A dilemma…

1. A dilemma… • Your MBA 6634 assignment is due today. But you’re not finished it yet! If you handed it in now it looks like you would only get about a 60% grade. Then an idea comes to you. You can make up a story that the data you needed wasn’t available until now, and ask for a 1-day extension. Dr. Buffett will buy that story. Getting one more day to work on it should allow you to get enough done to earn a 90% grade. • Assuming your only decision criteria is grade maximization, what should you do?

2. A second dilemma… • Your MBA 6634 assignment is due today. But you and your partner are not finished it yet! If you handed it in now it looks like you would only get about a 60% grade. Then an idea comes to you. You can make up a story that the data you needed wasn’t available until now, and ask for a 1-day extension. Dr. Buffett will buy that story. Getting one more day to work on it should allow you to get enough done to earn a 90% grade. • The problem is your partner hasn’t finished her part of the assignment, and is considering making up the same story and asking for an extension as well…

3. A second dilemma (cont’d) • You’re about to meet with Dr. Buffett and there is no time to communicate what you’ll do with your partner. You only know this: • If neither of you ask for an extension, you’ll get a grade of 60% • If you both ask for an extension, you’ll be granted it, and wind up with a grade of 90% • But if one makes up the story and the other hands in what’s done, the liar will be exposed. Dr. Buffett will have no choice but to give the liar 0%. The partner will be commended for being honest as well as recognized as being the only partner making an effort, and will get 100% • You also know that your partner knows all of these options and is weighing them similarly • What should you do???

4. Payoff Matrix Partner 2 Partner 1

5. Game Theory – Studying Behaviour in Social Networks • Normative and descriptive studies for interaction in various situations • Social network formation • Determining influential individuals • Viral marketing and information cascade • Incentive Networks • Query, discount, etc. • Game theory is all about social situations!

6. Games • Tic Tac Toe • Chess • Risk

7. Not just “games” Traffic example

8. Basic Components of a Game • Participants • Or “players” • Two or more • Strategies • Possible moves • Each strategy π: S -> A maps each state in S to an action in A • Likely multiple strategies to choose from • Payoffs • Outcomes • Each set of strategies (i.e. one per player) assigns a payoff to each player

9. Types of games • Cooperative or non-cooperative • Ability to form binding commitments, like negotiation • Symmetric or asymmetric • Asymmetric: Players play different roles, have different strategies/payoffs available to them • Zero-sum or non-zero-sum • Whether the total net payoff is always 0 (or the same). i.e. if one player gains, another loses • Simultaneous or sequential • Problem of whether to lie about late assignment vs tic tac toe, chess, etc • Perfect information or imperfect information • Sequential games • Whether there is perfect information about the previous moves by other players • Many more categories…

10. Back to the original problem… Partner 2 Partner 1

11. Back to the original problem… Partner 2 Partner 1 • Participants: • Partner 1 and Partner 2 • Strategies: • Ask for extension, Hand it in • Payoffs: • Given in table

12. Back to the original problem… Partner 2 Partner 1 • Type of game: • Cooperative or non-cooperative • Symmetric or asymmetric • Zero-sum or non-zero-sum • Simultaneous or sequential • Perfect information or imperfect information

13. Back to the original problem… Partner 2 Partner 1 • Type of game: • Cooperative or non-cooperative • Symmetric or asymmetric • Zero-sum or non-zero-sum • Simultaneous or sequential • Perfect information or imperfect information

14. Back to the original problem… Partner 2 Partner 1 • Type of game: • Cooperative or non-cooperative • Symmetricor asymmetric • Zero-sum or non-zero-sum • Simultaneous or sequential • Perfect information or imperfect information

15. Back to the original problem… Partner 2 Partner 1 • Type of game: • Cooperative or non-cooperative • Symmetricor asymmetric • Zero-sum or non-zero-sum • Simultaneous or sequential • Perfect information or imperfect information

16. Back to the original problem… Partner 2 Partner 1 • Type of game: • Cooperative or non-cooperative • Symmetricor asymmetric • Zero-sum or non-zero-sum • Simultaneousor sequential • Perfect information or imperfect information

17. Back to the original problem… Partner 2 Partner 1 • Type of game: • Cooperative or non-cooperative • Symmetricor asymmetric • Zero-sum or non-zero-sum • Simultaneousor sequential • Perfect information or imperfect information n/a

18. Back to the original problem… Partner 2 Partner 1 • What to do?

19. Back to the original problem… Partner 2 Partner 1 • What to do? • Each player should just hand it in and receive a 60% grade

20. Back to the original problem… Partner 2 Partner 1 • What to do? • Each player should just hand it in and receive a 60% grade • Why? • Because handing it in is a strictly dominant strategy • Meaning that, no matter what the other partner does, it is always the better choice in terms of payoff

21. Normal vs Extensive Form Games • The Late Assignment game is an example of a normal-form game • Games described in normal form typically • Are simultaneous • Can have payoffs represented in a matrix • Games described in extensive form typically • Are sequential • Have payoffs represented in a game tree

22. Example Game Tree • We`ll focus on normal form games for now

23. Prisoner’s Dilemma • Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent.

24. The Bargain: • If A and B both betray the other, each of them serves 2 years in prison • If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa) • If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

25. The Bargain: • If A and B both betray the other, each of them serves 2 years in prison • If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa) • If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge) • Betrayal is a strictly dominant strategy • Dominant strategies can lead to suboptimal results! • What if there is no dominant strategy?

26. Nash Equilibrium • Developed by John Forbes Nash Jr. • Concept of a non-cooperative games • Set of strategies (one for each player) that are all a best response to the others • Each player is assumed to know the equilibrium strategies of the other players • No player has anything to gain by changing only their own strategy

27. Nash Equilibrium • Developed by John Forbes Nash Jr. • Concept of a non-cooperative games • Set of strategies (one for each player) that are all a best response to the others • Each player is assumed to know the equilibrium strategies of the other players • No player has anything to gain by changing only their own strategy

28. Nash Equilibrium: An Example • Consider two competing companies that each sell “widgets”. Each needs to set a price for their widgets, with either $1, $2 or $3 being the options. Each company must also keep in mind that higher prices will bring in more profit for sale, but could hurt total sales, particularly if the other company sells for less. After accounting for costs, the two companies’ payoffs for each set of strategies is as follows (in millions): • What is the Nash equilibrium? B A

29. Nash Equilibrium: An Example • Consider two competing companies that each sell “widgets”. Each needs to set a price for their widgets, with either $1, $2 or $3 being the options. Each company must also keep in mind that higher prices will bring in more profit for sale, but could hurt total sales, particularly if the other company sells for less. After accounting for costs, the two companies’ payoffs for each set of strategies is as follows (in millions): • What is the Nash equilibrium? B A

30. Another Example • Imagine a couple that agreed to meet this evening.The husband would most of all like to go to the football game. The wife would like to go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate, where should they go? Wife Husband

31. Another Example • Imagine a couple that agreed to meet this evening.The husband would most of all like to go to the football game. The wife would like to go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate, where should they go? • This is an example of a coordination game, often called “Battle of the Sexes” • It is also an example of multiple equilibriums Wife Husband

32. Another Example • Imagine a couple that agreed to meet this evening.The husband would most of all like to go to the football game. The wife would like to go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate, where should they go? • This is an example of a coordination game, often called “Battle of the Sexes” • It is also an example of multiple equilibriums equilibria Wife Husband