Thinking Strategically

1. Thinking Strategically Prof. Yair Tauman

2. The Right Game From Lose-Lose to Win –Win“In the early 1990s, the U.S. automobile industry was locked into an all – too familiar mode of destructive competition. End of year rebates and dealer discounts were ruining the industry’s profitability. As soon as one company used incentives to clear excess inventory at year end, others had to do the same. Worse still, consumers came to expect the rebates. As a result, they waited for them to be offered before buying a car, forcing manufacturers to offer incentives earlier in the year.Was there a way out? Would some one find an alternative to practices that were hurting all the companies? General Motors may have done just that.

3. In September 1992, General Motors and Household Bank issues a new credit card that allowed cardholders to apply 5% of their charges toward buying or leasing a new GM car, up to $500 per year, with a maximum of $3,500. The GM card has been the most successful credit card launch in history. One month after it was introduced, there were 1.2 million accounts. Two years later, there were 8.7 million accounts. As Hank Weed, managing director of GM’s card program explained, the card helps GM build share through the “conquest” of prospective Ford buyers and others – a traditional win–lose strategy. But the program has engineered another, more subtle change in the game of selling cars. It replaced other incentives that GM had previously offered. The net effect has been to raise the price that non cardholder – someone who intends to buy a Ford, for example – would have to pay for a GM car.

4. The program thus gives Ford some breathing room to raise its prices. That allows GM, in turn, to raise its prices without losing customers to Ford. The result is a win-win dynamic between GM and Ford. If the GM card is as good as it sounds, what’s stopping other companies from copying it? Not much, it seems. First, Ford introduced its version of the program with Citibank. Then Volkswagen introduced its variation with MBNA Corporation. Doesn’t all this imitation put a dent in the GM program? Not necessarily. In business it is often thought to be a killer compliment. Textbooks on strategy warn that if others can imitate something you do, you can’t make money at it. Some go even further, asserting that business strategy cannot be codified. If it could, it would be imitated and any grains would evaporate.

5. Yet the proponents of this belief are mistaken in assuming that imitation is always harmful. It’s true that once GM’s program is widely imitated, the company’s ability to lure customers away from other manufacturers will be diminished. But imitation also can help GM. Ford and Volkswagen offset the cost of their credit card rebates by scaling back other incentive programs. The result was an effective price increase for GM customers, the vast majority of whom do not participate in the Ford and Volkswagen credit card programs. This gives GM the option to firm up its demand or raise its prices further. All three car companies now have a more loyal customer base, so there is less incentive to compete on price. To understand the full impact of the GM card program, you have to use game theory .The key is to anticipate how Ford, Volkswagen, and other auto-makers will respond to GM’s initiative.

6. When you change the game, you want to come out ahead. But what about the fact that GM’s strategy helped Ford? One common mind-set seeing business as war – says that others have to lose in order for you to win. There may indeed be times when you want to opt for a win-lose strategy. But not always. The GM example shows that there are also times when you want to create a win-win situation. Although it may sound surprising, sometimes the best way to succeed is to let others, including your competitors, do well. Looking for win-win strategies has several advantages. First, because the approach is relatively unexplored, there is greater potential for finding new opportunities. Second, because others are not being forced to give up ground, they may offer less resistance to win-win moves, making them easier to implement. Third, because win-win moves don’t force other players to retaliate, the new game is more sustainable. And finally, imitation of a win-win move is beneficial, not harmful.

7. The term coopetition encourages thinking about both cooperative and competitive ways to change the game. It means looking for win-win as well as win-lose opportunities. Keeping both possibilities in mind is important because win-lose strategies often backfire. Consider, for example, the common – and dangerous- strategy of lowering prices to gain market share. Although it may provide a temporary benefit, the gains will evaporate if others match the cuts to regain their lost share. The result is simply to reestablish the status quo but at lower prices – a lose-lose scenario that leaves all the players worse off. That was the situation in the automobile industry before GM changed the game.

