Ka-fu Wong University of Hong Kong

1. Strategic Choice in Oligopoly, Monopolistic Competition, and Everyday Life Ka-fu WongUniversity of Hong Kong

2. Games and Strategic Behavior • Thus far, we have viewed economic decision makers as confronting an environment that is essentially passive. • But there exist many cases in which relevant costs and benefits depend not only on the behavior of the decision makers themselves but also on the behavior of others.

3. Example 11.1. Should the prisoners confess?

4. Example 11.1. Should the prisoners confess? • Two prisoners, X and Y, are held in separate cells for a serious crime that they did, in fact, commit. • The prosecutor, however, has only enough hard evidence to convict them of a minor offense, for which the penalty is, say, a year in jail. • Each prisoner is told that if one confesses while the other remains silent, the confessor will go free while the other spends 20 years in prison. • If both confess, they will get an intermediate sentence, say five years.

5. Example 11.1. Should the prisoners confess? • It is often convenient to summarize the elements of a game in the form of a payoff matrix. • Three elements: • Players (2 prisoners) • Strategies (confess, remain silent) • Payoffs (jail sentences)

6. Example 11.1. Should the prisoners confess? The two prisoners are not allowed to communicate with one another. If the prisoners are rational and narrowly self-interested, what will they do?

7. Example 11.1. Should the prisoners confess? Their dominant strategy is to confess. No matter what Y does, X gets a lighter sentence by speaking out. 1. If Y too confesses, X gets five years instead of 20. 2. And if Y remains silent, X goes free instead of spending a year in jail. The payoffs are perfectly symmetric, so Y also does better to confess, no matter what X does. • Dominant Strategy: • One that yields a higher payoff no matter what the other players in a game choose.

8. Example 11.1. Should the prisoners confess? • The difficulty is that when each behaves in a self-interested way, both do worse than if each had shown restraint. • Thus, when both confess, they get five years, instead of the one year they could have gotten by remaining silent. • And hence the name of this game, prisoner's dilemma.

9. Example 11.2. • Why did students have to wait in line overnight to buy Cornell hockey tickets?

10. Example 11.2. • Each year Cornell announced a time at which its ticket window would open for the sale of a limited number of hockey tickets for students. Students showed up more than 24 hours in advance to wait in line for these tickets, even though no more tickets were available that way than if everyone had shown up only 1 hour in advance.

11. Example 11.2. • Suppose that if everyone shows up one hour in advance, everyone has a 50-50 chance of getting a ticket, and that the odds of getting a ticket are the same if everyone shows up 24 hours in advance. • If you show up 24 hours in advance and everyone else shows up one hour in advance, you are sure to get a ticket. • But if you show up 1 hour in advance and others show up 24 hours in advance, you have no chance to get a ticket. • The same applies to other students.

12. Example 11.2. • Waiting only one hour has no cost to you. But you would be willing to pay $40 to avoid having to wait 24 hours. • A 50-50 chance of getting a ticket is worth $50 to you and a 100 percent chance of getting a ticket is worth $100. • Other students value these outcomes just as you do. What will happen?

13. Example 11.2. • Your payoff if you and others arrive 24 hours early:

14. Example 11.2. Everyone's dominant strategy is to come 24 hours early, and so this is the equilibrium outcome of the game. But it would be better if everyone came one hour early.

15. Example 11.3. • Why do hockey players vote in secret ballots for helmet rules, even though they choose not to wear helmets when there is no rule?

16. Example 11.3. • Consider two hockey teams-- say, the Bruins and Rangers-- each of whose players can choose to wear helmets or not. • Not wearing a helmet increases the odds of winning, perhaps by making it slightly easier to see and hear, or perhaps by intimidating opposing players (on the view that it is not safe to challenge someone who is crazy enough to go without a helmet).

17. Example 11.3. At the same time, not wearing a helmet increases the odds of getting hurt. If players value the higher odds of winning more than they value the extra safety, explain why they will choose not to wear helmets, even though the odds of winning when players on both sides wear helmets are no different from the odds when no one wears helmets.

