Oligopoly. Johan Stennek
|
|
|
- Isabel Neal
- 5 years ago
- Views:
Transcription
1 Oligopoly Johan Stennek 1
2 Oligopoly Example: Zocord Reduces cholesterol Produced by Merck & Co Patent expired in April 2003 (in Sweden) Other companies started to sell perfect copies (= containing exactly the same acive ingredient SimvastaIn) 2
3 Examples Price of Zocord in Sweden Nominal price per daily dose (SEK) 3
4 Oligopoly QuesIon How does compeiion work? How strong is it? How does that depend on the market? Compare monopoly and duopoly Given market (technology, demand) Q: How does price depend on #firms? 4
5 A duopoly model (Bertrand)
6 Duopoly Timing 1. Firms set prices simultaneously 2. Consumers decide how much to buy and from whom NB: Firms have no Ime to react! 6
7 Duopoly Technology Constant marginal cost Firms have same marginal cost Demand Market demand: Linear (example) Firms goods homogenous 7
8 Duopoly Consumer behavior All buy from cheapest firm If same price: split 8
9 Duopoly Residual demand Market demand: D(p) 9
10 Duopoly Residual demand Market demand: D(p) Competitors price 10
11 Duopoly Residual demand Market demand: D(p) Residual demand: D i (p 1,p 2 ) Competitors price 11
12 Duopoly Profits π i ( p 1, p 2 ) = ( p i c) D i ( p 1, p 2 ) where D 1 ( p 1, p 2 ) = # % % $ % % & 1 D( p 1 ) p 1 < p 2 2 D p 1 ( ) if p 1 = p 2 0 p 1 > p 2 12
13 Duopoly Game Theory Inter-dependent decisions Firm 1 s opimal price depends on firm 2 s price Firm 2 s opimal price depends on firm 1 s price How to analyze Cannot simply assume profit maximizing behavior Game theory 13
14 Duopoly Game Theory Game in normal form Q: Elements of a game in normal form? Players, Strategies, Payoffs Players Firm 1 and Firm 2 Strategies Each firm chooses a price p i (a real number) Recall: Strategy profile = A price for each player (p 1, p 2 ) Payoffs Profits Recall: Payoff funcion assigns a payoff for every possible strategy profile, π i (p 1, p 2 ) 14
15 Duopoly Game Theory Nash equilibrium A common understanding among all players of how they are all going to behave A strategy profile such that no player can increase its payoff given that all other players follow their strategies 15
16 Duopoly Game Theory Nash equilibrium in duopoly game A pair of prices (p 1, p 2 ) such that π 1 (p 1, p 2 ) π 1 (p 1, p 2 ) for all p 1 π 2 (p 1, p 2 ) π 2 (p 1, p 2 ) for all p 2 16
17 Duopoly IntuiIve Analysis Q: Will the two firms charge p m? Each would sell q m /2 Each would earn π m /2 p m q m /2 q m 17
18 What if a firm undercuts to p m ε? It would sell q m It would earn π m Conclusion Duopoly IntuiIve Analysis Small reduction in price è Massive expansion of sales p m p m not reasonable prediction q m /2 q m 18
19 Duopoly IntuiIve Analysis Q: What if both charge p = c? - q i = q*/2 - π i = 0 p=c q*/2 q* 19
20 Duopoly IntuiIve Analysis No unilateral change profitable? -Higher price q = 0, π = 0 - Lower price q > 0, p < c, π < 0 p=c q*/2 q* 20
21 Duopoly IntuiIve Analysis If both firms charge p = c No incenive to change behavior Reasonable predicion Nash equilibrium 21
22 Duopoly Two formal proofs For every possible outcome, invesigate if someone has incenive to deviate Best reply analysis 22
23 Duopoly Candidate Profitable deviation p 1 > p 2 > c who? what? 23
24 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) 24
25 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) p 1 = p 2 > c who? what? 25
26 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) p 1 = p 2 > c Firm i p i = p j ε (max p m ) 26
27 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) p 1 = p 2 > c Firm i p i = p j ε (max p m ) p 1 > p 2 = c who? what? 27
28 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) p 1 = p 2 > c Firm i p i = p j ε (max p m ) p 1 > p 2 = c Firm 2 p 2 = p 1 ε (max p m ) 28
