Games and Strategic Behavior

Strategic Choice in Oligopoly, Monopolistic Competition, and Everyday Life
Slide 2:Games and Strategic Behavior
Thus far, we have viewed 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.
Slide 3:Thinking Strategically
Interdependencies In making choices, people must consider the effect of their behavior on others. E.g. Imperfectly competitive firms may consider how rivals will respond to price changes or new advertising.
Slide 4:Using Game Theory toAnalyze Strategic Decisions
This chapter aims at using Game Theories to explain how economic agents interact by using strategic behaviors Basic Elements of a Game in Game Theories The players Their strategies The payoffs
Slide 5:Standard format of a Payoff Matrix
Strategy 1 Strategy 2 Payoff for Player 2 Payoff for Player 1 Player 2 The Payoff Matrix Player 1 Strategy A Strategy B Payoff for Player 1 Payoff for Player 1 Payoff for Player 1 Payoff for Player 2 Payoff for Player 2 Payoff for Player 2
Slide 6:e.g. 11.1: Should UA spend more on advertising?
Suppose that United Airlines and American Airlines are the only carriers that serve the Chicago-St. Louis market. i.e. their behavior will affect each other�s profit (payoff)
Slide 7:Example Should United Airlines spend more on advertising? Assume The airline industry is an oligopoly with similar products Thus, airlines would try to signal the unique features of their products by advertising Also, assume each airline is well informed on its rival�s strategies and payoffs
e.g. 11.1: Should UA spend more on advertising?
Slide 8:e.g.11.1: The Payoff Matrix
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same $5,500 for American $5,500 for United American�s Choices United�s Choices $2,000 for American $8,000 for United $6,000 for American $6,000 for United $8,000 for American $2,000 for United Which strategy will be adopted?
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same $5,500 for American $5,500 for United American�s Choices United�s Choices $2,000 for American $8,000 for United $6,000 for American $6,000 for United $8,000 for American $2,000 for United If AA chooses raise ad, then UA should also raise ad
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same $5,500 for American $5,500 for United American�s Choices United�s Choices $2,000 for American $8,000 for United $6,000 for American $6,000 for United $8,000 for American $2,000 for United If AA chooses same spending, then UA should raise ad
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same $5,500 for American $5,500 for United American�s Choices United�s Choices $2,000 for American $8,000 for United $6,000 for American $6,000 for United $8,000 for American $2,000 for United If UA chooses raise ad, then AA should also raise ad
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same $5,500 for American $5,500 for United American�s Choices United�s Choices $2,000 for American $8,000 for United $6,000 for American $6,000 for United $8,000 for American $2,000 for United If UA chooses same spending, then AA should raise ad
Slide 13:We can see that both airlines will spend more on ad regardless of its rival�s strategy Thus, the action �raise spending on ad� is a dominant strategy in this game.
e.g. 11.1: Using Game Theory toAnalyze Strategic Decisions
Slide 14:Dominant Strategy Is the strategy that yields a higher payoff no matter what the other players in a game choose Dominated Strategy Any other strategy available to a player who has a dominant strategy
Using Game Theory toAnalyze Strategic Decisions
Slide 15:Nash Equilibrium Any combination of strategies in which each player�s strategy is her or his best choice, given the other player�s strategies When each player has a dominant strategy, equilibrium occurs when each player follows that strategy
Slide 16:e.g. 11.1: Nash Equilibrium
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same $5,500 for American $5,500 for United American�s Choices United�s Choices $2,000 for American $8,000 for United $6,000 for American $6,000 for United $8,000 for American $2,000 for United The Nash Equilibrium in this game is that both airlines spend more money on ad
Slide 17:Nash Equilibrium There can be an equilibrium even when players do not have a dominant strategy i.e. many games have a Nash equilibrium, even though not every player has a dominant strategy.
