Economics 202: Intermediate Microeconomic Theory 1.HW #6 on website. Due Thursday. 2.No new reading for Thursday, should be done with Ch 8, up to page 260.

Game Theory Let’s play “21 flags” Lessons learned … Let’s play “Guess 1/2 of the average” Lessons learned …

Game Theory Game Theory is a way to analyze situations in which the outcomes of your choices depend on others’ choices, & vice versa. Can apply it to a variety of issues: oligopoly, defense budget, politics 3 elements of the “game” are –Players, who make decisions and whose behavior we want to predict/explain –Strategies are the possible choices (campaign strategy, advertising $, location) –Payoffs are the outcomes of the chosen strategies Payoff Matrix shows how each combination of choices affects each firm’s  (normal form) Assume independent actions: firm A can choose a row, not a cell What is the equilibrium? –Both firms have a dominant strategy (a definite best choice) –Equilibrium is (High Q, High Q) Firm B Firm A Low Q High Q Low QHigh Q

Game Theory Change one # in the payoff matrix Now what happens? A’s best choice depends on B, so A has no dominant strategy. It tries to predict B’s choice. B will choose “High Q”, so A should choose “High Q” This is called a Nash equilibrium = a set of strategies such that each player’s choice is best given the strategy chosen by other players To see this, ask “Is A’s best choice “High Q” when B does “High Q” and is B’s best choice “High Q” when A does “High Q”? –Yes, Nash equil = (High Q, High Q) –No incentive to move from that cell Firm A Firm B Low Q High Q Low QHigh Q

The Prisoner’s Dilemma Butch Cassidy & the Sundance Kid (classic film, rent it tonight) rob a train. They get caught, are held in separate rooms & each offered this deal: 1. If both confess to stiffer charge of attempted murder, both get 5 years. 2. If neither confesses, both get 2 years for robbery. 3. If only one confesses, the rat gets lenient 1 year, other gets 10 years. Butch Confess Sundance Don’t Confess Don’t Confess When might they collude? –Repeated game Point is that self-interested behavior can sometimes lead to less than optimal outcomes for all Can apply to USA vs. USSR, elections, health care, etc. Confess is dominant strategy for each. But this makes them both worse off than if they could collude and both not confess, so why not collude? –Because it’s not in their self-interest. –Confession is not because they believe the other guy will confess also!

Game Theory 4 main categorizations –Static vs. Dynamic –Complete vs. Incomplete info Static games with complete information –Cournot duopoly –Iterated elimination of dominated strategies (how should you not play!) –Nash equilibrium Timing Static Nash Equilibrium Information Dynamic CompleteIncomplete Game 1 and Game 2 –Iterated elimination of D.S. solution? Game 1 and Game 2 –Unique Nash equilibrium? –Unique Nash equilibrium is not always efficient, e.g. Prisoner’s Dilemma Backward Induction Bayesian Nash Equilibrium Perfect Bayesian Equilibrium 0, 4 4, 0 5, 3 4, 0 0, 4 5, 3 3, 5 6, 6 1, 0 1, 2 0, 1 0, 3 0, 1 2, 0 Down Up LeftMiddleRight B A A B B M T LMR Game 1 Game 2

Game Theory “The Dating Game” –Multiple Nash equilibria –Nash equilibrium concept loses appeal “Copycat Game” –No Nash equilibrium –Players want to outguess the other –Introduce mixed strategies (in contrast to pure strategies) Timing Static Nash Equilibrium Information Dynamic CompleteIncomplete Mixed Strategy = a probability distribution over some or all of a player’s pure strategies Mixed strategies can add Nash equilbria Result: Any game with finite # players who have finite # pure strategies has a Nash equilibrium (possibly utilizing mixed strategies) Backward Induction Bayesian Nash Equilibrium Perfect Bayesian Equilibrium 2, 1 0, 0 1, 2 Chicken Steak RedWhite Pat Chris Jack Dating Game -1, 1 1, -1 -1, 1 Outside Inside Jill Inside Copycat Game