Introduction to Game Theory

1. Introduction to Game Theory Mrs. Heffernan’s AP Econ Class

2. Review of Oligopoly • An oligopoly is an industry dominated by a few sellers. • Firms face downward sloping demand and can influence market price. • Firms in oligopoly are interdependent: • Decisions of one firm influence the decisions of others • Last time we discussed some ways firms deal with this interdependence. • Today we will discuss how we can study decisions using Game Theory. • Next time we will analyze this interdependence using the kinked demand curve model.

3. Bonus Points Game! • You have each received two index cards • X = Cheat • O = Collude (Cooperate) • When I say “go” you are going to either hold up X or O

4. Majority of Other Students Compete Collude You Compete 10 40 Collude 0 20 Game Points • If more than half the students vote for "compete," then "compete" wins, and each student records his/her score (and vice versa when "collude" wins). We’ll play six rounds. • Bonus points on the next review quiz will be assigned to each student, based on the points earned • >=180 = 4 pts • 120-179 = 3 pts • 90-119 = 2 pts • 60-89 = 1pt • < 60 = 0 pts

5. Majority of Other Students Compete Collude You Compete 10 40 Collude 0 20 Play the Game • Round 1: NO discussion allowed • Rounds 2-6: Discussion allowed

6. Debriefing • Why did some of you try to collude? • Why did collusion fail so often? • What does this tell us about behavior of interdependent agents?

7. Game Theory History • Developed primarily by von Neumann and Morganstern in 1944. • Expanded by John Nash (of A Beautiful Mind fame) – he won a Nobel Prize for his work. • Helps us to analyze complex decision making situations that include a series of strategic moves. There are MANY “real world” applications. Think of some.

8. Some Important Terminology • strategy: operational plan for the participants in the game (possible action) • payoff: outcome once a strategy is chosen • payoff matrix: table of numbers reporting profits of each of the rivals (we used one in our game)

9. More Terms • dominant strategy: a strategy that is best no matter what the opposition does • maximin strategy: a strategy chosen by a player to yield maximum payoff, assuming the rival will do as much damage to you as they can

10. Sam’s Store No Ads Advertise Ashley’s Store No Ads A profit = $50,000 S profit =$50,000 A profit = $75,000 S profit =$25,000 A profit = $25,000 S profit =$75,000 Advertise A profit = $10,000 S profit =$10,000 Another Game • Identify the strategies • Identify the payoffs • What should Ashley and Sam do if they can collude? • What would the dominant strategy be for each with no collusion? Why?

11. Michelle No confession Confess Jane No confession J = 1 year M =1 year J = free M =7 years J = 7 years M = free Confess J = 5 years M =5 years Prisoners Dilemma The previous game is an example of a type of game calledthe Prisoner’s Dilemma. Here is another. What is the dominant strategy with no collusion?

12. Are there solutions to the dilemma? • Repeated Games: • If we can learn from past experiences we may be able to change the outcome. • How would Ashley and Sam’s game change if they played over and over again?

13. Another Look at Games – Game Trees • Profits • Evan Julie • -2 -2 • 4 0 • 2 2 • 6 0 Enter Julie’s options Don’t Enter Big factory Evan’s options Enter Small factory Julie’s options Don’t Enter • On a sheet of paper, draw the corresponding payoff matrix. • Come up and put it on the board. • What is Evan’s dominant strategy? • If the big factory has excessive capacity (he can’t get all 6 mill. • of profits), why would he build it?

14. Nash Equilibrium • Sometimes a player does NOT have a dominant strategy in a game, but the outcome is predictable. • C does not have a dominant strategy, BUT: • If D plays left, C plays top. • If D plays right, C plays bottom. • What strategy should D play? • If C knows the options, she will see D’s dominant strategy and play it. • C sees that D wants to play right. • Because D’s behavior is predictable, C will play bottom. • NOTICE: they will want to stick to this position – it is good for all! • When all players are playing their best strategy given what others are doing, the result is a Nash Equilibrium.

15. Alex’s Company High Price Low Price Dave’s Company High Price D = 10 mill A = 10 mill D = 12 mill A = -2 mill D = -2 mill A = 12 mill Low Price D = 3 mill A = 3 mill Pricing Application • Using the following payoff matrix, identify the possible outcomes. • What will happen if firms can confer? • What if they can’t? • What does this game remind you of?

16. Telecom Application • Mid 1990’s FCC announced auction of wavelengths of radio spectrum for cell phones and pagers. • Companies had to figure out how much to pay to service areas. • Bidding done by computer, so they didn’t know who their competition was. • Technology was so new it was difficult to predict outcomes. • After 3-month-long auction, FCC raised nearly $8 billion through sale of licenses. • FCC could have set prices for different licenses, but put onus on bidding companies.

17. General Electric Example When General Electric wanted to slow price competition in the steam turbine industry, it advertised its prices to customers and publicly promised not to sell products below these prices. In addition, GE promised to refund customers the difference if they further reduced prices in the future. These actions sent a clear message to GE competitors that price reductions would be very costly to GE, which is a clear signal of the intent to collude on prices and one that helped reduce price competition in this industry. Both prices and margins in the steam turbine industry remained stable for the next 10 years as GE and major competitor Westinghouse learned how to survive together in the industry.

18. Works Consulted Baumol and Blinder. Principles of Economics, Theory and Policy, 1998. Case and Fair. Principles of Economics.