Slide 18:e.g. 11.2: Airline with new payoff
Example Should American spend more on advertising? Assume Payoff of the previous example (e.g. 10.1) changes as shown in next slide
Slide 19:e.g. 11.2: Equilibrium When One Player Lacks a Dominant Strategy
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same American�s Choices United�s Choices If the relevant payoffs are as shown, does United have a dominant strategy? Does American?
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same American�s Choices United�s Choices American 's dominant strategy is to raise its ad spending. United, however, does not have a dominant strategy.
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same American�s Choices United�s Choices If each firm does the best it can, given what it knows about the incentives facing the other, what will happen in this game?
Raise ad spending Leave ad spending the same Raise ad spending Leave ad spending the same American�s Choices United�s Choices Since United can predict that American will follow its dominant strategy, United's best move is to leave its own ad spending the same. Nash Equi
Slide 23:The Prisoner�s Dilemma
Prisoners Dilemma A game in which each player has a dominant strategy, and when each plays it, the resulting payoffs are smaller than if each had played a dominated strategy This is a very classic example in games theories
Slide 24:e.g. 11.3: Should the prisoners confess?
Two prisoners, X and Y, are held in separate cells for a serious crime (so they cannot communicate) 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.
The Three elements in the payoff matrix: Players (2 prisoners) Strategies (confess, remain silent) Payoffs (jail sentences)
The two prisoners are not allowed to communicate with one another. If the prisoners are rational and narrowly self-interested, what will they do?
Their dominant strategy is to confess. No matter what Y does, X gets a lighter sentence by speaking out. 1. If Y confesses too, 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. In a prisoner's dilemma, the Nash equilibrium occurs when each player plays his dominant strategy.
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.
Note that if X & Y can cooperate (to remain silent), the outcome would be much better! (both get only 1 yr in jail) Do you think cooperation is possible? Or, is it possible for X & Y to commit in cooperation? Is this commitment credible?
Slide 32:The Economics of Cartels
Prisoner�s Dilemmas Confronting Imperfectly Competitive Firms Cartel A coalition of firms that agrees to restrict output for the purpose of earning an economic profit E.g. The Organization of Petroleum Exporting Countries (OPEC) Why are cartel agreements (raise profit by restricting output/ collude to form a monopoly) notoriously unstable?
Slide 33:e.g. 11.4: The Market Demandfor Soft drinks
Price $/bottle) Bottles/day Assume 2 firms (Coca Cola & Pepsi) MC = 0 Cartel is formed (and became a monopoly) & agree to split output and profits
Slide 34:e.g. 11.4: Temptation to Violate a Cartel Agreement
Price $/bottle) Bottles/day D 1.00 1,000 2,000 MR 2.00 Pepsi retaliates P = $.90/bottle Both firms split 1,100 bottles/day @ $.90 Profit = $495/day
Slide 35:e.g. 11.4: The Payoff Matrix for a Cartel Agreement
Charge $1/bottle Charge $0.90/bottle Charge $1/bottle Charge $0.90/bottle Pepsi Coca Cola $990/day for Pepsi $0 for Coca Cola $500/day for each $0 for Pepsi $990 for Coca Cola $495/day for each Is there any Nash Equilibria?
Slide 36:e.g. 11.4: Prisoner�s Dilemma under Cartel
Unless there is a way to monitor each firm and ensures that they will be obliged to the cartel agreement, it is easy to see that the dominant strategy is to betray the cartel for both firms. Thus, each firm will cut price and the cartel agreement will be breached
If the game repeats for a second round (or more rounds), we can predict that the price war will persist When will the rival firms stop cutting prices? When prices are being cut to a level close or equal to the Marginal Cost of production, firms will suffer a loss for further price cuts.
