Lecture 6: Network Effects and Externalities Outline Outline Three

II-6. II-6. Externalities Outline Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

(Part II: Security of Economics) Positive effects Positive effects Lecture 6: Network effects and Negative effects Introduction Negative effects externalities Positive network effects and self-fulﬁlling expectations

Dusko Pavlovic Negative network effects and minority game

Spring 2013

II-6. II-6. Outline Externalities Three witches Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects Introduction Negative effects Negative effects

Positive network effects and self-fulﬁlling expectations

Negative network effects and minority game

II-6. II-6. The Tragedy of Macbeth Externalities The Tragedy of Macbeth Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects Three witches’ prophecy Negative effects Self-fulﬁlling prophecy Negative effects

First Witch: All hail, Macbeth! Hail to thee, Thane of 1. Macbeth is just a little spooked that the witches knew Glamis! that he was Thane of Glamis. Second Witch: All hail, Macbeth, hail to thee, Thane of Cawdor! Third Witch: All hail, Macbeth, thou shalt be King hereafter! II-6. II-6. The Tragedy of Macbeth Externalities The Tragedy of Macbeth Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects Self-fulﬁlling prophecy Negative effects Self-fulﬁlling prophecy Negative effects

1. Macbeth is just a little spooked that the witches knew 1. Macbeth is just a little spooked that the witches knew that he was Thane of Glamis. that he was Thane of Glamis. 2. Macbeth gets promoted into Thane of Cawdor by the 2. Macbeth gets promoted into Thane of Cawdor by the King — and recognizes the prophecy. King — and recognizes the prophecy. 3. Macbeth kills the King — and realizes the prophecy.

II-6. II-6. How does future forecasting work? Externalities Is lying sometimes a rational strategy? Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects

Negative effects Negative effects

Why do we believe in stars at 30000 light years away? Is lying effective? If not, why do we lie?

II-6. II-6. Why do we advertise? Externalities Outline Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction Introduction Positive effects Positive effects

Demand Negative effects Externalities Positive network effects and self-fulﬁlling expectations Adoption equilibrium Self-fulﬁlling Economy of demand and intrinsic values Negative effects

Economy with externalities

Adoption equilibrium

Self-fulﬁlling

If the market is efﬁcient, and computes the right prices, Negative network effects and minority game why is it rational to invest in advertising? II-6. II-6. Demand and valuation Externalities Demand and valuation are inverses Externalities Dusko Pavlovic Dusko Pavlovic

Market computes the demand for a product Introduction Market computes the demand for a product Introduction

Positive effects Positive effects Demand ∈ , Demand demand: q(y)=x —thequantityrequiredatthepricey Externalities demand: q(r(x)) = x [0 1] —fractionofconsumers Externalities

Adoption equilibrium Adoption equilibrium valuation: r(x)=y —thereservepriceforx consumers Self-fulﬁlling valuation: r(q(y)) = y ∈ [0, ∞] —valuederivedfromuse Self-fulﬁlling

Negative effects Negative effects

II-6. II-6. Intuitions Externalities Intuitions Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

demand: consumers’ names are x ∈ [0, 1] Positive effects demand: consumers’ names are x ∈ [0, 1] Positive effects Demand Demand ! ordered by their valuations for the good Γ Externalities ! ordered by their valuations for the good Γ Externalities ! Adoption equilibrium ! Adoption equilibrium if x purchases Γ,then Self-fulﬁlling if x purchases Γ,then Self-fulﬁlling ! all x # ∈ [0, x] purchase Γ, Negative effects ! all x # ∈ [0, x] purchase Γ, Negative effects ! because r(x #) ≥ r(x),and ! because r(x #) ≥ r(x),and valuation: prices are y ∈ [0, ∞] ! ordered by the demand for Γ ! if y > y # then ! q(y) < q(y #),and ! all x ∈ [0, q(y #)] will buy Γ ! for r(x) ∈ [y #, 1]

II-6. II-6. Equilibrium of demand and supply Externalities Equilibrium of demand and supply Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction ! ∗ ! ∗ Let p = y be the ﬁxed (average) production cost. Positive effects Let p = y be the ﬁxed (average) production cost. Positive effects

Demand Demand

Externalities Externalities ∗ ∗ ! The products will be priced at y > y . Adoption equilibrium ! The products will be priced at y > y . Adoption equilibrium Self-fulﬁlling Self-fulﬁlling

Negative effects Negative effects ! The buyers x < x∗ = q(y∗) will purchase Γ at ! The buyers x < x∗ = q(y∗) will purchase Γ at

! the prices y > y∗ = r(x∗). ! the prices y > y∗ = r(x∗).

