1. A Brief Introduction to Game Theory Agenda: I.A framework for thinking about problems II.Imperfect competition assumptions III.The Oligopoly Game IV.The Prisoner’s Dilemma & Nash equilibrium V.Economic Survivor VI.The moral of the story…

2. A Framework for thinking about problems From Basar & Olsder Dynamic Noncooperative Game Theory (1999) p. 2 One decision makerMany decision makers One decision a series of independent decisions Static Multiple related decisions Dynamic Mathematical programming, Static optimization Optimal control theory, Dynamic optimization Static Game Theory Dynamic or differential game theory Applications of game theory: Economics, politics, war, infectious disease, engineering, artificial intelligence, portfolio management, product development

3. Models of imperfect competition Monopolistic competition Cournot Ologopoly Stackelberg Ologopoly Bertrand Ologopoly Limiting assumption Each firm pursues optimum independently; firms respond to profit, but not specifically to other firms’ actions. Each firm takes the other’s quantity as given and does not seek to change it. The second mover cannot respond to the first mover’s chosen quantity Each firm takes the other’s price as given and does not seek to change it.

4. Oligopoly Game Rules of the game: 1.Pick a red or a black card and put it against your chest so no one can see it. 2.I’ll pair you randomly with another player. 3.Show each other your cards and compute your pay-off Play red card: you get 2 (cut your price) Play black card: your opponent gets 3 (keep your price the same) 4.We’ll play 5 rounds – the first two with random partners and the last three with the same partner. 5.Highest earners get.5 bonus point (another.5 for the next game…) 8 (row, column)

5. The Prisoner’s Dilemma http://en.wikipedia.org/wiki/John_Forbes_Nash,_Jr. Von Neumann & Morgenstern Dominant Strategy: You do better no matter what your opponent does. Nash Equilibrium: No player has an incentive to change strategies. Often one player has a dominant strategy, and the other chooses a dominant strategy given their opponent’s dominant strategy. Maxmin: Pick the best of the worst-case scenarios Row: 10 or 2 > 8 or 0 Column: 10 or 2 > 8 or 0

6. Repeated Games “Tit for tat”: Cooperate first, but defect if your opponent defects. Richard Kirkland, Battle of Fredericksburg 12/13/1862 http://fredericksburg.com/CivilWar/Battle/kirkland.htm Collusion of bid-ask spreads on NASDAQ In essence, the Government found that these firms -- which besides Merrill Lynch include such Wall Street titans as Goldman, Sachs & Company, Morgan Stanley & Company and Smith Barney Inc. -- had conspired to maintain artificially wide margins between the bid price and the ask price for Nasdaq stocks. Traders who did not follow the market's convention of only quoting prices in spreads of at least a quarter of a dollar, and tried to quote in narrower one-eighth increments, were coerced and harassed, according to Anne K. Bingaman, the Assistant Attorney General in charge of the department's antitrust division. http://www.nytimes.com/1996/07/18/business/deal-reached-in-civil-suit-over-collusion-on- nasdaq.html “The great enforcer of morality in commerce is the continuing relationship” Frank p. 421

7. Economics SurvivorYour goal: To get the last card There will be 21 cards on the table. You can remove 1,2 or 3 cards each turn. The team that removes the last card wins.5 bonus point. http://en.wikipedia.org/wiki/Nim

8. Backwards induction – start with where you want to end! If you leave your opponent with 4 cards, you win! Your opponent needs to have 8 cards the round before 12 the round before that 16 the round before that 20 the round before that

9. The moral of the story… Neoclassical Economic Theory Behavioral Economics Game Theory + += Some really cool models of human behavior! All models are wrong, but some are useful.

10. “You have to learn the rules of the game. And then you have to play better than anyone else.” Albert Einstein