Bounded Rationality Lecture 2. Full (Substantive, Economic) Rationality

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1 Bounded Rationality Lecture 2 Full (Substantive, Economic) Rationality Mikhail Anufriev EDG, Faculty of Business, University of Technology Sydney (UTS) European University at St.Petersburg Faculty of Economics January, 2014

2 Outline 1 Examples of Substantive Rational Choice Model General Competitive Equilibrium Nash Equilibrium Monopoly problem Competitive Industry Cournot Oligopoly 2 Summary 3 Why Bounded Rationality?

3 Rational Choice Model What is Bounded Rationality? Suggested reading: Thomas Sargent (1993), Bounded Rationality in Macroeconomics, Oxford University Press, Chapter 2.

4 Rational Choice Model What is Bounded Rationality? Suggested reading: Thomas Sargent (1993), Bounded Rationality in Macroeconomics, Oxford University Press, Chapter 2. Alternative: the Rational Choice Model. Rational Choice Models consist of two elements: Individual Rationality: Economic agents make the best decision given their perceived opportunities. Mutual Consistency of Actions: Individual actions are mutually consistent.

5 Rational Choice Model What is Bounded Rationality? Suggested reading: Thomas Sargent (1993), Bounded Rationality in Macroeconomics, Oxford University Press, Chapter 2. Alternative: the Rational Choice Model. Rational Choice Models consist of two elements: Individual Rationality: Economic agents make the best decision given their perceived opportunities. Mutual Consistency of Actions: Individual actions are mutually consistent. Rational Choice Model = optimization + equilibrium

6 General Competitive Equilibrium Example 1. General Equilibrium 1 Individual rationality Household i = 1,..., I solves x i (p, ω i, θ ji ) = arg max U i(x) p x p ω i + x R L Firm j = 1,..., J solves y j (p) = arg max y {p y y Y j } J θ ji p y j (p) j=1 2 Mutual consistency of actions By definition equilibrium is a price vector p, such that z(p ) = I i=1 (x i (p, ω i, θ ji ) ω i ) J y j (p ) = 0. j=1

7 General Competitive Equilibrium Example 1. General Equilibrium. Critical Evaluation 1 Does the general equilibrium exist? Yes, but...

8 General Competitive Equilibrium Example 1. General Equilibrium. Critical Evaluation 1 Does the general equilibrium exist? Yes, but... 2 How does economy arrive to the equilibrium? Out-of-equilibrium behavior cannot be consistent with Rational Model!

9 General Competitive Equilibrium Example 1. General Equilibrium. Critical Evaluation 1 Does the general equilibrium exist? Yes, but... 2 How does economy arrive to the equilibrium? Out-of-equilibrium behavior cannot be consistent with Rational Model! 3 How long it takes to arrive to the equilibrium?

10 General Competitive Equilibrium Example 1. General Equilibrium. Critical Evaluation 1 Does the general equilibrium exist? Yes, but... 2 How does economy arrive to the equilibrium? Out-of-equilibrium behavior cannot be consistent with Rational Model! 3 How long it takes to arrive to the equilibrium? 4 What if the equilibrium is not unique? 5...

11 General Competitive Equilibrium Two provocative quotes from Bob Solow From Arjo Klamer, Conversations with Economists, 1983, p. 146.) Suppose someone sits down where you are sitting right now and announces to me he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the battle of Austerlitz. If I do that, I am tacitly drawn in the game that he is Napoleon.

12 General Competitive Equilibrium Two provocative quotes from Bob Solow From Arjo Klamer, Conversations with Economists, 1983, p. 146.) Suppose someone sits down where you are sitting right now and announces to me he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the battle of Austerlitz. If I do that, I am tacitly drawn in the game that he is Napoleon. Now, Bob Lucas and Tom Sargent like nothing better than to get drawn in technical discussions, because then you have tacitly gone along with their fundamental assumptions; your attention is attracted away from the basic weakness of the whole story. Since I find that fundamental framework ludicrous, I respond by treating it as ludicrous - that is, by laughing at it - so as not to fall in the trap of taking it seriously and passing on matters of technique

13 General Competitive Equilibrium Two provocative quotes from Bob Solow From David Colander, The Making of an Economist, Redux, Maybe there is in human nature a deepseated perverse pleasure in adopting and defending a wholly counterintuitive doctrine that leaves the uninitiated peasant wondering what planet he or she is on.

