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

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

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 Mike Shor 2

Rules of the Game The participants  Players ( who)  Strategies ( what )  Payoffs ( why) The rules  Timing of moves ( when)  Information ( ” ) The assumptions  Rationality  Common knowledge Mike Shor 3

The Participants 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 Mike Shor 4  Who?

The Participants 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 Mike Shor 5  What?

The Participants Notation:  s i a strategy for player i  s a vector of strategies (s 1, s 2, s 3, …)  s -i a strategy for all players except i  S i the set of all possible strategies for i Mike Shor 6  What?

The Participants 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 u i (s) = u i (s i,s -i ) Mike Shor 7  Why?

The Rules Timing of moves  Are moves simultaneous or sequential?  This is an information (not a timing) distinction Information  Who knows what and when? Mike Shor 8  When?

Changing the Rules Are the rules of the game fixed? Mike Shor 9

Example: Agenda Setting Graduation speaker Rand Paul, Jeb Bush, or Hilary Clinton? Four committee members prefer: Randto Jebto Hilary( R > J > H ) Three committee members prefer: Jebto Hilaryto Rand( J > H > R ) Two committee members prefer: Hilaryto Randto Jeb( H > R > J ) V oting by Majority Rule Mike Shor 10

Agenda Setting (continued) No majority in three way race Committee president sets voting rules:  First, Rand v. Jeb Then, Rand/Jeb winner versus Hilary  First, Jeb v. Hilary Then, Jeb/Hilary winner versus Rand  First, Hilary v. Rand Then, Hilary/Rand winner versus Jeb Mike Shor 11

Agenda Setting (continued) Recall member preferences: 4 (R>J>H) 3 (J>H>R) 2 (H>R>J) Majority rule results:  R beats J ; J beats H ; H beats R Voting results:  R vs. J then winner versus H  J vs. H then winner versus R  H vs. R then winner versus J Mike Shor 12

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

The Assumptions Rationality Common Knowledge Mike Shor 14

The Assumptions Rationality  Players aim to maximize their payoffs  Players are perfect calculators  Players know their own payoffs  Players never make mistakes Mike Shor 15

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. Mike Shor 16

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 (players, strategies, payoffs, timing, information) and each player’s rationality are common knowledge Mike Shor 17

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

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

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? Mike Shor 20

“_________ 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” Which Month Am I? Mike Shor 21

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

October Mike Shor October 19, 1987  Dow dropped 23% October 1-10, 2008  Dow dropped 22%

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! Mike Shor 24

The Worst Month for Stocks “October. This is one of the peculiarly dangerous months to speculate in stocks. Mike Shor 25 – Mark Twain ”

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

1988 Mike Shor 27 01234 MAYMAY

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? Mike Shor 28

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 Mike Shor 29

Excess Returns prior to IPO Lock-Up Expiration Mike Shor 30 Lock-up Expiration (Cumulative Abnormal) Return -20-16-12-8-40481216 0.005 0 -0.005 -0.010 -0.015 -0.020 -0.025 -0.030

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? Mike Shor 31

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