GAME THEORY John Nash and Albert Einstein Prisoner s dilemma TV contracts Beer wars Bottom of the ninth Recruiting violations Doping dilemma THE NCAA S MARKET POWER Monopsony power over athletes Drive down price of labor Problem schools cheat to recruit stars Monopoly power over TV contracts Benevolent beginnings STRATEGY MATTERS In a strategic setting a person may not always have an obvious choice What is best may depend on the actions of another person Two basic tasks when using game theory to analyze an economic situation 1 distill the situation into a simple game 2 solve the game results in a prediction about what will happen A BEAUTIFUL MIND 2001 Starring Russell Crowe Jennifer Connelly Fritz Crisler U of M coach and Dick Romney WAC Commissioner Limited to 3 TV games every 2 years Problem antitrust suit Oklahoma and Georgia brought suit NCAA loses case at the Supreme Court 1984 Now many broadcasts but less revenue Both can be understood with game theory NOBEL PRIZES IN ECONOMICS 1994 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 John Nash John Harsanyi Reinhard Selton Daniel Kahneman Vernon Smith Robert Engle Clive Granger Finn Kydland Edward Prescott Robert Aumann Thomas Schelling Edmund Phelps Leonid Hurwicz Eric Maskin Roger Myerson Paul Krugman Elinor Ostrom Oliver Williamson Peter Diamond Dale Mortensen Chris Pissarides Thomas Sargent Christopher Sims Alvin Roth Lloyd Shapley Best Picture Best Director Best Supporting Actress BASIC ELEMENTS Three elements to a game 1 players 2 strategies 3 payoffs Each decision maker is a player may be athletes conferences coaches Each course of action open to a player is a strategy a simple action or a complex plan of action Payoffs are measured in levels of utility or profit or reward obtained by the players PRISONERS DILEMMA This is one of the most famous games studied in game theory Two suspects Vito and Bugsy are arrested for a crime The DA wants to needs a confession so he offers each a deal PAYOFF MATRIX YEARS OF PRISON CHICKEN THE DEAL if you rat on your partner but your partner doesn t rat on you you go free and your partner gets a tenyear sentence if you both rat on each other you will each get a five year sentence if neither rats we will get tried for a lesser crime and each get a one year sentence Murder by Numbers 2002 CORPORATE STRATEGY BOTTOM OF THE NINTH TWO OUTS BASES LOADED GAME ROCK PAPER SCISSORS A BEAUTIFUL MIND 5 men in a bar 5 girls enter one is blond men prefer blonds all moves simultaneous http www youtube com watch v CemLiSI5ox8 Which game is this NASH EQUILIBRIUM DOMINANT STRATEGIES Assuming rationality A single strategy that is a best response to any strategy the other players might choose is called a dominant strategy Nash equilibrium involves strategic choices that once made provide no incentives for players to alter their behavior Rat is a dominant strategy for both prisoners When a mutual dominant strategy exists it is the unique Nash equilibrium Best choice for each player given the other players equilibrium strategies BOTH RATTING IS EQUILIBRIUM Game Theory 101 http www youtube com watch v IotsMu1J8fA feature relmfu EQUILIBRIUM Nash equilibrium is optimal for both Neither wants to change Equilibrium need not be the best outcome With Prisoners Dilemma both have a dominant strategy guarantees an equilibrium PAYOFF MATRIX FSU VS FLORIDA TV POLICY profit payoffs Univ of Miami Televise every game Televise away games only FSU gets 5 million Miami gets 5 million FSU gets 20 million Miami gets 3 million Televise FSU gets 3 away games million only Miami gets 20 million FSU gets 10 million Miami gets 10 million Televise every game Florida State University NEITHER WANTS TO CHANGE BUT BOTH COULD DO BETTER BIDDING WAR FOR FREE AGENTS Profit Payoffs OWNERS VICTIM OF PRISONER S DILEMMA Yankees million of Low salaries High salaries Low salaries Red Sox gets 100 Yankees gets 100 Red Sox gets 25 Yankees gets 200 High salaries Red Sox gets 200 Yankees gets 25 Red Sox gets 50 Yankees gets 50 Red Sox BEER ADVERTISING WARS Profit Payoffs Miller millions of No advertising No advertising Heavy advertising Budweiser gets 500 Miller gets 300 Budweiser gets 100 Miller gets 600 Budweiser gets 600 Miller gets 50 Budweiser gets 200 Miller gets 100 Budweiser Heavy advertising PRISONER S DILEMMA AGAIN APPLE DOES NOT HAVE A DOMINANT STRATEGY GOOGLE DOES MULTIPLE NASH EQUILIBRIUMS Drawbacks to Nash equilibrium There may be multiple Nash equilibriums and no dominant strategy It is unclear how a player can choose a best response strategy before knowing how rivals will play CHICKEN MIXED STRATEGIES When a player chooses one action or another with certainty he is following a pure strategy Players may also follow mixed strategies randomly select from several possible actions Footloose scene http www youtube com watch v 9TXwokp6lIc NO PURE STRATEGY CHOOSE AT RANDOM ROCK SCISSORS PAPER Game Theory 101 http www youtube com watch v 1GDMXoMdaY feature relmfu OTHER APPLICATIONS OF MIXED STRATEGIES Third Set against Serena Williams at Australian Open forehand or backhand Appendix 4A One on one between goalee and forward shoot puck high or low Shoot out to decide a tie in soccer kick right or left or center RECRUITING LEBRON BRYANT GAME NASH S NOBEL PRIZE Nash proved the existence of a Nash equilibrium in all finite games The existence theorem does not guarantee the existence of a pure strategy Nash equilibrium But if a pure strategy Nash equilibrium does not exist a mixed strategy Nash equilibrium does EXPECTATIONS OF A UNCERTAIN OUTCOME The general definition n E x x p x i i i 1 No bribes offered toss up contest Win p x win 0 5 x 3 million Lose p x lose 0 5 x 0 1 1 E x 3 0 1 5 2 2 Bribes offered toss up contest Win p x win 0 5 x 3 1 2 Lose p x lose 0 5 x 0 1 1 E x 2 0 1 2 2 VIOLATE IS THE NASH EQUILIBRIUM PERFORMANCE ENHANCING DRUGS Venus and Serena in the Final equally balanced probability of winning is 1 2 1 million for winning 100K for second place Drug is perfectly effective and risk free Drug test for each player but probability of getting caught is slight 5 penalty for doping is 1 year ban expected cost 5 million IMPOSSIBLE TEST OUTCOMES PROBABILITIES impossible DOPING IS THE NASH EQUILIBRIUM 5 CHANCE OF GETTING CAUGHT n Probabilities always sum to 1 0 E x x p x i i i 1 1 1 0 0025 0 0475 5 0 0475 1 0 9025 1 0 1 0 294 2 2 RISK AVERSE PLAYERS SURVEY OF OLYMPIC ATHLETES Expected utility instead of expected value Hypothetical n you