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Chapter 9: Games and Strategic Behavior
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  1. Chapter 9: Games and Strategic Behavior

  2. Learning Objectives • Describe the basic elements of a game • Define and find an equilibrium for a game • Recognize and show the effects of dominant strategies. • Define and explain the Prisoner's Dilemma and how it applies to real-world situations • Show how games in which timing matters differ from games in which it does not. • Discuss commitment problems and explain how altering preferences can solve commitment problems

  3. Story • At a dinner party in 1997, Hollywood actor Robert DeNiro pulled singer Tony Bennett aside: “Hey, Tony - there’s a film I want you in,” DeNirosaid • Bennett heard nothing further about the project for almost a year. Then his son and financial manager, got a phone call from Warner Brothers, in which the studio offered Tony $15,000 to sing in the movie’s final scene • As Danny described the conversation, “. . . they made a fatal mistake. They told me they had already shot the film • Warner Brothers wound up paying $200,000 for Bennett’s performance

  4. Strategies and Payoffs • Actions have payoffs that depend on • The actions • When they are taken • The actions of others • Some markets are characterized by interdependence • Apply to monopolistic competition and oligopoly • An imperfectly competitive firm weigh the likely responses of rivals when deciding whether to cut prices or to increase its advertising budget • Interdependencies of this sort are the rule rather than the exception in economic and social life

  5. Using Game Theory to Analyze Strategic Decisions • A game has three basic elements • The players • Their available strategies, actions, or decisions • The payoff to each player for each possible action

  6. Etihad Airways and Emirates – Scenario 1 • Players: Etihad and Emirates are the only carriers supplying non-stop service to Casablanca, Morocco • Assumption • Each earns an economic profit of $6,000 per flight • All payoffs are known to all parties • Strategies: Increase advertising by $1,000 or not

  7. Payoff Matrix • Payoff is symmetric • Dominant strategy is raise advertising spending • Both companies are worse off

  8. Etihad Airways and Emirates – Scenario 1 • In this particular game, no matter which strategy Emirates chooses, Etihad will earn a higher economic profit by increasing its spending on advertising • Since this game is perfectly symmetric, a similar conclusion holds for Emirates • A dominant strategy is one that yields a higher payoff no matter what the other player does • A Dominated strategy is any other strategy available to a player who has a dominant strategy

  9. Equilibrium in a Game • Nash equilibrium is any combination of strategies in which each player’s strategy is her or his best choice, given the other player’s strategies • Equilibrium occurs when each player follows his dominant strategy, if it exists • Following Scenario 1: (raise spending; raise spending) is a Nash equilibrium • However, a Nash equilibrium can also occur in games with no dominant strategy • Scenario 2

  10. Etihad and Emirates– Scenario 2 Lower-Left cell is a Nash equilibrium • Same situation • Different payoffs; non-symmetric • Emirates raises spending • Etihad anticipates Emirates action; does not raise

  11. Prisoner’s Dilemma • The advertising example belongs to an important class of games referred to as prisoner’s dilemma • prisoner’s 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

  12. Prisoner's Dilemma Dominant strategy Optimal strategy • The prisoner's dilemma has a dominant strategy • The resulting payoffs are smaller than if each had stayed silent

  13. The Economics of Cartels • A cartel is a coalition of firms that agree to restrict output to increase economic profit • Restrict total output • Allocate quotas to each player • The problem confronting oligopolists who are trying to form a cartel is a classic illustration of the prisoner’s dilemma

  14. Cartel in Action • Two suppliers (Aquapure and Mountain Spring) of bottled water agree to split the market equally • Each firm draws water free of charge from a mineral spring located on its own land. Customers supply their own bottles  Marginal cost is zero • Agreement is not legally enforceable • Price is set at monopoly level • If one party charges less, he gets all of the market

  15. Bottled Water Cartel • Each party has an incentive to lower the price a little to increase its economic profits • Successive reductions result in price equal to marginal cost • Monopoly price: $1 • Each firm profit = $500 • Decrease price to 0.9 and receive profit of $990

  16. Bottled Water Cartel

  17. Repeated Prisoner's Dilemma • Two players with repeated interactions • Tit-for-tat strategy says my move in this round is whatever your move was in the last round • If you defected, I defect • Tit-for-tat strategy limits defections • Tit-for-tat is rarely observed in the market • This strategy breaks down with more than two players or potential players • Each player has to have significant stake in future outcomes

  18. Ban on TV Ads for Cigarettes • Advertising shifts demand rightward for two reasons • First, people who have never used that type of product learn about it, and some buy it • Second, people who consume a different brand of the product may switch brands • The first effect boosts sales industry-wide; the second only redistributes existing sales among brands • Although advertising produces both effects in the cigarette industry, its primary effect is brand switching

  19. Ban on TV Ads for Cigarettes • U.S. Congressional ban started 1/1/1971 • Advertising spending decreased by $60 million • Legislation moved players to optimal outcome!!