14 Nash Equilibrium Example 2. Nash equilibrium in finite action games Prisoner s dilemma Cooperate Defect (Tchaikovsky is silent) (Tchaikovsky confesses) Cooperate (conductor is silent) ( 3, 3) ( 25, 1) Defect (conductor confesses) ( 1, 25) ( 10, 10)

15 Nash Equilibrium Example 2. Nash equilibrium in finite action games Prisoner s dilemma Cooperate Defect (Tchaikovsky is silent) (Tchaikovsky confesses) Cooperate (conductor is silent) ( 3, 3) ( 25, 1) Defect (conductor confesses) ( 1, 25) ( 10, 10) C is a dominated strategy. (D,D) is the only Nash-equilibrium.

16 Nash Equilibrium Example 2. Nash equilibrium in finite action games Prisoner s dilemma Cooperate Defect (Tchaikovsky is silent) (Tchaikovsky confesses) Cooperate (conductor is silent) ( 3, 3) ( 25, 1) Defect (conductor confesses) ( 1, 25) ( 10, 10) C is a dominated strategy. (D,D) is the only Nash-equilibrium. How would you play this game?

17 Nash Equilibrium Example 2. Nash equilibrium in finite action games Iterated Prisoner s dilemma Cooperate Defect Cooperate ( 3, 3) ( 25, 1) Defect ( 1, 25) ( 10, 10) How would you play the PD 100 times against the same opponent?

18 Nash Equilibrium Example 2. Nash equilibrium in finite action games Iterated Prisoner s dilemma Cooperate Defect Cooperate ( 3, 3) ( 25, 1) Defect ( 1, 25) ( 10, 10) How would you play the PD 100 times against the same opponent? Play (D,D) every time is the only Nash-equilibrium.

19 Nash Equilibrium Example 2. Nash equilibrium in finite action games Iterated Prisoner s dilemma Cooperate Defect Cooperate ( 3, 3) ( 25, 1) Defect ( 1, 25) ( 10, 10) How would you play the PD 100 times against the same opponent? Play (D,D) every time is the only Nash-equilibrium. Experiment: Armen Alchian (economist at UCLA) vs. John Williams (head of RAND s mathematics department), 1950.

20 Nash Equilibrium Example 2. Nash equilibrium in finite action games

21 Nash Equilibrium Example 2. Nash equilibrium in finite action games

22 Nash Equilibrium Example 2. Nash equilibrium in finite action games

23 Nash Equilibrium Example 2. Nash equilibrium in finite action games (C,C) : 60 times (D,D) : 14 times

24 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) How would you play this game?

25 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) How would you play this game? (A,A) and (B,B) are Nash-equilibria in pure strategies. Which of the two equilibria will be chosen?

26 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) How would you play this game? (A,A) and (B,B) are Nash-equilibria in pure strategies. Which of the two equilibria will be chosen? Another Nash-equilibrium (in mixed strategies): both randomize with probability 1 2.

27 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) How would you play this game? (A,A) and (B,B) are Nash-equilibria in pure strategies. Which of the two equilibria will be chosen? Another Nash-equilibrium (in mixed strategies): both randomize with probability Individual rationality : play best response...

28 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) How would you play this game? (A,A) and (B,B) are Nash-equilibria in pure strategies. Which of the two equilibria will be chosen? Another Nash-equilibrium (in mixed strategies): both randomize with probability Individual rationality : play best response... 2 Mutual consistency of actions :...on a correct action

29 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) Arguments against mixed equilibrium: Arguments for mixed equilibrium:

30 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) Arguments against mixed equilibrium: 1 Expected payoff in every Nash equilibrium is higher than in the mixed equilibrium. Arguments for mixed equilibrium:

31 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) Arguments against mixed equilibrium: 1 Expected payoff in every Nash equilibrium is higher than in the mixed equilibrium. Arguments for mixed equilibrium: 1 It is not obvious which of the two pure equilibria the opponent will play.

32 Nash Equilibrium Example 2. Nash equilibrium in finite action games Coordination game A B A (2, 2) (0, 0) B (0, 0) (2, 2) Arguments against mixed equilibrium: 1 Expected payoff in every Nash equilibrium is higher than in the mixed equilibrium. 2 If opponent plays a mixed equilibrium, then it does not matter what I play. Arguments for mixed equilibrium: 1 It is not obvious which of the two pure equilibria the opponent will play.

33 Nash Equilibrium Example 2. Nash equilibrium in finite action games Yet another Coordination game A B A (2, 2) ( 1.001, 0) B (0, 1.001) (1, 1) How would you play this game?