29 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) p 1 = p 2 > c Firm i p i = p j ε (max p m ) p 1 > p 2 = c Firm 2 p 2 = p 1 ε (max p m ) p 1 = p 2 = c who? what? 29
30 Duopoly Candidate Profitable deviation p 1 > p 2 > c Firm i p i = p j ε (max p m ) p 1 = p 2 > c Firm i p i = p j ε (max p m ) p 1 > p 2 = c Firm 2 p 2 = p 1 ε (max p m ) p 1 = p 2 = c
31 Duopoly Best-reply analysis 31
32 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Set of all strategy profiles c c p m p 1 32
33 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Q: What do we mean by firm 2 s best reply funcion? c A: Profit maximizing p 2 for every possible p 1 c p m p 1 33
34 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Q: What do we mean by firm 2 s best reply funcion? c A: Profit maximizing p 2 for every possible p 1 c p m p 1 34
35 Duopoly Best-reply analysis p 2 p 2 = p 1 p m c c p m p 1 What if p 1 > p m 35
36 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c p m p 1 36
37 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c p m What if c < p 1 p m p 1 37
38 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c p m p 1 38
39 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c What if p 1 = c p m p 1 39
40 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c p m p 1 40
41 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c p m p 1 What if p 1 < c 41
42 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply c c p m p 1 42
43 Duopoly Best-reply analysis p 2 p 2 = p 1 p m Firm 2 s best reply SelecIon c c p m p 1 43
44 Duopoly p 2 Firm 1 s best reply p 2 = p 1 p m c c p m p 1 44
45 Duopoly p 2 Firm 1 s best reply p 2 = p 1 p m Firm 2 s best reply c Nash equilibrium A (p 1, p 2 ) that lies on both best reply funcions c p m p 1 45
46 What is price compeiion? Compare monopoly and duopoly
47 What is price compeiion? PredicIon More firms è Lower prices Is this predicion true? 47
48 What is price compeiion? Extreme predicion ( Bertrand paradox ) 2 firms => p = c & π = 0 Q: Reason for extreme predicion? Reduce price one cent, get all customers Always profitable to reduce price below compeitor, as long as p > c. 48
49 What is price compeiion? More ooen More firms: p > c & π > 0 Reason: Don t get all customers Examples: Product differeniaion 49
50 What is price compeiion? EsImated Lerner indexes (mark-ups) in automobiles Model Belgium France Germany Italy UK Fiat Uno Ford Escort Peugeot Mercedes Conclusion CompeIIon does not eliminate all markups Also 3 rd degree price discriminaion also with compeiion High markups in home countries 50
51 What is price compeiion? TheoreIcally robust Many other models of oligopoly give same qualitaive predicion Empirically confirmed Many empirical studies suggest that compeiion leads to lower prices 51
52 Does CompeIIon Mawer? Duopoly Monopoly Consumer surplus p m p=c Consumer surplus Profit DWL q* q m 52
53 Sources of market power 1. Few firms & Entry barriers 2. Product differeniaion: horizontal & verical 3. QuanIty compeiion/capacity constraints 4. Cost advantage 5. Uninformed customers 6. Customer switching costs 7. Price discriminaion: informaion & arbitrage 8. CartelizaIon 53
54 Economic Methodology Economic model = An imaginary economy Include key features for issues at hand Remove all complicaions (eg compeiion) Add features sequenially (eg compeiion) Pros Easy to see principles Can do experiments (eg What is the effect of compeiion) Cons Not the full picture Are conclusions true or arifacts? 54
55 Cournot Model (AlternaIve to Bertrand)
56 QuanIty CompeIIon Bertrand model Firms set prices Consumers decide quaniies (firms must deliver) Cournot model Firms chose quaniies Then price is set to clear the market Note 1: Difference mawers (contrast to monopoly) Note 2: Two different interpretaions 56