! The market will demand x∗ = q(y∗) of Γ. ! The market will demand x∗ = q(y∗) of Γ.

! &x∗, y∗' is the demand-supply equilibrium ! where y ∗ = r(x ∗) II-6. II-6. Social beneﬁt at the equilibrium Externalities Intrinsic values and externalities Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction ∗ x Positive effects Positive effects ∗ ∗ ∗ SB(x )= r(x)dx − x r(x ) Demand Demand !0 Externalities Externalities Adoption equilibrium Adoption equilibrium Self-fulﬁlling Intrinsic values of goods are expressed through their Self-fulﬁlling x∗ is the difference of the total utility r x dx and the 0 ( ) Negative effects market prices and their production costs. Negative effects production cost x∗p = x∗r(x∗),i.e.theuppertrianglein" Externalities are the values of goods taken by those who are neither producers nor consumers of these goods.

II-6. II-6. Examples of externalities Externalities Valuations with externalities Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Market adoption influences the valuation Introduction Positive effects Positive effects ! Demand Demand Positive: public health, security, education Externalities Externalities ! freeware, creative commons Adoption equilibrium Adoption equilibrium Self-fulfilling v(x, z)=r(x) · f (z) Self-fulfilling ! social adoption of shared applications Negative effects Negative effects where Negative: ! pollution, environmental change ! exploitation of resources (e.g. fishing) ! r(x) is the intrinsic valuation ! systemic risk (e.g. in banking) ! x’s reserve price if market fully adopts Γ ! congestion ! price increase due to demand ! f (z) is the network effect ! price change if z-part of the market adopts Γ

II-6. II-6. Valuations with positive externalities Externalities Network adoption equilibrium Externalities Dusko Pavlovic Dusko Pavlovic ! Let p∗ be the ﬁxed (average) production cost. Introduction Introduction

Positive effects Positive effects ! r :[0, 1] → [0, 1] is monotone decreasing function Demand Demand Externalities Externalities ! Adoption equilibrium Adoption equilibrium e.g. r(x)=1 − x Self-fulﬁlling Self-fulﬁlling ! ∗ r(0)=1: Γ is not valued at ∞ by anyone Negative effects Negative effects ! r(1)=0: Γ has no value for some consumers

! f :[0, 1] → [0, 1] is monotone increasing function

! e.g. f (z)=z ! f (0)=0: Γ has no value if no adoption ! f (1)=1: Γ has full value with full adoption

∗[0, 1] represents the price interval [0, ∞]. II-6. II-6. Network adoption equilibrium Externalities Network adoption equilibrium Externalities Dusko Pavlovic Dusko Pavlovic ! Let p∗ be the ﬁxed (average) production cost. ! Let p∗ be the ﬁxed (average) production cost. Introduction Introduction

Positive effects Positive effects ! ! Suppose that x knows that Demand Suppose that x knows that Demand Externalities Externalities

! ∗ Adoption equilibrium ! ∗ Adoption equilibrium z -part of the market has adopted Γ Self-fulﬁlling z -part of the market has adopted Γ Self-fulﬁlling

Negative effects * Negative effects ! for all x # holds x # ∈ [0, z∗] ⇐⇒ x # has bought Γ

II-6. II-6. Network adoption equilibrium Externalities Network adoption equilibrium Externalities Dusko Pavlovic Dusko Pavlovic ! Let p∗ be the ﬁxed (average) production cost. ! Let p∗ be the ﬁxed (average) production cost. Introduction Introduction

Positive effects Positive effects ! ! Suppose that x knows that Demand Suppose that x knows that Demand Externalities Externalities

! ∗ Adoption equilibrium ! ∗ Adoption equilibrium z -part of the market has adopted Γ Self-fulﬁlling z -part of the market has adopted Γ Self-fulﬁlling