34 Nash Equilibrium Example 2. Nash equilibrium in finite action games Yet another Coordination game A B A (2, 2) ( 1.001, 0) B (0, 1.001) (1, 1) How would you play this game? (A,A) and (B,B) are Nash-equilibria in pure strategies, and there is an equilibrium in mixed strategies. Which of the two pure Nash equilibria will be chosen?

35 Nash Equilibrium Example 2. Nash equilibrium in finite action games Yet another Coordination game A B A (2, 2) ( 1.001, 0) B (0, 1.001) (1, 1) How would you play this game? (A,A) and (B,B) are Nash-equilibria in pure strategies, and there is an equilibrium in mixed strategies. Which of the two pure Nash equilibria will be chosen? (A,A) Pareto dominates (B,B). (B,B) risk dominates (A,A).

36 Nash Equilibrium Example 2. Nash equilibrium: Critical Evaluation 1 Does Nash equilibrium exist? Yes, but not always in pure strategies...

37 Nash Equilibrium Example 2. Nash equilibrium: Critical Evaluation 1 Does Nash equilibrium exist? Yes, but not always in pure strategies... 2 Why people would play Nash equilibrium?

38 Nash Equilibrium Example 2. Nash equilibrium: Critical Evaluation 1 Does Nash equilibrium exist? Yes, but not always in pure strategies... 2 Why people would play Nash equilibrium? 3 If they accept Nash equilibrium as a way to play, how long it takes to them to find it?

39 Nash Equilibrium Example 2. Nash equilibrium: Critical Evaluation 1 Does Nash equilibrium exist? Yes, but not always in pure strategies... 2 Why people would play Nash equilibrium? 3 If they accept Nash equilibrium as a way to play, how long it takes to them to find it? 4 What if Nash equilibrium is difficult to compute?

40 Nash Equilibrium Example 2. Nash equilibrium: Critical Evaluation 1 Does Nash equilibrium exist? Yes, but not always in pure strategies... 2 Why people would play Nash equilibrium? 3 If they accept Nash equilibrium as a way to play, how long it takes to them to find it? 4 What if Nash equilibrium is difficult to compute? 5 What if the Nash equilibrium is not unique? 6...

41 Monopoly problem Example 3. Monopoly problem Let inverse demand function P(Q) and cost function C(Q), satisfying the usual assumptions, be given. (Q is total output.) 1 Individual rationality Monopolist solves max {P (q) q C (q)}. q 2 Mutual consistency of actions No need in this case, because q = Q.

42 Monopoly problem Example 3. Monopoly problem: Critical Evaluation 1 What must monopolist know in order to solve his problem?

43 Monopoly problem Example 3. Monopoly problem: Critical Evaluation 1 What must monopolist know in order to solve his problem? 2 How can he get this knowledge? Is it costly?

44 Monopoly problem Example 3. Monopoly problem: Critical Evaluation 1 What must monopolist know in order to solve his problem? 2 How can he get this knowledge? Is it costly? 3 What would you do at the monopolist s place?

45 Competitive Industry Example 4. Competitive industry with n identical firms Let inverse demand function P(Q), cost function c(q) and number of firms n be given. (q is output of a firm, Q is total output.)

46 Competitive Industry Example 4. Competitive industry with n identical firms Let inverse demand function P(Q), cost function c(q) and number of firms n be given. (q is output of a firm, Q is total output.) 1 Individual rationality Any firm solves max {pq c(q)}, q derives p = c (q) and produces an output q = g(p) = g(p(q)). What must firm know in order to use this solution?

47 Competitive Industry Example 4. Competitive industry with n identical firms Let inverse demand function P(Q), cost function c(q) and number of firms n be given. (q is output of a firm, Q is total output.) 1 Individual rationality Any firm solves max {pq c(q)}, q derives p = c (q) and produces an output q = g(p) = g(p(q)). What must firm know in order to use this solution? Expectations about total output in the industry, e.g., Q = n q, where q is an average firm s choice.

48 Competitive Industry Example 4. Competitive industry with n identical firms Let inverse demand function P(Q), cost function c(q) and number of firms n be given. (q is output of a firm, Q is total output.) 1 Individual rationality Any firm solves max {pq c(q)}, q derives p = c (q) and produces an output q = g(p) = g(p(q)). What must firm know in order to use this solution? Expectations about total output in the industry, e.g., Q = n q, where q is an average firm s choice.