  20. Why do People Shout at Parties? • If everyone spoke at a normal volume at parties, the overall noise level would be lower, and people would hear just as well So why do people shout? • Party begins with everyone speaking at normal volume • More people arrive  conversation partners have difficulty hearing one another (its getting crowded) • The natural solution, from the point of the individual, is to simply raise one’s voice a bit • But that is also the natural solution for everyone else • No matter what others do, the individual will do better by speaking more loudly Shouting is the dominant strategy

  21. Sometimes Timing Matters • In the games discussed so far, players were assumed to choose their strategies simultaneously, and which player moved first didn’t matter • For example, in the prisoner’s dilemma, self-interested players would follow their dominant strategies even if they knew in advance what strategies their opponents had chosen • But in other situations, such as the negotiations between Warner Brothers and Tony Bennett described at the beginning of this chapter, timing is of the essence

  22. Simultaneous Decisions

  23. Sometimes Timing Matters • From the previous slide, we can see that neither company has a dominant strategy, but we can see that • In the upper-right cell, Chevrolet wouldn’t want to change (that cell is, after all, the best possible outcome for Chevrolet) and neither would Dodge (since switching to a hybrid would reduce its profit from $70 million to $60 million) • Same applies to the lower-left cell • Both these cells represent Nash equilibria • However, without being told more, we simply cannot predict where the two companies will end up

  24. Sometimes Timing Matters • For games in which timing matters, a decision tree, or game tree, is a more useful way of representing the payoffs than a traditional payoff matrix • Decision tree: a diagram that describes the possible moves in a game in sequence and lists the payoffs that correspond to each possible combination of moves • One party moves first • The second can adjust his strategy accordingly

  25. Suppose Dodge Moves First $60 million for Chevy $60 million for Dodge D Offer hybrid B Don’t offer hybrid Offer hybrid $70 million for Chevy $80 million for Dodge E A F $80 million for Chevy $70 million for Dodge Don’t offer hybrid Offer hybrid C Don’t offer hybrid $50 million for Chevy $50 million for Dodge G Dodge decides Chevrolet decides Final Outcome

  26. Sometimes Timing Matters • In thinking strategically about this game, the key for Dodge is to put itself in Chevrolet’s shoes and imagine how Chevrolet would react to the various choices it might confront • In general, it will make sense for Dodge to assume that Chevrolet will respond in a self-interested way • So when Dodge has the first move in this game, its best strategy is to offer a hybrid • Chevrolet then follows by choosing not to offer one

  27. Threats and Promises • Could Chevrolet have deterred Dodge from offering a hybrid by threatening to offer a hybrid of its own, no matter what Dodge did? • The problem with this strategy is such a threat would not have been credible • Credible threat is a threat to take an action that is in the threatener's best interest to carry out • Analyze This and Tony Bennett's compensation

  28. Threats and Promises • Just as in some games credible threats are impossible to make, in others credible promises are impossible • A credible promise is a promise to take an action that is in the promiser's interest to carry out • The owner of a thriving business wants to start up an office in a distant city • If she hires someone to manage the new office, she can afford to pay a weekly salary of $1,000 • The manager could earn $500 working elsewhere • The owner earns a weekly economic profit of $1,000 for herself

  29. The Remote Office • The owner’s concern is that she will not be able to monitor the manager’s behavior • The owner knows that by managing the remote office dishonestly, the manager can boost his take-home pay to $1,500 while causing the owner an economic loss of $500 per week. Will she open the new office? • Players: Business owner and remote office manager • Options: • Business owner can open the office or not • Manager can be honest or not

  30. Remote Office Pay-Off Honest manager Owner: $1,000 Manager: $1,000 C Open remote office Dishonest Manager Owner: -$500 Manager: $1,500 A B No remote office Managerial candidate promises honesty Owner: $0 Manager: $500 working elsewhere

  31. Monopolistic Competition and Location • First mover advantage • With Viper and Corvette, firms did better if products were different • Tic-tac-toe • If the differentiator is time or location, the last mover may have the advantage • Suppose that customers go to the nearest convenience store • Store A is located 1 mile from Freeway • Where will Store B be located?

  32. Store B's Location • A chooses its location • New business plans to enter the market • Location C minimizes customer's travel distance • Location B maximizes customers Freeway 1 mile1,200 people A B ⅓ mile 800 people ⅓ mile 800 people ⅓ mile 800 people C 1 mile1,200 people

  33. Commitment Problems • A commitment problem arises from an inability to make credible threats or promises • Example: prisoner’s dilemma • Commitment problems could be solved with a device • A commitment device changes incentives to make threats or promises credible • Tips for waiters

  34. Restaurant Service • Restaurant wants to provide superior service • Increases pay of wait-staff; monitoring problem • If wait-staff are not diligent, restaurant wasted money • Restaurant cannot insure good service by paying higher wages • Repeat customers can ensure good service by tipping • A one-time, self-interested diner will not tip

  35. The Strategic Role of Preferences • Game theory assumes that the goal of the players is to maximize their outcome • Get the highest monetary payoff, the shortest jail sentence, the best chance to be heard, etc… • Ironically, in most games, players do not attain the best outcomes • Altering psychological incentives may improve the outcome of a game

  36. Honest Manager for Remote Office Honest Manager Owner: $1,000 Manager: $1,000 An honest manager earns more than a dishonest manager C Openremote office Dishonest Manager Owner: $500 Manager: – $8,500 A B No remote office Managerial candidate promises honesty Owner: $0 Manager: works elsewhere for $500

  37. Self-Interest Evaluated • There are exceptions to outcomes based on self-interest • Tips at out-of-town restaurants • Revenge • Passing on "unfair" opportunities

  38. The Strategic Role of Preferences • Preferences are given; however: • Preferences affect choices through • Sympathy for an adversary • Generosity • Honesty • Commitment problem is reduced if preferences can be known to the other party and affect the other party • Example: Trustworthy employee

  39. Character Judgments • If character were known perfectly, businesses could avoid the costs of dishonesty, shirking, etc. • Since people are victimized, make hiring mistakes, and so on, either • Character cannot be judged perfectly OR • Character information is expensive.

  40. Caveat Emptor • The payoff of deceit • Advantage to seeming honest while being dishonest • Greater opportunities • Greater exploitation of opportunities