* Negative effects * Negative effects ! for all x # holds x # ∈ [0, z∗] ⇐⇒ x # has bought Γ ! for all x # holds x # ∈ [0, z∗] ⇐⇒ x # has bought Γ * * ! for all x # holds x # ∈ [0, z∗] ⇐⇒ r(x #)f (z∗) ≥ p∗ ! for all x # holds x # ∈ [0, z∗] ⇐⇒ r(x #)f (z∗) ≥ p∗ ⇓ ! r(x)f (z∗) ≥ p∗ ⇐⇒ x ∈ [0, z∗]

Positive effects Positive effects ! ! Suppose that x knows that Demand Suppose that x knows that Demand Externalities Externalities

! ∗ Adoption equilibrium ! ∗ Adoption equilibrium z -part of the market has adopted Γ Self-fulﬁlling z -part of the market has adopted Γ Self-fulﬁlling

! &z∗, p∗' is the network adoption equilibrium ! where p∗ = r(z∗)f (z∗) II-6. II-6. Calculating equilibria Externalities Dynamics of market adoption Externalities Dusko Pavlovic Dusko Pavlovic

Given # ∗ Introduction ! z ∈ [0, z ): v(z) < p causes z / 0 Introduction ∗ ! fixed production price p Positive effects Positive effects ! # ∗ Demand z = z : v(z)=p makes z stable Demand ! reserved price function r(z)=1 − z Externalities Externalities Adoption equilibrium Adoption equilibrium ! # ## ∗ ## Self-fulfilling z ∈ (z , z ): v(z) > p causes z 0 z Self-fulfilling ! network effect f (z)=z Negative effects Negative effects ## ∗ ! valuation v(z)=z(1 − z)=z − z2 ! z = z : v(z)=p makes z stable

the equilibria &zˆ, p∗' satisfy zˆ − zˆ2 = p∗. ! z ∈ (z##, 1]: v(z) < p∗ causes z / z##

II-6. II-6. Tipping point Externalities Tipping point Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects Demand The Silicon Valley Imperative (Brian Arthur) Demand The Secret of Network Startups Externalities Externalities

Adoption equilibrium Adoption equilibrium # Self-fulﬁlling Self-fulﬁlling The unstable equilibrium z is a tipping point: ! # Negative effects Push down z : Negative effects ! lower the price p∗ (free trials . . . ) ! If the adoption is not pushed to z#,thedemandwill ! widen the parabola v(z) by speeding up f (z) drop to 0.

! If the adoption is pushed past z#,thedemandwill grow to z”.

II-6. II-6. Tipping point Externalities Self-fulﬁlling expectation equilibrium Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction ! Let p∗ be the ﬁxed (average) production cost. Positive effects Positive effects The Silicon Valley Imperative (Brian Arthur) Demand Demand Externalities Externalities

Adoption equilibrium Adoption equilibrium

Self-fulﬁlling Self-fulﬁlling ! # Push down z : Negative effects Negative effects ! lower the price p∗ (free trials . . . ) ! widen the parabola v(z) by speeding up f (z)

⇓

! The adoption attractor z” will go up. II-6. II-6. Self-fulﬁlling expectation equilibrium Externalities Self-fulﬁlling expectation equilibrium Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction ! Let p∗ be the ﬁxed (average) production cost. ! Let p∗ be the ﬁxed (average) production cost. Positive effects Positive effects

II-6. II-6. Self-fulﬁlling expectation equilibrium Externalities Self-fulﬁlling expectation equilibrium Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction ! Let p∗ be the ﬁxed (average) production cost. ! Let p∗ be the ﬁxed (average) production cost. Positive effects Positive effects

Demand Demand ! Externalities ! Externalities Suppose that x believes that z-part of the market has Adoption equilibrium Suppose that x believes that z-part of the market has Adoption equilibrium adopted Γ (which may not be true). Self-fulﬁlling adopted Γ (which may not be true). Self-fulﬁlling Negative effects Negative effects ! x purchases Γ ⇐⇒ r(x)f (z) ≥ p∗ ! x purchases Γ ⇐⇒ r(x)f (z) ≥ p∗ * * ∗ ∗ ! ⇐⇒ ≤ −1 p ! ⇐⇒ ≤ −1 p x purchases Γ x r f (z) x purchases Γ x r f (z) # $ # $ ! The true market adoption (depending on the belief z)is

p∗ g(z)=q %f (z)&

because r −1 = q.