49 Competitive Industry Example 4. Competitive industry with n identical firms Let inverse demand function P(Q), cost function c(q) and number of firms n be given. (q is output of a firm, Q is total output.) 1 Individual rationality Any firm solves max {pq c(q)}, q derives p = c (q) and produces an output q = g(p) = g(p(q)). What must firm know in order to use this solution? Expectations about total output in the industry, e.g., Q = n q, where q is an average firm s choice. 2 Mutual consistency of actions In equilibrium firm s expectations are rational (self-fulfilling) since all firms are identical. Q = nq,

50 Competitive Industry Example 4. Competitive industry with n identical firms 1 Does the firm indeed have no incentives to deviate from equilibrium?

51 Competitive Industry Example 4. Competitive industry with n identical firms 1 Does the firm indeed have no incentives to deviate from equilibrium? 2 And what happens if one firm does deviate from equilibrium?

52 Competitive Industry Example 4. Competitive industry with n identical firms 1 Does the firm indeed have no incentives to deviate from equilibrium? 2 And what happens if one firm does deviate from equilibrium? 3 How shall we model out-of-equilibrium situation? (It involves specification of perception about perceptions, etc.)

53 Cournot Oligopoly Example 5. Cournot oligopoly Let inverse demand function P(Q) (Q is industry supply) and cost functions C i (q i ), satisfying the usual assumptions, be given. 1 Individual rationality Each firm solves q i = R ( Q e ( i) = R q e q e i 1 + qe i ) qe n { = arg max P(Q e q i + q i ) q i C i (q i ) }. i

54 Cournot Oligopoly Example 5. Cournot oligopoly Let inverse demand function P(Q) (Q is industry supply) and cost functions C i (q i ), satisfying the usual assumptions, be given. 1 Individual rationality Each firm solves q i = R ( Q e ( i) = R q e q e i 1 + qe i ) qe n { = arg max P(Q e q i + q i ) q i C i (q i ) }. i 2 Mutual ( consistency of actions q 1, q 2,..., ) q n is a Nash-equilibrium such that q i = R i ( Q i ) for all i.

55 Cournot Oligopoly Example 5. Cournot oligopoly: Critical Evaluation 1 Does the equilibrium exist?

56 Cournot Oligopoly Example 5. Cournot oligopoly: Critical Evaluation 1 Does the equilibrium exist? 2 What firms should know to compute the equilibrium?

57 Cournot Oligopoly Example 5. Cournot oligopoly: Critical Evaluation 1 Does the equilibrium exist? 2 What firms should know to compute the equilibrium? 3 Is the equilibrium unique?

58 Cournot Oligopoly Example 5. Cournot oligopoly: Critical Evaluation 1 Does the equilibrium exist? 2 What firms should know to compute the equilibrium? 3 Is the equilibrium unique? 4 What would you do at the duopolist s place?

59 Cournot Oligopoly Example 5. Cournot oligopoly: Adjustment model Duopoly: Let inverse demand function P(Q) (Q is industry supply) and cost functions C 1 (q 1 ) and C 2 (q 2 ), satisfying the usual assumptions, be given. time is discrete, t = 1, 2,... firms start from initial point (q 1,0, q 2,0 ) each period every firm chooses the best response to the previous period, i.e., q i,t+1 = R i (q i,t )

60 Cournot Oligopoly Example 5. Cournot oligopoly: Adjustment model Duopoly: Let inverse demand function P(Q) (Q is industry supply) and cost functions C 1 (q 1 ) and C 2 (q 2 ), satisfying the usual assumptions, be given. time is discrete, t = 1, 2,... firms start from initial point (q 1,0, q 2,0 ) each period every firm chooses the best response to the previous period, i.e., q i,t+1 = R i (q i,t ) This is the first historical example of procedural rationality (Cournot, 1838).

61 Summary Outline 1 Examples of Substantive 2 Summary Individual Rationality Mutual Consistency of Actions Bounded Rationality 3 Why Bounded Rationality?

62 Summary Individual Rationality What does Individual Rationality include? a. The rational agent knows the set of alternatives available to him/her and knows the consequences associated to each of these alternatives. b. The rational agent has a (transitive and complete) preference ordering over the set of consequences and is able to determine his/her most preferred (best) alternative. A monopolist produces, given the demand he faces, that quantity that maximizes her profits. Households make optimal savings decisions, based upon expected inflation and interest rates. Students select a Master or PhD program, based upon their skills, their preference ordering and the perceived future wage opportunities.

