Game Theory

1. Game Theory Mike ShorTopic 1 (continued) “I don’t skate to where the puck is, I skate to where it’s going to be.” - Wayne Gretzky

2. Defining the Game • Review • Strategic interdependence of players • You pursue your goals • So does everyone else • Your actions change the environment for others • Outline: • Defining the rules of the game • Manipulating the rules if they are flexible • Questioning game theory’s assumptions

3. Rules of the Game • The participants • Players ( who ) • Strategies ( what ) • Payoffs ( why ) • The rules • Timing of moves ( when ) • Information ( ? ) • The assumptions • Rationality • Common knowledge

4. The Participants • Who? • Players • Everyone who impacts your earnings • Everyone whose actions you care about • Notation: • N players indexed i,j or 1,2,3,… • Nature (randomness) is player 0

5. The Participants • What? • Strategies • A comprehensive plan of action for every contingency in a game • An action specifies a move at a specific stage of a game • A strategy specifies an action for every possible decision a player can face

6. The Participants • What? • Notation: • si a strategy for player i • s a vector of strategies (s1, s2 , s3 , …) • s-i a strategy for all players except i • Si the set of all possible strategies for i

7. The Participants • Why? • Payoffs • Numbers associated with each outcome • Reflect the interests of the players • Sometimes just ordinal (A better than B) • Sometimes need cardinal (e.g., A = 2B) • Notation: • Player i’s payoffs given by ui(s) = ui(si,s-i )

8. The Rules • Timing of moves • Are moves simultaneous or sequential? • Information • Who knows what and when?

9. Changing the Rules • Are the rules of the game fixed?

10. Example:Agenda Setting Graduation speaker Ron Paul, Sarah Palin, or Al Gore? • Four committee members prefer: Ron to Sarah to Al ( R > S > A ) • Three committee members prefer: Sarah to Al to Ron ( S > A > R ) • Two committee members prefer: Al to Ron to Sarah ( A > R > S ) • Voting by Majority Rule

11. Agenda Setting (continued) • No majority in three way race • Committee president sets voting rules: • First, Ron v. Sarah Then, Ron/Sarah winner versus Al • First, Ron v. Al Then, Ron/Al winner versus Sarah • First, Sarah v. Al Then, Sarah/Al winner versus Ron

12. Agenda Setting (continued) • Recall member preferences: 4 (R>S>A) 3 (S>A>R) 2 (A>R>S) • Majority rule results: • R beats S ; S beats A ; A beats R • Voting results: • R vs. S then winner versus A • R vs. A then winner versus S • S vs. A then winner versus R

13. Changing the Rules • Are the rules of the game fixed? “The battle is won before it is ever fought” — Sun Tzu When the rules of the game are flexible manipulate them to your advantage.

14. The Assumptions • Rationality • Common Knowledge

15. The Assumptions • Rationality • Players aim to maximize their payoffs • Players are perfect calculators • Players know their own payoffs • Players never make mistakes

16. The Assumptions • Common Knowledge • Each player knows the rules of the game • Each player knows that each player knows the rules • Each player knows that each player knows that each player knows the rules • Each player knows that each player knows that each player knows that each player knows the rules • Each player knows that each player knows that each player knows that each player knows that each player knows the rules • Etc. Etc. Etc.

17. The Assumptions • Some piece of information X • Knowledge: I know X • Mutual knowledge: Each of us knows X • Common Knowledge: Each of us knows that each of us knows X, … • The rules of the game are common knowledge (players, strategies, payoffs, timing, information) are common knowledge

18. Common Knowledge • Do people really behave as the theory predicts? • If not, what good is the theory?

19. Common Knowledge • Behavioral game theory: The rule of three • Game theory: The rule of infinity • Example: the stock market

20. The Stock Market& Rationality “I can calculate the motions of heavenly bodies, but not the madness of people” - Sir Isaac Newton (upon losing £20,000 in the South Sea Bubble in 1720) If you knew the exact date of the next stock market crash, what would you do?

21. Which Month Am I? “_________ “_________ “_________ “_________ “_________ “_________ “_________ “_________ • often is a good month for stocks” • is typically a strong month for stocks” • tends to be a good month for stocks” • is usually a good month for stocks” • is typically a bad month for the stock market” • is usually the worst month for stocks” • is traditionally a cruel month for stocks” • is the worst month for stocks”

22. Fun with Probabilities “Almost every generation, it seems, has its October stock-market crash.” — Wall Street Journal, October 2008 • Why is October so bad?

23. October • October 19, 1987 • Dow dropped 23% • October 1-10, 2008 • Dow dropped 22%

24. Fun with Probabilities If, in each month, the stock market is equally likely to go up or go down, then there is over an 80% chance that some month will be “bad” three years in a row!

25. The Worst Month for Stocks “ October. This is one of the peculiarly dangerous months to speculate in stocks. ” – Wall Street Journal, quoting Mark Twain

26. Wall Street JournalMay 1988 Front Page Story: “Clear Road Ahead …” • “Will record gains through the fall” • “October looms on the horizon … the dreaded though inevitable slide.”

27. 1988 MAY 4 3 2 1 0

28. IPO Lock-Ups • A company wishes to “go public” • It offers to sell shares to the public • Typically only 20% of the total shares are offered • The remained are held by “insiders” • Lock-up • precludes insiders from selling shares, typically for six months • What happens when the lock-up expires?

29. IPO Lock-Ups “Increased supply after the lock-up expiration will drive price down. It is simply economics of supply and demand.” — Wall Street Journal reporter

30. 0.005 0 -0.005 -0.010 (Cumulative Abnormal) Return -0.015 -0.020 -0.025 -0.030 -20 -16 -12 -8 -4 0 4 8 12 16 Event Day Excess Returns prior to IPO Lock-Up Expiration

31. Summary • You’re always in a game • The rules are likely to be flexible • Think one step ahead • The rule of three steps • Looking ahead: • Equilibrium: What are the outcome of games?