If P=MC, (let�s assume there�s no fixed cost for simplicity) firms will find this industry no longer profitable So, if firms (under an oligopoly) can strengthen and enforce their cartel agreement at the beginning, they could earn a more attractive outcome In the following, we will study a strategy that could enforce cooperation under a repeated game scenario--- the tit-for-tat strategy
Tit-for-tat and the Prisoner�s Dilemma under Repeated Games Cooperation between players will increase the payoff in a prisoner�s dilemma. There is a motive to enforce cooperation.
Tit-for-tat strategy for repeated games Tit-for-tat strategy Players cooperate on the first move, then mimic their partner�s last move on each successive move Tit-for-tat strategy requirements Two players A stable set of players Players recall other player�s moves Players have a stake in future outcomes
Slide 41:e.g. 11.5: 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.
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?
The dominant strategy for everyone is to speak more loudly, and we get a worse outcome than if everyone speaks normally.
If same party will be held on a weekly basis, then tit-for-tat strategy can be applied to restrain the conversation volume. We can predict that people will talk in a normal volume instead of yelling at each other since they have to attend the same party every week! If one person starts to yell, tit-for-tat suggests every player to mimic this move. Then, everyone will be going home with a sore throat every week Thus, cooperation will be wise under a repeated game
Slide 46:Sequential game
In previous discussion, all players are assumed to move simultaneously (although they are well informed about each players� strategies and corresponding payoffs) In the next section, we will study another type of game in which players take turns in implementing strategies i.e. sequential game
Slide 47:e.g. 11.6: Games in Which Timing Matters
Sony Playstation and Nintendo compete for the domestic video games market Both know the other is considering launching a new model If both firms launch the new model, they each make $60 million If neither of them launch, they make $50 million If Playstation launches and Nintendo does not, Playstation will earn $80 million and Nintendo earns $70 million. If Nintendo launches and Playstation does not, Nintendo earns $80 million and Playstation $70 million.
Slide 48:e.g. 11.6: The Advantage of Being Different
launch Don�t launch Playstation Nintendo launch Don�t launch $60 million/yr for Playstation $60 million/yr for Nintendo $70 million/yr for Playstation $80 million/yr for Nintendo $80 million/yr for Playstation $70 million/yr for Nintendo $50 million/yr for Playstation $50 million/yr for Nintendo If this is a simultaneous game, is there a Nash Equilibrium?
There are 2 Nash Equilibria if both firms choose their action simultaneously What would happen if Nintendo manage to choose its strategy first? (followed by Playstation�s decision in the second stage) Unlike simultaneous 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.
Slide 50:e.g. 11.6: Decision Tree
Which outcome will be the equilibrium?
Simultaneous game: 2 Nash Equilibria Sequential game: only ONE outcome is possible In a sequential game, Nintendo enjoys �first-mover advantage�: being the first mover, Nintendo can take an action that induces Playstation to follow and choose a favorable outcome for both of them
What Do You Think? Why couldn�t Playstation deter Nintendo from launching by threatening to launch in second stage, no matter what Nintendo did in its first stage? Is this threat even credible?
Slide 53:Games in Which Timing Matters
Credible Threats and Promises Credible Threat A threat to take an action that is in the threatener�s interest to carry out Credible Promise A promise to take action that is in the promiser�s interest to keep
Slide 54:e.g. 11.7: Should the business owner open a remote office?
Should a business owner open a remote office? 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?
Step 1: Construct the game tree for the distant-outlet game
Step 2: To predict how the game will play out, work backward from end of the tree.
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.
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 remote office.
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. How about cooperation? If the manager vows to be honest, would you believe her?
Slide 61:e.g. 11.8: Monopolist CompetitionWhen Location Matters
Why do we often see convenience stores located on adjacent street corners? Assume 1 mile street with 1,400 shoppers evenly distributed along the street Store A is located at the West end of the mile Question Where would you open a new store on the mile?
