Game theory. Análisis Económico de la Empresa. M. En C. Eduardo Bustos Farías 1

Transcription

1 Game theory M. En C. Eduardo Bustos Farías 1

2 Oligopoly Games Game theory is a tool for studying strategic behavior, which is behavior that takes into account the expected behavior of others and the mutual recognition of interdependence. What Is a Game? All games share four features: Rules Strategies Payoffs Outcome. M. En C. Eduardo Bustos Farías 2

3 Game Theory and the Economics of Cooperation Game theory is the study of how people behave in strategic situations. Strategic decisions are those in which each person, in deciding what actions to take, must consider how others might respond to that action. M. En C. Eduardo Bustos Farías 3

4 Game Theory and the Economics of Cooperation Because the number of firms in an oligopolistic market is small, each firm must act strategically. Each firm knows that its profit depends not only on how much it produced but also on how much the other firms produce. M. En C. Eduardo Bustos Farías 4

5 Oligopoly Games The Prisoners Dilemma The prisoners dilemma game illustrates the four features of a game. The rules describe the setting of the game, the actions the players may take, and the consequences of those actions. In the prisoners dilemma game, two prisoners (Art and Bob) have been caught committing a petty crime. Each is held in a separate cell and cannot communicate with each other. M. En C. Eduardo Bustos Farías 5

6 The Prisoners Dilemma The prisoners dilemma provides insight into the difficulty in maintaining cooperation. Often people (firms) fail to cooperate with one another even when cooperation would make them better off. M. En C. Eduardo Bustos Farías 6

7 Oligopoly Games Each is told that both are suspected of committing a more serious crime. If one of them confesses, he will get a 1-year sentence for cooperating while his accomplice get a 10-year sentence for both crimes. If both confess to the more serious crime, each receives 3 years in jail for both crimes. If neither confesses, each receives a 2-year sentence for the minor crime only. M. En C. Eduardo Bustos Farías 7

8 Oligopoly Games In game theory, strategies are all the possible actions of each player. Art and Bob each have two possible actions: Confess to the larger crime Deny having committed the larger crime. Because there are two players and two actions for each player, there are four possible outcomes: Both confess Both deny Art confesses and Bob denies Bob confesses and Art denies M. En C. Eduardo Bustos Farías 8

9 Oligopoly Games Each prisoner can work out what happens to him can work out his payoff in each of the four possible outcomes. We can tabulate these outcomes in a payoff matrix. A payoff matrix is a table that shows the payoffs for every possible action by each player for every possible action by the other player. The next slide shows the payoff matrix for this prisoners dilemma game. M. En C. Eduardo Bustos Farías 9

10 The Prisoners Dilemma Bonnie s Decision Clyde s Decision Confess Remain Silent Confess Clyde gets 8 years Clyde gets 20 years Bonnie gets 8 years Bonnie goes free Remain Silent Clyde goes free Clyde gets 1 year Bonnie gets 20 years Bonnie gets 1 year M. En C. Eduardo Bustos Farías 10

11 The Prisoners Dilemma The dominant strategy is the best strategy for a player to follow regardless of the strategies pursued by other players. M. En C. Eduardo Bustos Farías 11

12 The Prisoners Dilemma Cooperation is difficult to maintain, because cooperation is not in the best interest of the individual player. M. En C. Eduardo Bustos Farías 12

13 Oligopolies as a Prisoners Dilemma High Production Iraq s Decision Low Production High Production Iran s Decision Low Production Iran gets $40 billion Iran gets $30 billion Iraq gets $40 billion Iraq gets $60 billion Iran gets $60 billion Iran gets $50 billion Iraq gets $30 billion Iraq gets $50 billion M. En C. Eduardo Bustos Farías 13

14 Oligopolies as a Prisoners Dilemma Self-interest makes it difficult for the oligopoly to maintain a cooperative outcome with low production, high prices, and monopoly profits. M. En C. Eduardo Bustos Farías 14

15 An Arms-Race Game Decision of the United States (U.S.) Arm Disarm Decision of the Soviet Union (USSR) Arm Disarm USSR at risk USSR at risk and weak U.S. at risk U.S. safe and powerful U.S. at risk and weak USSR safe and powerful USSR safe U.S. safe M. En C. Eduardo Bustos Farías 15

16 An Advertising Game Advertise Camel s Decision Don t Advertise Advertise Marlboro gets $3 billion profit Camel gets $3 billion profit Marlboro gets $5 billion profit Camel gets $2 billion profit Marlboro s Decision Don t Advertise Marlboro gets $2 billion profit Camel gets $5 billion profit Marlboro gets $4 billion Camel gets profit $4 billion profit M. En C. Eduardo Bustos Farías 16