II-6. II-6. Example of adoption function Externalities Finding self-fulﬁlling equilibrium Externalities Dusko Pavlovic Dusko Pavlovic Given ! g(z)=z ≤ z ∈ [0, z#): v(z) < p∗ causes z / 0 Introduction Introduction ! ∗ ! # ∗ ﬁxed production price p Positive effects g(z)='z = z : v(z)=p 'makes z stable' Positive effects

Demand Demand ! −1 reserved price r(z)=1 − z,demandq(z)=r (z)=1 − z Externalities ! g(z)='z ≥ z ∈ (z#,'z##): v(z) > p∗'causes z 0 z## Externalities Adoption equilibrium Adoption equilibrium ! network effect f (z)=z Self-fulﬁlling Self-fulﬁlling ! g(z)='z = z##: v(z)=p∗ 'makes z stable' Negative effects Negative effects ! ' ## ' ∗ ' ## 0ifz ≤ p∗ g(z)=z ≤ z ∈ (z , 1]: v(z) < p causes z / z the true adoption is z = g(z)= ∗ 1 − p otherwise ' ' '  z '  

for g(z) as in the example II-6. II-6. Finding self-fulﬁlling equilibrium Externalities Self-fulﬁlling equilibrium when f (0) > 0 Externalities Dusko Pavlovic Dusko Pavlovic ! g(z)=z ≤ z ∈ [0, z#): v(z) < p∗ causes z / 0 Introduction Introduction ! # ∗ g(z)='z = z : v(z)=p 'makes z stable' Positive effects Positive effects

Demand Demand ! g(z)='z ≥ z ∈ (z#,'z##): v(z) > p∗'causes z 0 z## Externalities Externalities Adoption equilibrium Adoption equilibrium

Self-fulﬁlling Self-fulﬁlling ! g(z)='z = z##: v(z)=p∗ 'makes z stable' Negative effects Negative effects ! g(z)='z ≤ z ∈ (z##,'1]: v(z) < p∗ causes' z / z##

' ' '

for general g(z)

∗ II-6. II-6. Self-fulﬁlling equilibrium when f (0) > p Externalities Summary Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction Why do we lie? Positive effects Positive effects

Demand Demand

Externalities Externalities # Adoption equilibrium ! If you convince > z people that you are King, Adoption equilibrium Self-fulﬁlling Self-fulﬁlling ! Negative effects then they will help you to sujugate z” people. Negative effects

II-6. II-6. Outline Externalities El Farol Bar, Santa Fe NM Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects Introduction Negative effects Negative effects

Positive network effects and self-fulﬁlling expectations

Negative network effects and minority game II-6. II-6. El Farol Problem: Minority Game Externalities Minority Game Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects

Negative effects Negative effects ! capacity: 60 places ! players: i = 1, 2,...,100

! ! attraction: music nights moves: Ai = {Y , N},foralli

! customers: 100 music fans ! payoffs: ! #visitors≤ 60 =⇒ pleasant ! #visitors> 60 =⇒ unpleasant 1if#{k|ak = ai } ≤ 60 ui (a)= −1if#{k|a = a } > 60 ! goal of the game: visit El Farol when # visitors ≤ 60  k i  

II-6. II-6. Minority Game Externalities Minority Game Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects

Negative effects Negative effects Negative feedback

Exercise ! The members of the majority have a joint incentive to switch. Analyze Nash equilibria in this game. ! "No one goes to El Farol. It’s too busy."

! The Nash equilibria are unstable.

II-6. II-6. Recall: Network effects Externalities Negative network effects Externalities Dusko Pavlovic Dusko Pavlovic

Introduction Introduction

Positive effects Positive effects ! ∗ Let p be the ﬁxed (average) production cost. Negative effects Negative effects

! Suppose that x believes that z-part of the market has Given adopted Γ (which may not be true). ! ﬁxed production price p∗ ! The true market adoption (depending on the belief z)is ! reserved price r(z)=1 − z,demandq(z)=r −1(z)=1 − z p∗ g(z)=q z if z ≤ .6 %f (z)& ! network effect f (z)= 1 − z if z >.6  because r −1 = q.   0ifz ≤ p∗  p∗ the true adoption is z = g(z)= 1 − p∗ < z ≤ .6  z  ∗ 1 − p .6 < z '  1−z   II-6. Dynamics of El Farol Bar Externalities Dusko Pavlovic

Introduction

Positive effects

Negative effects

ongoing research