8. The Three-Door ProblemCreated by Dov Samet Monty Hall This is a problem presented to contestants in the TV game show Let’s make a deal , hosted by Monty Hall (1967-1990).

9. Let the game begin… There are three doors on stage. Behind one door is a car; behind the others, goats. The contestant does not know where the car is. She/he picks one of the doors. X

10. The host intervenes… The host, who knows what’s behind the doors, opens one of the other two doors which hides a goat. The contestant can now choose to open the door which he first chose, or to open the one door left closed. If there is a car behind the door opened, he\she wins it. X

11. To stick or to switch? That is the question!

12. What does it matter? From the participant’s point of view, each door has equal likelihood of revealing the car. Once the host opened an “empty” door, the car is behind one of the two remaining doors with equal likelihood. Hence there is no advantage or disadvantage in changing the initial choice. Is this so?

13. Please meet…. Marilyn vos Savant Columnist of the “Ask Marilyn” column in Parade magazine. Listed in the Guinness Book of World Records for the “highest I.Q.” (228).

14. Marilyn’s Claim In her weekly column, she claimed that the participant would do better switching doors. She has received about 10,000 letters, the great majority disagreeing with her. About 1000 letters were written by mathematicians and scientists. During the heat of this debate, the New York Times published a large front page article in the July 21st, 1991, Sunday issue.

15. A typical letter… This was written by Robert Sachs, a professor of mathematics at George Mason University: “You blew it! Let me explain: If one door is shown to be a loser, that information changes the probability of either remaining choice - neither of which has any reason to be more likely -  to 1/2. As a professional mathematician, I am very concerned with the general public's  lack of mathematical skills. Please help by confessing your error and, in the future, being more careful.”

16. In situations involving uncertainty, we tend to assume that the possible outcomes are equally likely.

17. There are two possible strategies: • To stick to the door which has chosen first • To switch, and open the other door

18. Clearly if the contestant chooses the “sticky” strategy his probability to win the car is 1/3 • If he chooses the “switchy” strategy he will win the car with probability of 2/3

19. Why? Suppose that he chooses to switch doors. If he chooses first an empty door (happens with probability 2/3) he wins for sure: the host opens the other empty door and he then switches to the door with the car.

20. An alternative explanation: Suppose we change the rules of the game. Following the initial selection of a door, the contestant can either open it, or open both the remaining doors and win the car if it is behind one of them. It is obvious that now the contestant should choose to open the two remaining doors. This way, the odds of winning double! But this is exactly the situation in the original game. Except that there the host is helping the contestant by opening one of the two remaining doors for him – an empty one.

21. Decision Making about Medical Diagnosis • In a certain population one out of 1,000 people carries the HIV virus • Testing device is 100% accurate on HIV carriers (every HIV carrier is positively diagnosed) • The testing device is 99% accurate on non-HIV carriers (99 out of 100 non-carriers are diagnosed negatively) • A person chosen at random is tested positively. What is the chance (probability) that he is an HIV carrier?

22. A surprising answer: Less than 10%, Why? Suppose for example that the population is of 100,000 people and all of them take the test: 100,000 Non-carriers Carriers 99,900 100 - + - + 98,901 999 0 100 • Total number of plus outcome is 1,099 • But, only 100 of them are HIV- carriers • The probability that a person tested positive is indeed an HIV-carrier is therefore: 100 1 ~ ~ 9% ~ ~ 1,099 11

23. Simultaneous GamesDominant and Dominated Strategies

24. A Couple Dispute A couple: Alice an Bob decide to divorce. Their total asset is $500K. They need to reach an agreement of how to divide their asset. Each one of them has two choices: to hire a Brilliant lawyer who charges for his work $150K or to hire an Ordinary lawyer who charges a fee of $50K. If both of them hire the same type of lawyer they will split the asset equally. Namely each will receive $250K. A Brilliant lawyer who faces an Ordinary lawyer will achieve $375K for her client, leaving $125K for the other side.