17 A Common-Resources Game Drill Two Wells Arco s Decision Drill One Well Drill Two Wells Arco gets $4 million profit Arco gets $3 million profit Exxon s Decision Exxon gets $4 million profit Exxon gets $6 million profit Drill One Well Arco gets $6 million profit Exxon gets $3 million profit Exxon gets $5 million profit Arco gets $5 million profit M. En C. Eduardo Bustos Farías 17

18 Why People Sometimes Cooperate Firms that care about future profits will cooperate in repeated games rather than cheating in a single game to achieve a one-time gain. M. En C. Eduardo Bustos Farías 18

19 Jack and Jill s Oligopoly Game Jill s Decision Sell 40 gallons Sell 30 gallons Sell 40 gallons Jill gets $1,600 profit Jill gets $1,500 profit Jack s Decision Jack gets $1,600 profit Jack gets $2,000 profit Sell 30 gallons Jill gets $2,000 profit Jill gets $1,800 profit Jack gets $1,500 profit Jack gets $1,800 profit M. En C. Eduardo Bustos Farías 19

20 Oligopoly Games M. En C. Eduardo Bustos Farías 20

21 Oligopoly Games If a player makes a rational choice in pursuit of his own best interest, he chooses the action that is best for him, given any action taken by the other player. If both players are rational and choose their actions in this way, the outcome is an equilibrium called Nash equilibrium first proposed by John Nash. The following slides show how to find the Nash equlibrium. M. En C. Eduardo Bustos Farías 21

22 Bob s view of the world M. En C. Eduardo Bustos Farías 22

23 Bob s view of the world M. En C. Eduardo Bustos Farías 23

24 Art s view of the world M. En C. Eduardo Bustos Farías 24

25 Art s view of the world M. En C. Eduardo Bustos Farías 25

26 Equilibrium M. En C. Eduardo Bustos Farías 26

27 Oligopoly Games An Oligopoly Price-Fixing Game A game like the prisoners dilemma is played in duopoly. A duopoly is a market in which there are only two producers that compete. Duopoly captures the essence of oligopoly. Figure on the next slide describes the demand and cost situation in a natural duopoly. M. En C. Eduardo Bustos Farías 27

28 Oligopoly Games Part (a) shows each firm s cost curves. Part (b) shows the market demand curve. 28

29 Oligopoly Games This industry is a natural duopoly. Two firms can meet the market demand at the least cost. 29

30 Oligopoly Games How does this market work? What is the price and quantity produced in equilibrium? 30

31 Oligopoly Games Suppose that the two firms enter into a collusive agreement. A collusive agreement is an agreement between two (or more) firms to restrict output, raise price, and increase profits. Such agreements are illegal in the United States and are undertaken in secret. Firms in a collusive agreement operate a cartel. M. En C. Eduardo Bustos Farías 31

32 Oligopoly Games The possible strategies are: Comply Cheat Because each firm has two strategies, there are four possible outcomes: Both comply Both cheat Trick complies and Gear cheats Gear complies and Trick cheats M. En C. Eduardo Bustos Farías 32

33 Oligopoly Games The first possible outcome both comply earns the maximum economic profit, which is the same as a monopoly would earn. 33

34 Oligopoly Games To find that profit, we set marginal cost for the cartel equal to marginal revenue for the cartel. Figure shows this outcome. 34

35 Oligopoly Games The cartel s marginal cost curve is the horizontal sum of the MC curves of the two firms and the marginal revenue curve is like that of a monopoly. 35

36 Oligopoly Games The firm s maximize economic profit by producing the quantity at which MC I = MR. 36

37 Oligopoly Games Each firm agrees to produce 2,000 units and each firm shares the maximum economic profit. 37

38 Oligopoly Games When each firm produces 2,000 units, the price is greater than the firm s marginal cost, so if one firm increased output, its profit would increase. 38

39 Oligopoly Games Figure shows what happens when one firm cheats and increases its output to 3,000 units. Industry output rises to 5,000 and the price falls. 39

40 Oligopoly Games For the complier, ATC now exceeds price. For the cheat, price exceeds ATC. 40

41 Oligopoly Games For the complier incurs an economic loss. The cheat earns an increased economic profit. 41

42 Oligopoly Games Either firm could cheat, so this figure shows two of the possible outcomes. Next, let s see the effects of both firms cheating. 42

43 Oligopoly Games Figure shows the outcome if both firms cheat and increase their output to 3,000 units. 43

44 Oligopoly Games Industry output is 6,000 units, the price falls, and both firms earn zero economic profit the same as in perfect competition. 44

