Problem Sets:


Session: Date: Lecture description: Problem set: Due Date
1 Jan 11 Introduction of Game Theory (Ch. 1)

Set 1 (From Textbook)
1] 5.3 (Altruistic Preference) = 5.3 in online chapter
2] 6.1 (Alternative represenations of preferences) = 6.1 in online chapter
3] 16.1 (Working on a joint project) = 14.1 in online chapter
4] 17.1 (Games equivalent to the prisoner's dilemma) = (See below this table)
5] 18.1 (Hermaphroditic fish) = 16.1 in online chapter

Jan 18
2 Jan 18 Nash Equilibrium: Theory (Ch. 2)

Set 2 (From Textbook except Qs. 6)
1] 27.1 (Variant of PD w/ altruistic preferences) = 25.1 in online chapter
2] 27.2 (Selfish & altrustic social behavior) = 25.2 in online chapter
3] 30.1 (Variants of the stag-hunt) = 28.1 in online chapter
4] 33.1 (Contributing to a public good) = 31.1 in online chapter
5] 38.2 (Dividing money) = 37.1 in online chapter
6] A Beautiful Mind with a wrong answer (See below this table)

Jan 25
3 Jan 25 Nash Equilibrium: Illustrations (Ch. 3) Set 3 (From Textbook except Qs. 6)
1] 42.1 (Finding NEs using BR fn.) = 40.1 in online chapter
2] 42.2 (A joint project) = 40.2 in online chapter
3] 44.1 (Contributing to a public good) = 43.1 in online chapter
4] 59.1 (Cournot w/ quadratic cost fn) = 57.2 in online chapter
5] 59.2 (Cournot w/ fixed cost) = 57.3 in online chapter
6] 67.2 (Bertrand w/discrete prices) = 65.2 in online chapter
Feb 1
4 Feb 1 Mixed Strategy Equilibrium (Ch. 4) No PS.  
5 Feb 8 Extensive Games: Theory (Ch. 5) Set 4 (From Textbook)
1] 114.2 (Games w/ Mixed strategy equilibria)
2] 114.3 (A coordination game)
3] 118.1 (Silverman's game)
4] 121.2 (Eliminating dominated actions when finding equilibria)
5] 128.1 (Choosing a seller)
6] 132.3 (Contributing to a public good)
Feb 15
6 Feb 15 Extensive Games: Illustrations (Ch. 6)

Set 5 (From Textbook) - See comments
1] 156.2 (Examples of extensive games with perfect info)
2] 161.1 (Strategies in extensive games)
3] 163.2 (Voting by alternating veto)
4] 173.2 (Finding SPEs)
5] 173.3 (Voting by alternating veto)
6] 173.4 (Burning a bridge)
7] 177.2 (The "rotten kid theorem")

Feb 22*
* Feb 22 Reading Week    
7 Mar 1 Midterm    
8 Mar 8 Extensive Games: Illustrations (Ch. 6 & 7) Set 6 (From Textbook)
1] 183.3(Dictator game & impunity game)
2] 185.1 (Bargaining over 2 indivisible objects)
3] 189.1 (Stackelberg's duopoly game with quadratic costs)
4] 191.1 (Stackelberg's duopoly game with fixed costs)
5] 192.1 (Sequential variant of Bertrand's duopoly game)
Mar 15
9 Mar 15 Bayesian Games I (Ch. 9) Set 7 (From Textbook)
1] 210.3 (Two-period PD)
2] 211.1 (Timing claims on an investment)
3] 214.1 (Bertrand's duopoly game with entry)
4] 227.2 (Firm-union bargaining)
5] 230.1 (Nash equilibria when players may make mistakes)
Mar 22
10 Mar 22 Bayesian Games II (Ch. 9)

Set 8 (From Textbook)
1] 276.1 (Equilibria of a variant of BoS w/ imperfect info)
2] 277.1 (Expected payoffs in a variant of BoS w/ imperfect info)
3] 282.1 (Fighting an opponent of unknown strength)
4] 282.2 (An exchange game)
5] 282.3 (Adverse selection)

Mar 29
11 Mar 29 Extensive Games with Imperfect Information I (Ch. 10) Set 9 (From Textbook)
1] 284.1 (Infection)
2] 287.1 (Cournot's duopoly game w/ imperfect info)
3] 288.1 (Cournot's duopoly game w/ imperfect info)
4] 291.1 (Reporting crime w/ an unknown no. of witnesses)
Apr 5
12 Apr 5 Extensive Games with Imperfect Information II (Ch. 10) Set 10 (From Textbook)
1] 316.1 (Variant of card game)
2] 318.2 (Strategies in variants of card game & entry game)
3] 319.3 (Nash equilibria of card game)
4] 320.1 (Nash equilibria of variant of card game)
5] 331.1 (Selten's horse)
6] 331.2 (2 similar games w/ different equilibria)
I hope to receive your email saying u've done PS 10 before the final.

Set 2.6] A beautiful mind with a wrong answer

In the movie A Beautiful Mind, there was a shot in which John Nash and 3 of his fellow classmates saw 4 brunettes and a blonde in a bar. John suggested that they should all approach the brunettes. Suppose that for these 4 gentlemen, each of them prefer getting the attention of the blonde, than getting the attention of any brunette (they "value" the attention of any brunette of the 4 equally), than getting no attention at all. 1 guy will get the attention of the girl he's approaching if he's the only one approaching her. More than 1 guy approaching any girl will result in rejection. Getting attention of any girl after having a rejection is not feasible (coz' no one wants to be "Plan B").
(a) Explain why John's proposal is wrong.
(b) Give me at least one explanation that John may intentionally make it wrong.
(c) Find the Nash equilibrium/equilibria of the game.

Set 1.4] 17.1 (Games equivalent to the prisoner's dilemma in the textbook)

Determine whether each of the games in Figure 17.1 differs from the Prisoner's Dilemma only in the names of the players' actions, or whether it differs also in one or both the players' preferences.

X
Y
X
3,3
1,5
Y
5,1
0,0

X
Y
X
2,1
0,5
Y
3,-2
1,-1

Figure 17.1 The strategic games for Exercise 17.1.