Game Theory

1. Game Theory “The Power to Constrain an Adversary Depends Upon the Power to Bind Oneself.” - Thomas Schelling Mike Shor Lectures 7&8

2. Review • Cooperation requires sacrificing immediate profits for a future relationship • The sacrifice is only made if the punishment is severe enough • Finite interaction does not allow cooperation Game Theory - Mike Shor

3. Finite Repetition • Unraveling prevents cooperation if the number of periods is fixed and known • Probabilistic termination • The “game” continues another round with some probability p: • Equivalent to infinite game • ’ =   p • Value of future = { value if there is a future }  { probability of a future } Game Theory - Mike Shor

4. Lessons • Be careful of “finite games” • Always a chance of another encounter • Balance severity of punishment! • Mild punishment may not deter cheating • Severe punishments may not be credible Game Theory - Mike Shor

5. Credibility “The difference between genius and stupidity is that genius has its limits.” • Albert Einstein. • A commitment that is not credible “I do not believe that you will carry out your threat given your rationality, and the strategies and payoffs that you will have.” Game Theory - Mike Shor

6. Talk is Cheap • Promises “Continental Airlines said yesterday that it would raise airfares on about two-thirds of its routes … to take effect September 5.” - The New York Times August 29, 1992 “Continental Airlines has dropped its plan to raise domestic airfares by 5%.” - USA Today September 4, 1992 Game Theory - Mike Shor

7. Talk is Cheap … • Threats “On January 5, Boeing, the world’s top aircraft maker, announced it was building a plane with 600 to 800 seats, the biggest and most expensive airliner ever. Some in the industry suggest Boeing’s move is a bluff to preempt Airbus from going ahead with a similar plane.” - Business Week, 1993 Game Theory - Mike Shor

8. … And Getting Cheaper Airbus announces commercial launch of the A3XX, the largest civil aircraft ever built. “Boeing … has said that there is no market for such a large plane and has decided to modernize its trustworthy 747 family of planes rather than build its own megaseater.” - Associated press, June 23 2000 Game Theory - Mike Shor

9. Strategic Commitment • Observable • Understandable • Irreversible • Talk is cheap • How to be credible? • Important: You are not credible if, as a rational actor, you propose to take actions among your available strategies which earn you less-than-optimal profit! Game Theory - Mike Shor

10. Credibility • Remove from your own set of future choices the strategies that may tempt you in the future • Reduce your own payoffs from those strategies that may tempt you • Become irrational Game Theory - Mike Shor

11. Removing Strategies I • Delegation • In contract negotiation, can “squabble” over many details • Instead, send an agent with power of attorney to “sign as is” or “walk away” • Haggling over prices in a department store Learn from government bureaucracy: “The rules won’t allow me to do what you ask” Game Theory - Mike Shor

12. Removing Strategies II • Burning Bridges • Power comes from not being able to retreat • Remove retreating strategies • Allow opponent to retreat (Sun Tzu) • Example: semiconductor patent sharing • Share patent with another competing firm • Commit to chip supply to production plants • Commit to no opportunistic behavior • Example: capacity constraints • New entrant commits to low production • The “puppy-dog ploy” Game Theory - Mike Shor

13. Removing Strategies III • Irrationality • U.S. / U.S.S.R. nuclear deterrence Mutually Assured Destruction (MAD) like Grim Trigger Strategy Proportional Response like Tit-for-Tat • Want a lot of deterrence • Want irrationality to be credible • Dr. Strangelove & the Doomsday device Game Theory - Mike Shor

14. Dr. Strangelove • Severity Create fear in the mind of the enemy • Irreversibility Must be irreversible • Irrationality Not something a sane man would do • Practicality Punishment shouldn’t be too harsh • Clarity “Tell the world” Game Theory - Mike Shor

15. Use of Contracts • Promises vs. Threats • Promises can sometimes be credible through a contract with the party to whom you are making the promise • Not always: Mario Puzo’s The Godfather • Threats can never become credible by use of a contract with the party you are threatening • Must contract with third party Game Theory - Mike Shor

16. Aside: Don’t Demand Overcommitment • Supplier promises to deliver production inputs by next Monday • Cost of inputs is $20,000 • Value of inputs is $40,000 • Demand in contract $1M if not delivered on time • 5% risk of non-delivery • Contract Price: 20,000+.05x$1M = $70,000 Game Theory - Mike Shor

17. Reducing Payoffs • Contracting with customers to commit to competitors • Price-matching • Most Favored Customer clauses • Contracting with lenders to commit to a take-over • Interest-rate rise if loan amount increases Game Theory - Mike Shor

18. Example From Last Time … • Two firms: Firm 1 and Firm 2 • Two prices: low ($6) or high ($8 ) • 1000 captive consumers per firm • 2000 floating go to firm with lowest price Game Theory - Mike Shor

19. Contracting with Customers • The game is a prisoner’s dilemma • Both firms prefer: {High,High} • Only equilibrium: {Low , Low} • Cannot credibly promise to play High • Even if committed to High, other firm would still respond with Low • How to resolve this? • Third party contracts with customers Game Theory - Mike Shor

20. Most Favored Customer • Say in period 1, the firms colluded and each sold to 2000 customers • In period 2, firms must refund to last period’s customers $2 each if price is low Game Theory - Mike Shor