57 QuanIty CompeIIon First interpretaion Stage 1: Firms produce: q 1, q 2 Stage 2: Firms bring produce to aucion: p = P(q 1 +q 2 ) Example Fishing village Note Pricing decision is delegated But equilibrium price affected by amount produced We omit the issue why p = P(q 1 +q 2 ) 57
58 QuanIty CompeIIon Second interpretaion: Two-stage game Stage 1: Firms chose capaciies: k 1, k 2 Stage 2: Firms set prices: p 1, p 2 Note: Under some condiions p 1 = p 2 = P(k 1 +k 2 ) Then study choice of capacity (= quanity) 58
59 Duopoly Game Theory Game in normal form Q: Elements of a game in normal form? Players, Strategies, Payoffs Players Firm 1 and Firm 2 Strategies Each firm chooses a quanity q i (a real number) Recall: Strategy profile = A quanity for each player (q 1, q 2 ) Payoffs Profits: π i (q 1, q 2 ) = P(q 1 + q 2 ) q i C(q i ) Recall: Payoff funcion assigns a payoff for every possible strategy profile, π i (p 1, p 2 ) 59
60 Exogenous condiions Simplify 1: Technology Constant marginal cost Firms have same marginal cost Simplify 2: Demand Firms goods homogenous Market demand: Linear 60
61 Cournot Duopoly Technology Constant marginal costs, c Demand (linear) Individual demand: q = a p Number of consumers: m Market demand: Q = m*(a p) 61
62 Cournot Duopoly Exercise: Solve the model Steps: 1. Set up profit funcions 2. Find best-reply funcions 3. Find equilibrium quaniies 4. Find equilibrium price 62
63 Define the game Profit ( ) = P q 1 + q 2 π 1 q 1,q 2 Rewrite π 1 q 1,q 2 ( ) q 1 C q 1 ( ) = a m 1 ( q 1 + q 2 ) c ( ) ( ) q 1 Demand ( ) = m ( a p) Q p Indirect demand ( ) p = a 1 m q 1 + q 2 63
64 Derive best-reply funcions Profit ( ) = P q 1 + q 2 π 1 q 1,q 2 ( ) q 1 C q 1 ( ) Rewrite ( ) = a m 1 ( q 1 + q 2 ) c π 1 q 1,q 2 ( ) q 1 FOC ( ) π 1 q 1,q 2 = a m 1 q 1 + q 2 q 1 ( ( ) c) m 1 q 1 = 0 Solve for best reply function ( ) q 1 = m a c q 2 64
65 Derive best-reply funcions q 1 Firm 1's best-reply function q 1 = ( a c) m q 2 ( a c) m 2 q 2 65
66 Derive best-reply funcions q 1 Firm 1's best-reply function q 1 = ( a c) m q 2 ( a c) m 2 Firm 2's best-reply function q 2 = ( a c) m q 1 a c ( ) m 2 q 2 66
67 Compute equilibrium quaniies q 1 q 1 * q 2 * q 2 67
68 Compute equilibrium quaniies Equilibrium q 1 = ( a c) m q 2 q 2 = ( a c) m q 1 Find q 1 * q * 1 = ( a c) m ( a c) m q * 1 Solve for q 1 * q 1 * = a c ( ) m 3 68
69 Compute equilibrium quaniies q 1 Equilibrium q * 1 = ( a c) m 3 q 2 * = a c ( ) m 3 q 1 * q 2 * q 2 69
70 Compute equilibrium price Equilibrium price p * = a 1 m q * * ( 1 + q 2 ) p * = a 1 m ( a c) m 3 p * = a + 2 c 3 + ( a c) m 3 70
71 Compare with monopoly Question: Effect of competition on price? p * = a + 2 c 3 p m = a + c 2 Conclusion: More firms implies lower prices Answer: Duopoly price lower p * < p m a + 2 c 3 c < a < a + c 2 71
72 Compare Cournot - Bertrand Bertrand p * = c Cournot p * = a + 2 c 3 > c 72
73 Compare Cournot - Bertrand Bertrand: Cheap to steal customers Lower price a liwle Steal all consumers Cournot: Expensive to steal customers To steal a lot of consumers, a firm needs to increase its producion a lot large reducion in equilibrium price 73
74 Compare Cournot - Bertrand Market demand Residual demand Market demand Residual demand Competitors price Competitors quantity Bertrand Cournot 74
75 Compare Cournot - Bertrand Market demand Residual demand Market demand Residual demand Competitors price Competitors quantity Bertrand Cournot 75
76 Cournot Duopoly: Graphical SoluIon 76
77 Cournot Duopoly Residual Demand Market clearing price Assume firm 2 will produce q 2. How will market price vary with q 1? q 2 D q 1 77
78 Cournot Duopoly Residual Demand Market clearing price Assume firm 2 will produce q 2. How will market price vary with q 1? P(0+q 2 ) * If q 1 = 0, then p = P(0+q 2 ) 0 q 2 D q 1 78