18. Example 11.3. The dominant strategy for each team is to go without helmets, even though this combination of choices is worse for both teams than the alternative in which each team wears helmets.

19. Example 11.4. Why do people shout at cocktail parties?

20. Example 11.4. Why do people shout at cocktail parties? • Whenever large numbers of people gather for conversation in a closed space, the ambient noise level rises sharply. • After attending such gatherings, people often complain of sore throats and hoarse voices from having to speak so loudly to be heard.

21. Example 11.4. Why do people shout at cocktail parties? • If everyone instead spoke at a normal voice level at cocktail parties, they would avoid these symptoms. • And because the overall noise level would be lower, they would hear just as well as when they all shout at one another. So why shout?

22. Example 11.4. Why do people shout at cocktail parties? The dominant strategy for everyone is to speak more loudly. But when all follow their dominant strategies, we get a worse outcome than if everyone had continued speaking normally.

23. Nash Equilibrium Nash equilibrium: a combination of strategies such that each player's strategy is the best he/she can choose given the strategy chosen by the other player. John F. Nash Jr. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1994

24. Nash equilibrium in prisoner’s dilemmas In prisoner's dilemmas, the Nash equilibrium occurs when each player plays his dominant strategy. Many games have a Nash equilibrium, even though not every player has a dominant strategy.

25. Example 11.5. Should American spend more on advertising? • Suppose that United Airlines and American are the only carriers that serve the Chicago-St. Louis market.

26. Example 11.5. Should American spend more on advertising? If the relevant payoffs are as shown, does United have a dominant strategy? Does American?

27. Example 11.5. Should American spend more on advertising? American 's dominant strategy is to raise its ad spending. United, however, does not have a dominant strategy.

28. Example 11.5. Should American spend more on advertising? If each firm does the best it can, given what it knows about the incentives facing the other, what will happen in this game? Since United can predict that American will follow its dominant strategy, United's best move is to leave its own ad spending the same. The Nash equilibrium is that American will Raise ad spending and United will leave spending the same.

29. Example 11.6. Should Michael accept Tom's offer? • Tom and Michael are subjects in an experiment. • The experimenter begins by giving $100 to Tom, who must then propose how to divide the money between himself and Michael. • He can propose any division he chooses, provided the proposed amounts are integers and he offers Michael at least one dollar. • Suppose he proposes $X for himself and $(100-X) for Michael. Michael must then say whether he accepts the proposal. • If he does, they each get the amounts proposed. • But if Michael rejects the proposal, each player gets zero, and the $100 reverts to the experimenter. • It is common knowledge that Tom and Michael will play this game only once and that each has the goal of making as much money for himself as possible. What should Tom propose?

30. Example 11.6. Should Michael accept Tom's offer? • Unlike earlier games, the timing of each player’s decision in this game is important. • The payoffs for this game are better represented in a game tree, rather than a payoff matrix.

31. Example 11.6. Should Michael accept Tom's offer? • Suppose Tom proposes $99 for himself, $1 for Michael. This is the most advantageous offer Tom can make, and at point B, Michael's best bet is to accept it. Michael's problem is that he cannot make a credible threat to refuse Tom's one-sided offer.

32. Example 11.7. Should the business owner open a distant branch? • The owner of a thriving local business wants to start up a satellite outlet in a distant city.

33. Example 11.7. Should the business owner open a distant branch? • If the outlet is managed honestly, the owner can pay the manager $1000 per week and still earn an economic profit of $1000 per week from the outlet. • The manager’s best alternative employment pays $500 per week. • The owner's concern is that she will not be able to monitor the behavior of the outlet manager, and that this person would therefore be in a position to embezzle heavily from the business. • The owner knows that if the distant outlet is managed dishonestly, the manager can earn $1500 per week, while causing the owner a financial loss of $500 per week. If the owner believes that all managers are selfish income-maximizers, will she open the new outlet?

34. Example 11.7. Should the business owner open a distant branch? First step: Construct the game tree for the distant-outlet game .

35. Example 11.7. Should the business owner open a distant branch? To predict how game will play out, work backward from end of the tree.

