Understanding Game Theory: Strategies, Players, and Outcomes in Strategic Interactions

1. Game Theory “In War the Will Is Directed at an Animate Object That Reacts.” - Karl Von Clausewitz, On War Mike Shor Lecture 2

2. Review • Game Theory • Description of strategic interaction between mutually aware players • You are self-interested and selfish • So is everyone else • Tools • Recognize you are in a game • Recognize the type of game • Know the possible outcomes • Manipulate the game structure Game Theory - Mike Shor

3. Rules of the Game • The strategic environment • Players • Strategies • Payoffs • The rules • Timing of moves • Nature of conflict and interaction • Informational conditions • Enforceability of agreements or contracts • The assumptions • Rationality • Common knowledge Game Theory - Mike Shor

4. The Strategic Environment • Players • Everyone who has an effect on your earnings • Strategies • Complete plan of action • Computer program • Tactics vs. Strategies vs. Moves • Payoffs • Numbers associated with each possible outcome • Expected payoffs if outcomes are random Game Theory - Mike Shor

5. The Rules • Timing of moves • Are the moves simultaneous? Sequential? • Nature of conflict and interaction • Are players’ interests in conflict? Cooperation? • Will players interact once, or repeatedly? • Informational conditions • Is there full information? Advantages? • Enforceability of agreements or contracts • Can agreements to cooperate work? Game Theory - Mike Shor

6. Example: Toys “R” Us • Players • Toys R Us • Warehouse clubs: Costco, Pace • Manufacturers: Hasbro, Mattel, etc. • Strategies • To threaten or not to threaten • To follow through on threats or not • To deal or not to deal with warehouse clubs Game Theory - Mike Shor

7. Rules • Sequential timing • Threats • Manufacturer’s decisions • Decisions to follow through on threats • Simultaneous timing • Manufacturer’s decisions • Information • Who understands the future profitability of warehouse clubs • Agreements • Can manufacturers collude? Game Theory - Mike Shor

8. Changing the Rules • Are the rules of the game fixed? • Example: voting and agenda setting COMMANDMENT When the rules of the game are flexible manipulate them to your advantage. Game Theory - Mike Shor

9. Executive Committee • Three members • Director of marketing • Director of engineering • Director of research & development • Three possible expansion projects • More money to marketing • More money to engineering • More money to research & development • Majority rule voting Game Theory - Mike Shor

10. Member Preferences • Director of marketing • Marketing > Engineering > R&D • Director of engineering • Engineering > R&D > Marketing • Director of research & development • R&D > Marketing > Engineering • Majority rule results: • M beats E ; E beats R ; R beats M Game Theory - Mike Shor

11. Rules of Voting • Majority rule results: • M beats E ; E beats R ; R beats M • M vs. E then winner vs. R  R • M vs. R then winner vs. E  E • E vs. R then winner vs. M  M Game Theory - Mike Shor

12. The Assumptions • Rationality • Players aim to maximize their payoffs • Players are perfect calculators • 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. Game Theory - Mike Shor

13. Examples • Biased beauty contest • (3/4)  100 = 75 • (3/4)  75  56 • (3/4)  56  32 • 24, 18, 14, 10, 8, 6, 4, 3, 2, 1, 0 • Coordination • Intentional failure to coordinate Game Theory - Mike Shor

14. Equilibrium • What is likely to happen when rational players interact in a game? • Type of equilibrium depends on the game • Simultaneous or sequential • Perfect or limited information • Concept always the same: • Each player is playing the best response to other players’ actions • No unilateral motive to change • Self-enforcing Game Theory - Mike Shor

15. Summary • Recognizing that you are in a game • Identifying players, strategies, payoffs • Understanding the rules • Manipulating the rules • Searching for possible outcomes Game Theory - Mike Shor