25. Bob B O Alice The situation can be described by the following table: What will happen? B O

26. No matter what Bob decides to do – Alice is best off hiring a Brilliant lawyer. Similarly, no matter what Alice does, Bob is best off also hiring a Brilliant lawyer. Bob B O Alice * B O

27. The only rational outcome is that both Alice and Bob hire Brilliant lawyers and net $100K each. Who makes the most of it? The Lawyers

28. Now, let’s assume each that both Alice and Bob have the option to negotiate without a lawyer • Assumptions: • When one side is represented by a brilliant lawyer and the other side is not represented by a lawyer, the lawyer will get for his client 420,000 and leave the other side with 80,000 • When one side is represented by an average lawyer and the other side is not represented by a lawyer, the lawyer will get for his client 315,000 and leave the other side with 185,000 • Now, the table is as follows:

29. Again the dominant strategy of each one of them is to choose the brilliant lawyer  Inferior outcome

30. The Prisoners’ Dilemma In 1950 Melvin Dresher and Merrill Flood (RAND cooperation) formulate a game that subsequently named the Prisoner’s Dilemma by Albert Tucker (Princeton). Tucker came up with the following story which motivated an equivalent version of Dresher and Flood.

31. Two suspects in a major crime are held in custody. There is enough evidence to convict each of them of a minor offense, but not enough evidence to convict either of them on a major crime, unless one of them acts as an informer against the other. If they both stay quiet, each will be convicted of the minor offense and spend one year in prison.

32. If one and only one of them admits he will be freed and used as a witness against the other, who will spend life in prison. If both admit each will spend 15 years in prison. suspect 2 suspect 1 Quiet Admit 15 years in prison 15 years in , prison Life in prison Admit free , 1 year in , prison Life in prison 1 year in prison Quiet , free

33. suspect 2 suspect 1 Quiet Admit 15 years in prison 15 years in , prison Life in prison Admit free , 1 year in , prison Life in prison 1 year in prison Quiet , free A dominant strategy of each one of them is to admit. The only Rational Outcome is for them to spend 15 years in prison.

34. Definition: A game is a Prisoners’ Dilemma game if the following two conditions are satisfied: Every player has a strictly dominant strategy (a strategy that is strictly better than any of the other strategies, irrespective of the choice of strategies of the other players) When the players choose their dominant strategies the outcome is inferior (namely, there is another outcome that is strictly better for all players)

35. The Tension Between Game Theory and the Invisible Hand Principle Adam Smith in 1776 (The Wealth of Nations) advocated that competition between consumers who are allowed to choose freely what to buy and producers who are allowed to choose freely what and how to produce will lead to a product distribution that are beneficial to society as a whole.

36. That is, individual efforts to maximize their own gains (a selfish behavior) in a free market will benefit society even if the ambitious has no benevolent intention. Smith refers to such phenomenon as “invisible hand”. This term applies to any individual action that has unplanned or unintended consequence, particular those that arise from actions not orchestrated by a central planner (a government) and have a “pleasant surprise” on society.

37. In a free and competitive market place where every consumer and every producer has only negligible effect on the market, individual self-interest produces the maximization of society’s total utility. The sad reality is that most markets are not perfectly competitive and include “significant” players (firms) that their actions have non-negligible impact on all other players (imperfect competition). In such markets the distribution of products are in general not efficient.

38. In environments with significant players, the players are acting strategically and when choosing their strategy must take into account the counter actions of their rivals and their counter actions to the rivals’ actions, etc. As the Prisoner's Dilemma demonstrates, the strategic outcome can be very inefficient. That is, every player might do the individually best thing, but this may ends up worst from their collective view point.

