdf) (Nov. 22)

 Except Proposition 9.B.3 (MWG) and the last example, we have reviewed Chapter 8. 
 Next week, we will review the rest of Chapter 8 (the above topics) and move on to
 Chapter 9. Furthermore, if possible, we review some part of Chapter 10.
 I will put the slide of Chapter 10 by the end of 5 December. (Nov. 30)
 I expect that we will skip Chapter 11 (Bargaining). 
 TA session will deal with the topic (Nov. 30)

 I put the slide of Chapter 10 (pdf) and Supplement of Chap 9.5 (pdf) 
 I forgot to upload the slide on the web. I am sorry for the delay. (Dec. 6)

 We have completely checked the end of Chapter 9. We also checked several concepts
 in Chapter 10. Please check the proofs of Propositions and Theorems in Chapters 8
 and 9 if you would like to get the full mark of the midterm examination.
 Next week, we will check the rest of Chapter 10 and review the matter(s) you ask if
 possible. After that, we hold the second short answer question. As a preparation for it, 
 it is better to understand how to convert extensive form to normal form. (Dec. 8)

 I put the second SAQ. and the proofs of Prop 10.3 and Th10.1 in Chapter 10.
 The midterm examination covers Chapters 3 to 10.
 Please check one of the proofs of Propositions and Theorem
 (Proposition 8.1, Proposition 9.B.3 (MWG), Proposition 9.B.4 (MWG), Theorem 9.1)
 in Chapters 8 and 9. I will assign the following type of question: 
 Choose one from the following propositions and theorem and prove it. 

 80% questions will be standard levels and the remaining will be difficult. 
 I will give you a chance to recover the outcome in the 1st and 2nd SAQs. (Dec 14)

 The outcome of the 2nd SAQ is not so good. The TA session dealt with related  
 problems. It would be better to check how to convert extensive form to normal form.
 Also, it would be better to check the definition of strategy. (Dec 16)

 I will put the slide of Chapter 12 by the end of 3 January. (Dec 25)
 I have checked the answer sheets of the midterm examination although I need to
 check it again.
 The average score is 19.86 (#students 35).
 The average scores for the six questions are 1.80, 2.66, 3.69, 4.69, 3.06, 3.97. 
 If you would like to know your tentative score, please contact me. (Dec 25)

 I put the slide of Chapter 12 (pdf).
 In the slide, I add Section 13.B in Mas-Colell et al (see pages from 52 to the end).
 I am so sorry for the delay. (Jan 3)

 I will put the slide of Chapter 13 by the end of 15 January.
 On 4 January, we have studied the content of Chapter 12 from the beginning
 to 44th slide. The key point is to understand how to make players' strategies
 in incomplete information game. Each player forms a type-dependence strategy.
 On 18 January, we will study the rest of the slide of Chapter 12. 
 After that, we move onto Chapter 13. We will skip Chapter 14. (Jan 4)

 I put the slide of Chapter 13 (pdf). (Jan 14)
 I am going to put the slide of Chapter 14 in MWG (1995) because this chapter
 includes "moral hazard problem" and "revelation principle." 
 We learn the slide (Chap14 MWG) after we learn Chapter 15 in Tadelis.
 I will put the slide of Chapter 14 in MWG by the end of 23 January. (Jan 14)

 We have learn Chapter 12 although I did not explicitly explain a few slides of
 Secton 13.B in Mas-Colell et al. (1995). The next week, we will learn the slide of
 Chapter 13. After that, the 3rd SAQ is assigned. 
 If possible, we will learn some part of Chapter 15 before the SAQ. (Jan 18)

 I put the slide of Chapter 15 (pdf). (Jan 21)
 I wrote "I will put the slide of Chapter 14 in MWG by the end of 23 January. (Jan 14)".
 However, before I put it, I should put the slide of Chapter 15 in Tadelis because 
 we learn Chapter 15 earlier. I was quite stupid, when I wrote the information on Jan 14.
 I will put the slide of Chapter 14 in MWG by the end of 27 January. 
 I am so sorry for the confution. (Jan 21)

 I put the slide of Chapter 14 in Mas-Colell et al. (pdf), which is used after 
 we learn Chapter 15 in Tadelis (Jan 23)

 We studied the content of Chapter 13 in Tadelis and briefly checked the first slide of
 Chapter 15 on 25 January. (Jan 27)

 We have two lectures. The sequence of the lectures is as follows: 
 1. Chapter 15 in Tadelis (the slide of Chapter 15 (pdf)).
 I do not explain the detail of the slide but point out the important concepts.
 We do not deal with the slides from 35th to 44th in the class. 
 I strongly recommend you to read the slide before the class on the 1st February.
 2. Chapter 16 in Tadelis (the slide of Chapter 16 (pdf))
 I recommend you to read the slide (Basic assumption in the 2nd to the 6th slides)
 before the class on the 1st February.
 If the time constraint is severe, I will skip "limit pricing".
 3. Chapter 14 in MWG (Chapter 14 in Mas-Colell et al. (pdf))
 We do not deal with the slides from 59th slide. (Jan 27)

 Today, I thank you very much for your patience. 
 We have learn the following on 1st February 2016: Chapter 15 in Tadelis and 
 the basic setting of the signaling game.
 I put the slides used in the class:
 (the slide of Chapter 15 (pdf)), (the slide of Chapter 16 (pdf))
 You do not need to check the detail of the concept "sequential equilirium".
 Although this concept is a powerful tool to refine equilibria, applied theorists 
 often employ (weak) Perfect Bayesian Equilibrium as solution concept. 
 Related to today's lecture, please concentrate your efforts on understanding 
 how to use the concept of (weak) Perfect Bayesian Equilirbium.

 It is quite helpful if you check how to derive the equilibrium in the slide of
 Chapter 16 before the class on 8th February. A signaling game will be assigned
 in the final examination.

 I also put the important notice related to the cancellation of the 4th SAQ and 
 the final examination. (Feb 1)

 We mainly learned the slide of Chapter 16 (pdf), and briefly checked the problem of 
 hidden action. I already mentioned that a signaling game will be assigned in the final 
 exam.. (Feb 8)


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