If you locate your store at the East end, 50% of shoppers will buy from you, while 50% of the other shoppers will buy from store A If you move a bit towards the West end, what would happen? West East Store A midpoint Note: 1400 shoppers are evenly distributed along this line B
If you locate at B, all shoppers on your right will buy from you As for the left side, again, you will split the market share with store A equally So, by moving towards the West End, you will gain more customers! West East Store A midpoint Note: 1400 shoppers are evenly distributed along this line B
Every time when you get closer to A, you will get more customers as all people from the East will buy from you and you will split the West end market with A equally So, if A do not relocate, the outcome would be: You will locate your store just next to Store A. West East Store A midpoint Note: 1400 shoppers are evenly distributed along this line B
Of course, A will retaliate and relocate to your right hand side What would you do? When will the relocation process stop? West East Store A midpoint Note: 1400 shoppers are evenly distributed along this line B
Outcome: Store A & B both locate at the midpoint, adjacent to each other. This example illustrate a classic theory in Games Theories--- the Hotelling model West East Store A midpoint Note: 1400 shoppers are evenly distributed along this line B
Slide 67:Resolving Prisoner's Dilemmas and Other Commitment Problems
In games like the prisoner's dilemma, the cartel and the remote office, players have troubles in arriving at the outcomes they desire (through cooperation) because they are unable to make credible commitments. Commitment Problem A situation in which people cannot achieve their goals because of an inability to make credible threats or promises
Slide 68:Commitment Problems
Commitment Device A way of changing incentives so as to make otherwise empty threats or promises credible e.g. Military arms control agreements/ Tips for waiters
Slide 69:e.g. 11.9: how to enhance service quality?
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, he would be willing to provide good service. The owner's problem is that he cannot tell whether the waiter has provided good service. (let�s assume customers are reluctant to complaint �) Would you expect good service in this restaurant?
Each side has a dominant strategy: Restaurateur- pay $60/day; waiter- provide bad service. Outcome is lower-right cell and that is inefficient. Thus, tipping is a solution to this commitment problem.
Slide 72:Solution to commitment problem
tipping for waiters -- it solves the commitment problem by changing the material incentives facing the relevant decision makers. But it is not always practical to change material incentives in precisely the desired ways.
Slide 73:e.g. 11.10: Tipping
What if the restaurant is located in a rural area and diners do not expect a second visit? Unlike case of restaurant with local patrons, waiters have no way to penalize diners in the future if he leaves no tip for their first visit.
Slide 74:e.g. 11.10: Tipping
Dominant strategy for the waiter: provide bad service. Dominant strategy for diner: leave no tip. Again a worse outcome for both players than if waiter had provided good service and diner had tipped.
Slide 75:Moral Sentiments as Commitment Devices
In previous example, even commitment devices (tipping) cannot solve the commitment problem 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.
Slide 76:Moral Sentiments as Commitment Devices
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 etc These feelings may lessen the incentive to behave in opportunistic and mutually destructive ways.
Slide 77:Question In a moral society, will the business owner open a remote office (as in e.g. 10.7)?
e.g. 11.11: The Strategic Role of Preferences
Slide 78:e.g. 11.11: The Remote Office Game with an Honest Manager
The value of dishonesty to the manager is $10,000
Slide 79:The Strategic Roleof Preferences
Are People Fundamentally Selfish? Do you tip at out-of town restaurants? Still, will you rescue a little boy in the street if you see something heavy is falling on him? If narrow self-interest is not the only motive in making choices, then other motives (e.g. religious belief) must be understood in order to predict and explain human behavior.
Slide 80:The Strategic Roleof Preferences
Preferences as solutions to commitment problems Concerns about fairness, guilt, humor, sympathy, etc. do influence the choices people make in strategic interactions. Although these feelings help in solving the commitment problems occasionally (e.g. the honest manager in the remote office) Still, without a robust economic model in converting these �feelings� into economic jargons, it is very difficult for economists to predict such human behaviour
End of Chapter

Games and Strategic Behavior

Games and Strategic Behavior

Presentation Transcript

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