21. Contracting with Lenders • Takeover offer: $200 million • You can “afford” $20 million / year • Finance takeover for 20 years at 7% • Add penalty: if amount greater than $200 million, +1.5 points on interest rate • Annual Payments: • $200 million: $18.6 million / year • $210 million: $19.6 million / year • with penalty: $21.9 million / year Game Theory - Mike Shor

22. Irrationality • “Burning money” • Commit to long-term market plan • Commit to high quality products • Firm can produce high or low quality • Customers cannot observe quality • Once customers buy a product the first time, observe quality, punish dishonest firms Game Theory - Mike Shor

23. Burning Money • Producing high quality is more profitable • $50 - $8 = $42 > $16 = $20-$4 • Pretending you are high quality is best • $50 - $4 = $46 • Incentive to lie: • Customers do not believe in high quality • Customers only pay for low quality • Firm only produces low quality INEFFICIENT AND UNPROFITABLE Game Theory - Mike Shor

24. Burning Money • Announce “high quality” and burn $50 Game Theory - Mike Shor

25. Burning Money • By “burning” $50, convince customers of your high quality: • $8 loss this year, $42 profit in the future • Without “burning money”, can only sell low quality: • $16 profit this year and in the future • Gaining credibility by burning $50 • Invest in future relationship with customers Game Theory - Mike Shor

26. Vagueness • If you can’t be irrational, be vague. • Example: collusion with indirectly observable cheating • Be committed to your punishment • Be flexible about what triggers punishment Game Theory - Mike Shor

27. Summary of Commitment Methods • Strategies • Remove options • Automate responses • Reduce payoffs • Introduce uncertainty - irrationality Game Theory - Mike Shor

28. Forcing Your Opponent • Similar tactics for making your opponent commit to strategies in your favor • Increasing his strategy space • Excluding bargaining agents • Lowering his payoffs • Poison pills • Raising his payoffs • Reputation bolstering Game Theory - Mike Shor

29. Price Matching • If one firm charges low, it does not gain any additional customers, since the competitor “automatically” matches it: • NASDAQ order preferencing? Game Theory - Mike Shor

30. Commitment Is Counterintuitive COMMANDMENT. Reduce your strategy space and decrease your own payoffs to commit. Increase your opponent’s strategy space and alter your opponent’s payoffs to preclude the rival from committing. • Hurt yourself to help yourself • Help your opponent to help yourself Game Theory - Mike Shor

31. Precommitment Under Uncertainty • An offer you can’t refuse • After a seemingly successful interview, the interviewer asked where the firm ranks on your list of potential employees • Before answering, you are told: • The firm only hires applicants who rank it first • If the firm is in fact your first choice, then you must accept a job offer in advance, should one be made Game Theory - Mike Shor

32. Precommitment Under Uncertainty • What to do? • Binding early-decision college applications • Why make such proposals? • Take advantage of your uncertainty • Take advantage of your risk-aversion • Make you commit before they do! Game Theory - Mike Shor

33. Flexibility vs. Commitment • Flexibility in light of uncertainty about eventual outcomes generates value • Keeping your options open • Must be balanced against strategic value of commitment • Option Value: • The additional expected profit from remaining flexible above the expected profit earned from committing Game Theory - Mike Shor

34. ExampleOption Value of Delay • A firm can spend $100 million on an investment to enter a new market • Market demand uncertain: High acceptance: revenues of $300m (Probability=0.5) Low acceptance: revenues of $50m (Probability=0.5) • Two options: • Invest today in the presence of uncertainty • Wait a year for full revelation of information Game Theory - Mike Shor

35. Calculating Option Value • Immediate investment: E[]=(1/2)(300-100) + (1/2)(50-100) = $75 million • Delayed investment: Only invest if high acceptance E[]=(1/2)(300-100) + (1/2)(0) = $100 million • Option value: $100 - $75 = $25 million Countervailing force: by waiting, the firm risks having the opportunity pre-empted by competitors Game Theory - Mike Shor

36. Philips, N.V. • Capacity commitment in CD introduction • Philips: innovator’s advantage • Initiate construction of plant ahead of competitors • Decision problem of Philips in 1982: • Build a disk-pressing plant in the U.S. And invest in a substantial amount of capacity to deter potentially entry (Sony, etc.) • Delay decision until commercial appeal of CDs can be determined. Import CDs to the U.S. To “test the waters.” Game Theory - Mike Shor

37. Option Value: Three Cases q probability of mass acceptance of CDs • Monopoly Benchmark: • Philips should wait if q < 0.380 • Sony competition, equal information • Philips should wait if q < 0.006 • Sony competition, better information • Philips should wait if q < 0.130 Game Theory - Mike Shor

38. Summary • Pure option value • In the absence of competition, Philips would have been better off waiting and retaining flexibility if the probability of acceptance was 0.38 or lower • Commitment value • Faced with competitors who are as well informed, Philips would be better off building the U.S. plant right away even in the presence of uncertainty • Informational advantage • Given proprietary information through its CD operations in Europe, Philips should remain flexible if the probability of acceptance was 0.13 or lower Game Theory - Mike Shor

39. Evidence • Philips did not build a U.S. Plant in 1983 • Its assessment of the likelihood of general acceptance did not meet the threshold • Market realization (surprise!) • Sony constructed a U.S. Plant in 1984 • Terry haute, Indiana • Philips attempted to compete • Increased capacity in Hanover, Germany plant • Philips decided to invest in a U.S. Plant • Only after the Sony plant was fully operational Game Theory - Mike Shor