63 Summary Individual Rationality What does Individual Rationality mean?

64 Summary Individual Rationality What does Individual Rationality mean?

65 Summary Mutual Consistency of Actions What does the Mutual Consistency of Actions means? In an economic system, the decision of one agent forms part of constraints upon others.

66 Summary Mutual Consistency of Actions What does the Mutual Consistency of Actions means? In an economic system, the decision of one agent forms part of constraints upon others. In General Equilibrium model, when solving their individual optimization problem, individuals take prices as given. Prices then are responsible to find an equilibrium.

67 Summary Mutual Consistency of Actions What does the Mutual Consistency of Actions means? In an economic system, the decision of one agent forms part of constraints upon others. In General Equilibrium model, when solving their individual optimization problem, individuals take prices as given. Prices then are responsible to find an equilibrium. When solving their individual problem, people may need to form beliefs about others decisions, and about others beliefs. Mutual Consistency requires that the beliefs and actions of everybody are consistent (rational expectations, Nash Equilibrium). A monopolistic, oligopolistic or competitive n-firms market Saving households Master students

68 Summary Mutual Consistency of Actions What does the Mutual Consistency of Actions means? In game theory Full Rationality requires common knowledge of rationality and coordination.

69 Summary Mutual Consistency of Actions What does the Mutual Consistency of Actions means?

70 Summary Bounded Rationality What is Bounded Rationality? Models of Rational Choice: 1 assume there are no limits on informational cognitive computational capacities of individual agents. 2 ignore the details on how mutual consistency of actions is achieved.

71 Summary Bounded Rationality What is Bounded Rationality? Models of Rational Choice: 1 assume there are no limits on informational cognitive computational capacities of individual agents. 2 ignore the details on how mutual consistency of actions is achieved. Models of Bounded Rationality deal with deviations from the rational choice paradigm, where limits on individual rationality are imposed and often explicitly model out-of-equilibrium behavior.

72 Why Bounded Rationality? Outline 1 Examples of Substantive 2 Summary 3 Why Bounded Rationality? Pro Contra

73 Why Bounded Rationality? Pro Why do we need to study Bounded Rationality? Suggested reading: John Conlisk (1996): Why Bounded Rationality? Journal of Economic Literature, 34, Even small behavioral deviations may lead to significant changes in the predictions. 2 Unbounded rationality uninformative in cases of multiple equilibria and coordination problems. Models with bounded rationality may support outcomes of rational choice models or may be used as an equilibrium selection device. 3 Models with bounded rationality perform better in explaining certain phenomena. Empirical and experimental evidence (e.g. financial market and macro-observations)

74 Why Bounded Rationality? Contra In defense of full rationality Drawbacks of Bounded Rationality: 1 The as if defense: people do not possess the information gathering and processing abilities to make rational decisions, but they act as if they do: 1 People learn to behave rationally. 2 Boundedly rational behavior is driven out by evolutionary pressure or arbitrage opportunities.

75 Why Bounded Rationality? Contra In defense of full rationality Drawbacks of Bounded Rationality: 1 The as if defense: people do not possess the information gathering and processing abilities to make rational decisions, but they act as if they do: 1 People learn to behave rationally. 2 Boundedly rational behavior is driven out by evolutionary pressure or arbitrage opportunities. 2 Assumption of rational choice disciplines economic modelling, whereas there is a wilderness of bounded rationality (with typically an ad hoc nature)

76 Why Bounded Rationality? Contra Important drawback of Bounded Rationality The Wilderness of Bounded Rationality: There are infinitely many ways to be boundedly rational and only one way to be rational. In other words: the rational choice model disciplines us in our modelling of economic phenomena.

77 Why Bounded Rationality? Contra Important drawback of Bounded Rationality The Wilderness of Bounded Rationality: There are infinitely many ways to be boundedly rational and only one way to be rational. In other words: the rational choice model disciplines us in our modelling of economic phenomena. All happy families are alike; every unhappy family is unhappy in its own way. Leo Tolstoy, Anna Karenina.

78 Why Bounded Rationality? Contra Important drawback of Bounded Rationality The Wilderness of Bounded Rationality: There are infinitely many ways to be boundedly rational and only one way to be rational. In other words: the rational choice model disciplines us in our modelling of economic phenomena. All happy families are alike; every unhappy family is unhappy in its own way. Leo Tolstoy, Anna Karenina. Bounded Rationality / Behavioral Economics is a very broad field with applications in all parts of economic theory.

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