79 Cournot Duopoly Residual Demand Market clearing price Assume firm 2 will produce q 2. How will market price vary with q 1? P(0+q 2 ) * P(q 1 +q 2 ) * If q 1 = q 1, then p = P(q 1 +q 2 ) 0 q 2 q 1 q 2 +q 1 D q 1 79
80 Cournot Duopoly Residual Demand Market clearing price Assume firm 2 will produce q 2. How will market price vary with q 1? P(0+q 2 ) * Two point on firm 1 s residual demand P(q 1 +q 2 ) * 0 q 2 q 1 q 2 +q 1 D q 1 80
81 Cournot Duopoly Residual Demand Market clearing price Assume firm 2 will produce q 2. How will market price vary with q 1? P(0+q 2 ) * D 1 is a parallel shift of D by q 2 units P(q 1 +q 2 ) * 0 q 2 q 1 q 2 +q 1 D 1 D q 1 81
82 Cournot Duopoly Best Reply Market clearing price Assume firm 2 will produce q 2. How much will firm 1 produce? D 1 D Quantity 82
83 Cournot Duopoly Best Reply Market clearing price Assume firm 2 will produce q 2. How much will firm 1 produce? P(q 2 + q* 1 ) c q* 1 D 1 D Quantity 83
84 Cournot Duopoly Best Reply Assume firm 2 will increases production. How will firm 1 react? 84
85 Cournot Duopoly Best Reply Market clearing price If Firm 2 produces more, Firm 1 produces less -Δq 1 +Δq 2 D Quantity 85
86 Cournot Duopoly Best Reply Market clearing price Note: P(q 1 + q 2 ) is reduced Hence: q 1 + q 2 is increased Hence: q 1 reduced by less than q 2 increased -Δq 1 +Δq 2 D Quantity 86
87 Cournot Duopoly Best Reply Market clearing price If q 2 = 0 Then q 1 = q m q m D Quantity 87
88 Cournot Duopoly Best Reply Market clearing price If q 2 = q c Then q 1 = 0 D 1 q c D Quantity 88
89 Cournot Duopoly Best Reply q 1 q* 1 (0) = q m Negative slope Less than -1 q m q* 1 (q c ) = 0 q c q 2 89
90 Cournot Duopoly Equilibrium q 1 q c Firm 2 s best reply 2q n q m Equilibrium: Both a doing their best, given what the other does q m < 2q n < q c q n * q 1 +q 2 =q c q n q m q c q 2 90
Noncooperative Oligopoly
Noncooperative Oligopoly Oligopoly: interaction among small number of firms Conflict of interest: Each firm maximizes its own profits, but... Firm j s actions affect firm i s profits Example: price war
ECO410H: Practice Questions 2 SOLUTIONS
ECO410H: Practice Questions SOLUTIONS 1. (a) The unique Nash equilibrium strategy profile is s = (M, M). (b) The unique Nash equilibrium strategy profile is s = (R4, C3). (c) The two Nash equilibria are
EC 202. Lecture notes 14 Oligopoly I. George Symeonidis
EC 202 Lecture notes 14 Oligopoly I George Symeonidis Oligopoly When only a small number of firms compete in the same market, each firm has some market power. Moreover, their interactions cannot be ignored.
DUOPOLY. MICROECONOMICS Principles and Analysis Frank Cowell. July 2017 Frank Cowell: Duopoly. Almost essential Monopoly
Prerequisites Almost essential Monopoly Useful, but optional Game Theory: Strategy and Equilibrium DUOPOLY MICROECONOMICS Principles and Analysis Frank Cowell 1 Overview Duopoly Background How the basic
Exercises Solutions: Oligopoly
Exercises Solutions: Oligopoly Exercise - Quantity competition 1 Take firm 1 s perspective Total revenue is R(q 1 = (4 q 1 q q 1 and, hence, marginal revenue is MR 1 (q 1 = 4 q 1 q Marginal cost is MC
Lecture 9: Basic Oligopoly Models
Lecture 9: Basic Oligopoly Models Managerial Economics November 16, 2012 Prof. Dr. Sebastian Rausch Centre for Energy Policy and Economics Department of Management, Technology and Economics ETH Zürich
Elements of Economic Analysis II Lecture XI: Oligopoly: Cournot and Bertrand Competition
Elements of Economic Analysis II Lecture XI: Oligopoly: Cournot and Bertrand Competition Kai Hao Yang /2/207 In this lecture, we will apply the concepts in game theory to study oligopoly. In short, unlike
These notes essentially correspond to chapter 13 of the text.
