Principles of Game Theory

1. Principles of Game Theory Lecture 1: Introduction John Gasper

2. What is Game Theory? • Study of rational behavior in interactive situations • Decision Theory: You are self-interested and selfish • Game Theory:So is everyone else. • We’ll assume rational agents (weaker than selfish) • Lots of ways we aren’t “rational.” LOTS. • Bad news: • Knowing the theory doesn’t guarantee you’ll win. • Not always applicable. (see rationality assumption) • Good news: • Should help you think about strategic interactions • We don’t live in a vacuum – broadly applicable. Gasper: Principles of Game Theory

3. Games we play Some examples: • Group projects free-riding, reputation • Mean professors commitment • Grade curves prisoner’s dilemma • Football/soccer mixed strategies • Bridge/Poker credibility • Traffic congestion • Dating information manipulation Gasper: Principles of Game Theory

4. Games Businesses Play • Market entry commitment • Drug testing mixed strategies • Supply chains auctions • Corporate takeovers winner’s curse • Fishing coordination • Patent races game of chicken • Stock options compensation schemes • OPEC output collusion & enforcement Gasper: Principles of Game Theory

5. Administrative • Course website • Piazza: should be set up by this afternoon • https://piazza.com/qatar.cmu/fall2013/70442/home • Discussion, Q&A, etc, should happen there – help each other!! • About Me • Office hours: Tuesday 2-4pm • otherwise schedule an appointment • My background • Your background? • Stop by this week for 10min • Even if I’ve had you in class before… Gasper: Principles of Game Theory

6. Administrative: the basics • This is a mini course • Lot of material + less time = fast pace • Attendance • I expect you in class. • If you miss it, you’ll be behind. Full stop. • This is a 400 level course and you’re adults. • Phones / computers • If you’d rather check FB than pay attention, don’t come to class. Gasper: Principles of Game Theory

7. Administrative: grades Course grades will be based on: • Participation 10% • Problem sets 20% • Check system: • ✔ = reasonable attempt at problem (right or wrong) • ✔- = poor/deficient attempt • ✔+ = exemplary work (must be correct) • Midterm exam 20% • Final exam 20% • Quizzes 30% (10% each, best 3 of 4) • First quiz next Sunday Gasper: Principles of Game Theory

8. Keys to doing well • After each class: • Do the assigned problems • Read for the next class • Ask questions! • The discussion board can be very helpful. • Answer questions!! • You learn a lot by trying to explain something. • Don’t fall behind • It’s really easy to push stuff off (I did; I do), but it’s much harder to catch up given the short time we have. Gasper: Principles of Game Theory

9. Game Theory • Often taught from a very technical point of view • History in applied mathematics / mathematical econ • This course: still theory + applications, but less math • This is an intro; save the technical stuff in grad school Gasper: Principles of Game Theory

10. Game Theory • Game theory often thought of as “hard.” It’s not. • Key thing to remember: Never assume that your opponents’ behavior is fixed. Predict their reaction to your behavior. Gasper: Principles of Game Theory

11. Game Theory • GT often called a study of conflict. NO. It’s not. • The main component in using game/decision theoretic reasoning comes down to understanding incentives. • Do safety devices cause less injuries? • Why go for an MBA if you aren’t going to learn anything new? • Why shut down a plant operating at capacity? • Why offer price guarantees? Gasper: Principles of Game Theory

12. Classifying games Major distinctions (more precise later): • Sequential or simultaneous move? • Does a player get to condition his/her actions on others behavior? • Zero-sum or not? • Constant sum– purely competitive; winner and loser. • Gains from interaction? • One shot or repeated? • Either one is not necessarily easier or harder. • Opportunity to build reputation (for good or bad) Gasper: Principles of Game Theory

13. Classifying games Major distinctions (more precise later): • Any uncertainty? Full, partial, or asymmetric information? • Imperfect information – knowing who and which possible moves, just not which one • Incomplete information – not knowing something about the player’s “type” • Manipulation of information: signaling and screening, • Fixed rules or manipulable? • (i.e., is there a pre-game to the game?) • Non-cooperative or cooperative • (i.e., are agreements enforceable) Gasper: Principles of Game Theory

14. Defining the game for yourself Always ask yourself: • What is the strategic environment • Who are the players? (Decision makers) • What strategies are available? (Feasible actions) • What are the payoffs? (Objectives) • What are the rules of the game? • What is the time-frame for decisions? • What is the nature of the conflict? • What is the nature of interaction? • What information is available? Gasper: Principles of Game Theory

15. Terminology & Assumptions Conceptual introduction (precise definitions later) • Actions and Strategies • Actions: the available action taken at any singular point • Strategy: complete, contingent, plan of action • Different than “tactics and strategies” • Payoffs • Objective isn’t necessarily “winning.” Represent preferences with a payoff function. • Can be monetary but will be represented by utility f() Gasper: Principles of Game Theory

16. Terminology & Assumptions • Rationality • Overloaded word. • Specific meaning: complete and consistent ranking over possible outcomes (payoffs) and optimizes over strategies to best serve those interests. • Empirically often not supported. But still useful. • Logical implications of knowledge • Assume that players have logical omniscience: if player 1 knows A, then 1 knows all of the logical implications of A • Often assume “Positive introspection:” 1 knowing A, implies that 1 knows that ‘1 knows A’ • Often assume “Negative introspection:” 1not knowing A, implies that 1 knows that 1 doesn’t know A. Gasper: Principles of Game Theory

17. Terminology & Assumptions • Common Knowledge • For two players, 1 and 2, to commonly know A, it is not enough for 1 and 2 to know A. • Player 1 must know that 2 knows that 1 knows A. • And that 1 knows that 2 knows that 1 knows, … ad infinitum. • We’ll assume the structure of the game and the rationality of the players are 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. • (FYI philosophers like to play with points 4 and 5 above) • Equilibrium • Concept of equilibrium should be familiar to most of you. Mutual best response. Mathematically, it’s a fixed point. Gasper: Principles of Game Theory

18. Common knowledge Gasper: Principles of Game Theory

19. Homework assignment For next class • Review chapters 1 and 2 (easy) • Do problems in Chapter 2: • U2 parts b and d • U4 parts a-e (all parts) • Read chapter 3. Gasper: Principles of Game Theory