36. Example 11.7. Should the business owner open a distant branch? If the outlet is opened, the manager must decide at C whether to manage honestly. If his only goal is to make as much money for himself as he can, he will manage dishonestly (bottom branch at C), since that way he earns $500 more than by managing honestly (top branch at C). So if the owner opens the new office, she will end up with a financial loss of $500.

37. Example 11.7. Should the business owner open a distant branch? If instead she had chosen not to open the office (bottom branch at point B), she would have ended up with a financial return of zero. Owner gets -$500 Manager gets $1500 Open outlet And since zero is better than -$500, she will choose not to open the satellite office.

38. Example 11.7. Should the business owner open a distant branch? Even though opening the outlet and managing it honestly would be better for both the owner and manager, purely self-interested persons cannot achieve this outcome.

39. A Thought Experiment • I have just gotten home from a crowded concert and discover I have lost $1000 in cash. The cash had been in my coat pocket in a plain envelope with my name and address written on it. • Do you know anyone who you feel certain would return it to me if he or she found it?

40. Resolving Prisoner's Dilemmas and Other Commitment Problems • In games like the prisoner's dilemma, the hockey helmet game, the ultimatum bargaining game, and the satellite office game, players have trouble arriving at the outcomes they desire because they are unable to make credible commitments.

41. Resolving Prisoner's Dilemmas and Other Commitment Problems • For example, if both players in the prisoner's dilemma could somehow reach a binding agreement to remain silent, each would be assured of getting a shorter sentence. Hence the logic of the underworld code of Omerta, under which the family of anyone who provided evidence against a fellow mob member would be killed.

42. Resolving Prisoner's Dilemmas and Other Commitment Problems Likewise, the helmet rule results in a better outcome for hockey players by committing them to wear helmets in circumstances in which they would otherwise choose not to do so.

43. Example 11.8. Will the restaurateur pay the waiter extra to provide good service? The restaurateur wants his waiter to provide good service so that customers will enjoy their meals and come back in the future. If the waiter provides good service, the owner can pay him $100 per day. But if the waiter provides bad service, the most he can pay the waiter is $60 per day. The waiter is willing to provide bad service for $60 per day, and for $30 extra would be willing to provide good service. The owner's problem is that he cannot tell whether the waiter has provided good service.

44. Example 11.8. Will the restaurateur pay the waiter extra to provide good service? Each side has a dominant strategy: Restaurateur- pay $60/day; waiter- provide bad service. Outcome is lower-right cell and that is inefficient. The tip is a solution to this commitment problem.

45. Changing material incentive as a solution to commitment problem • The Mafia's code of silence, hockey helmet rules, tips for waiters -- all work by changing the material incentives facing the relevant decision makers. • But it is not always practical to changes material incentives in precisely the desired ways.

46. Example 11.9. Tipping • What if the restaurant is located in a distant city the diner doesn’t expect to visit again?

47. Example 11.9. Tipping • Unlike case of restaurant with local patrons, this waiter has no way to penalize the diner in the future if he leaves no tip. Dominant strategy for the waiter: provide bad service. Dominant strategy for diner: leave no tip. Again a worse outcome for each than if waiter had provided good service and diner had tipped.

48. Moral Sentiments as Commitment Devices • If commitment problems cannot be solved by altering the relevant material incentives, it may nonetheless be possible to solve them by altering people's psychological incentives. • For example, feelings of guilt when they cause harm to others, feelings of sympathy for the interests of their trading partners, feelings of outrage when they are treated unjustly, and so on. • These feelings may lessen the incentive to behave in opportunistic and mutually destructive ways.

49. Two Standards of Rationality • The Self-interest Standard: • A person is rational if she is efficient in pursuit of her own interests. • The self-interest model is often not descriptive. Return wallets Rescues Bone marrow donation Blood donation

50. Two Standards of Rationality • The Adaptive Rationality Standard: • A taste can be added to the self-interest model, but only upon a plausible showing that someone motivated by that taste would not be handicapped in the quest to acquire the resources needed for survival and reproduction.. Return wallets Rescues Bone marrow donation Blood donation