45 Oligopoly Games You ve now seen the four possible outcomes: If both comply, they make $2 million a week each. If both cheat, they earn zero economic profit. If Trick complies and Gear cheats, Trick incurs an economic loss of $1 million and Gear makes an economic profit of $4.5 million. If Gear complies and Trick cheats, Gear incurs an economic loss of $1 million and Trick makes an economic profit of $4.5 million. The next slide shows the payoff matrix for the duopoly game. M. En C. Eduardo Bustos Farías 45

46 Payoff Matrix M. En C. Eduardo Bustos Farías 46

47 Trick s view of the world M. En C. Eduardo Bustos Farías 47

48 Trick s view of the world M. En C. Eduardo Bustos Farías 48

49 Gear s view of the world M. En C. Eduardo Bustos Farías 49

50 Gear s view of the world M. En C. Eduardo Bustos Farías 50

51 Equilibrium M. En C. Eduardo Bustos Farías 51

52 Oligopoly Games The Nash equilibrium is where both firms cheat. The quantity and price are those of a competitive market, and the firms earn normal profit. Other Oligopoly Games Advertising and R & D games are also prisoners dilemmas. An R & D Game Procter & Gamble and Kimberley Clark play an R & D game in the market for disposable diapers. M. En C. Eduardo Bustos Farías 52

53 Oligopoly Games Here is the payoff matrix for the Pampers Versus Huggies game. M. En C. Eduardo Bustos Farías 53

54 Oligopoly Games The Disappearing Invisible Hand In all the versions of the prisoners dilemma that we ve examined, the players end up worse off than they would if they were able to cooperate. The pursuit of self-interest does not promote the social interest in these games. M. En C. Eduardo Bustos Farías 54

55 Oligopoly Games A Game of Chicken In the prisoners dilemma game, the Nash equilibrium is a dominant strategy equilibrium, by which we mean the best strategy for each player is independent of what the other player does. Not all games have such an equilibrium. One that doesn t is the game of chicken. M. En C. Eduardo Bustos Farías 55

56 Payoff Matrix M. En C. Eduardo Bustos Farías 56

57 KC s view of the world M. En C. Eduardo Bustos Farías 57

58 KC s view of the world M. En C. Eduardo Bustos Farías 58

59 P&G s view of the world M. En C. Eduardo Bustos Farías 59

60 P&G s view of the world M. En C. Eduardo Bustos Farías 60

61 Equilibrium M. En C. Eduardo Bustos Farías 61

62 Repeated Games and Sequential Games A Repeated Duopoly Game If a game is played repeatedly, it is possible for duopolists to successfully collude and earn a monopoly profit. If the players take turns and move sequentially (rather than simultaneously as in the prisoner s dilemma), many outcomes are possible. In a repeated prisoners dilemma duopoly game, additional punishment strategies enable the firms to comply and achieve a cooperative equilibrium, in which the firms make and share the monopoly profit. M. En C. Eduardo Bustos Farías 62

63 Repeated Games and Sequential Games One possible punishment strategy is a tit-for-tat strategy, in which one player cooperates this period if the other player cooperated in the previous period but cheats in the current period if the other player cheated in the previous period. A more severe punishment strategy is a trigger strategy in which a player cooperates if the other player cooperates but plays the Nash equilibrium strategy forever thereafter if the other player cheats. M. En C. Eduardo Bustos Farías 63

64 Repeated Games and Sequential Games Table 13.5 shows that a tit-for-tat strategy is sufficient to produce a cooperative equilibrium in a repeated duopoly game. Price wars might result from a tit-for-tat strategy where there is an additional complication uncertainty about changes in demand. A fall in demand might lower the price and bring forth a round of tit-for-tat punishment. M. En C. Eduardo Bustos Farías 64

65 Repeated Games and Sequential Games A Sequential Entry Game in a Contestable Market In a contestable market a market in which firms can enter and leave so easily that firms in the market face competition from potential entrants firms play a sequential entry game. M. En C. Eduardo Bustos Farías 65

66 Repeated Games and Sequential Games Figure shows the game tree for a sequential entry game in a contestable market. M. En C. Eduardo Bustos Farías 66

67 Repeated Games and Sequential Games In the first stage, Agile decides whether to set the monopoly price or the competitive price. M. En C. Eduardo Bustos Farías 67

68 Repeated Games and Sequential Games In the second stage, Wanabe decides whether to enter or stay out. M. En C. Eduardo Bustos Farías 68

69 Repeated Games and Sequential Games In the equilibrium of this entry game, Agile sets a competitive price and earns a normal profit to keep Wanabe out. A less costly strategy is limit pricing, which sets the price at the highest level that is consistent with keeping the potential entrant out. M. En C. Eduardo Bustos Farías 69