39. Example: The Collapse of a Cartel Two countries Iran and Iraq can either produce 2 million or 4 million of barrels of crude oil a day The daily demand for oil is: P is the market price and Q is the total output Extraction costs are $2 per barrel in Iran and $4 per barrel in Iraq 120 120 Q= P= - 5 equivalently P + 5 Q

40. The following tables are for the market price and the profits of the two countries as a result of their outputs: Table 1: Market Prices Table 2: Profits (Iran, Iraq)

41. Clearly, q1= q2= 4 (Q=8) are strictly dominant strategies of each country The outcome of their choice is (32, 24) which is inferior to the cooperative outcome (46, 42) that is obtained when both countries trust each other and produce 2 millions of barrels each This cartel game is another example of the Prisoners’ Dilemma

42. Example Consider the following two persons game: What are the possible values of x and y that turn this game into prisoners’ dilemma? 2<x<4 1<y<4

43. The Public Transportation Dilemma Commuters from A to B can choose between public transportation (a bus) and private cars. Denote by p the percentage of commuters by car. Traveling time is: • by bus: 45 + 0.5p • by car: 30 + 0.5p The car ride is shorter regardless of the percentage of car drivers. Therefore, everyone uses the car rather than take the bus. Hence, the trip takes 30 + 0.5*100 = 80minutes. If all took a bus, it would take 45 + 0.5*0 = 45 minutes.

44. Is the More the Better? Increasing exclusively all payoffs of one player Does it make him happier? Not Necessarily! Consider the following simultaneous two person-game G: • The strategy U is a strictly dominant for Player 1- therefore, he will choose it • Player 2 knows this and her best reply to U is to play R • The outcome is (7, 7) Game G

45. Now D is a strictly dominant strategy of 1 and 2 knows this hence 2 will choose L to obtain 5 (and not 4) • The outcome is (6,5) • The exclusive bonus of 1 hurts him! Suppose next that only player 1 is getting a bonus If he plays U his payoff will increase by 1 no matter what 2 chooses If I plays D his payoff will increase by 3, again no matter what 2 chooses What can 1 lose?  All his payoffs increased Is that so? The new game G1 is: Game G1 Game G Remark: This last game is not a prisoners’ dilemma game. Yes, the outcome (6, 5) is interior to (8,7). Yes, player 1 has a strictly dominant strategy- D. But 2 does not have a dominant strategy.

46. Adding a dominant strategy to one player does it make him happier? Not Necessarily! • Consider next the game G2 where N is a new strategy of 1 which strictly dominates the other two strategies U and D: Consider again the game G: The only sensible outcome of G2 is (5, 5) which is inferior to (7, 7)

47. More on: Is the More the Better? Example 1: A firm has three board members: B1, B2 & B3 One of them B1 is the CEO The board has to choose a strategy for the firm out of the following three strategies: S1, S2 & S3 The strategy is selected by a vote Each board member selects a strategy and submits his choice in a sealed envelope The strategy that obtains a majority wins If no strategy has a majority (all three board members select different strategies) the strategy of the CEO (B1) is implemented The CEO is therefore endowed with an extra power

48. The following table represents the ranking of the three board members over the possible strategies: E- Excellent G- Good B- Bad Table 1 • The three board members act strategically • How would they vote? • What strategy will be implemented?

49. Solution First observe that it is a (weakly) dominant strategy for the CEO to vote for S1 (the best for him). If he does so S1 will win except only if both B2 and B3 vote for S2 or both of them vote for S3. In these two cases the CEO has no impact on the outcome (no matter how he votes). Consequently, B1 will vote S1. The two other board members understand this and their strategic game can be described in the following table (under the assumption that B1 votes for S1):

50. The table shows the wining strategy given the decisions of B2 and B3 The ranking of B2 and B3 of S1 is (B, G)- see Table 1 Their ranking of S2 is (G, E) and their ranking of S3 is (E, B) We can use Table 2 to write the outcome for B2 and B3 as a function of their decisions Table 2