These notes essentially correspond to chapter 13 of the text. 1 Oligopoly The key feature of the oligopoly (and to some extent, the monopolistically competitive market) market structure is that one rm
MICROECONOMICS AND POLICY ANALYSIS - U8213 Professor Rajeev H. Dehejia Class Notes - Spring 2001
MICROECONOMICS AND POLICY ANALYSIS - U813 Professor Rajeev H. Dehejia Class Notes - Spring 001 Imperfect Competition Wednesday, March 1 st Reading: Pindyck/Rubinfeld Chapter 1 Strategic Interaction figure
ECON/MGMT 115. Industrial Organization
ECON/MGMT 115 Industrial Organization 1. Cournot Model, reprised 2. Bertrand Model of Oligopoly 3. Cournot & Bertrand First Hour Reviewing the Cournot Duopoloy Equilibria Cournot vs. competitive markets
CUR 412: Game Theory and its Applications, Lecture 9
CUR 412: Game Theory and its Applications, Lecture 9 Prof. Ronaldo CARPIO May 22, 2015 Announcements HW #3 is due next week. Ch. 6.1: Ultimatum Game This is a simple game that can model a very simplified
Answer Key. q C. Firm i s profit-maximization problem (PMP) is given by. }{{} i + γ(a q i q j c)q Firm j s profit
Homework #5 - Econ 57 (Due on /30) Answer Key. Consider a Cournot duopoly with linear inverse demand curve p(q) = a q, where q denotes aggregate output. Both firms have a common constant marginal cost
A monopoly is an industry consisting a single. A duopoly is an industry consisting of two. An oligopoly is an industry consisting of a few
27 Oligopoly Oligopoly A monopoly is an industry consisting a single firm. A duopoly is an industry consisting of two firms. An oligopoly is an industry consisting of a few firms. Particularly, l each
Microeconomics I - Seminar #9, April 17, Suggested Solution
Microeconomics I - Seminar #9, April 17, 009 - Suggested Solution Problem 1: (Bertrand competition). Total cost function of two firms selling computers is T C 1 = T C = 15q. If these two firms compete
UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A) Fall 2012
UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 01A) Fall 01 Oligopolistic markets (PR 1.-1.5) Lectures 11-1 Sep., 01 Oligopoly (preface to game theory) Another form
Econ 302 Assignment 3 Solution. a 2bQ c = 0, which is the monopolist s optimal quantity; the associated price is. P (Q) = a b
Econ 302 Assignment 3 Solution. (a) The monopolist solves: The first order condition is max Π(Q) = Q(a bq) cq. Q a Q c = 0, or equivalently, Q = a c, which is the monopolist s optimal quantity; the associated
Static Games and Cournot. Competition
Static Games and Cournot Competition Lecture 3: Static Games and Cournot Competition 1 Introduction In the majority of markets firms interact with few competitors oligopoly market Each firm has to consider
Introduction to Industrial Organization Professor: Caixia Shen Fall 2014 Lecture Note 5 Games and Strategy (Ch. 4)
Introduction to Industrial Organization Professor: Caixia Shen Fall 2014 Lecture Note 5 Games and Strategy (Ch. 4) Outline: Modeling by means of games Normal form games Dominant strategies; dominated strategies,
Math 152: Applicable Mathematics and Computing
Math 152: Applicable Mathematics and Computing May 22, 2017 May 22, 2017 1 / 19 Bertrand Duopoly: Undifferentiated Products Game (Bertrand) Firm and Firm produce identical products. Each firm simultaneously
When one firm considers changing its price or output level, it must make assumptions about the reactions of its rivals.
Chapter 3 Oligopoly Oligopoly is an industry where there are relatively few sellers. The product may be standardized (steel) or differentiated (automobiles). The firms have a high degree of interdependence.
Advanced Microeconomic Theory EC104
Advanced Microeconomic Theory EC104 Problem Set 1 1. Each of n farmers can costlessly produce as much wheat as she chooses. Suppose that the kth farmer produces W k, so that the total amount of what produced
CUR 412: Game Theory and its Applications Final Exam Ronaldo Carpio Jan. 13, 2015
CUR 41: Game Theory and its Applications Final Exam Ronaldo Carpio Jan. 13, 015 Instructions: Please write your name in English. This exam is closed-book. Total time: 10 minutes. There are 4 questions,
MICROECONOMICS II. Author: Gergely K hegyi. Supervised by Gergely K hegyi. February 2011
MICROECONOMICS II. Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics, Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department
MKTG 555: Marketing Models
MKTG 555: Marketing Models A Brief Introduction to Game Theory for Marketing February 14-21, 2017 1 Basic Definitions Game: A situation or context in which players (e.g., consumers, firms) make strategic
AS/ECON 2350 S2 N Answers to Mid term Exam July time : 1 hour. Do all 4 questions. All count equally.
AS/ECON 2350 S2 N Answers to Mid term Exam July 2017 time : 1 hour Do all 4 questions. All count equally. Q1. Monopoly is inefficient because the monopoly s owner makes high profits, and the monopoly s
Oligopoly (contd.) Chapter 27
Oligopoly (contd.) Chapter 7 February 11, 010 Oligopoly Considerations: Do firms compete on price or quantity? Do firms act sequentially (leader/followers) or simultaneously (equilibrium) Stackelberg models:
Static Games and Cournot. Competition
Static Games and Cournot Introduction In the majority of markets firms interact with few competitors oligopoly market Each firm has to consider rival s actions strategic interaction in prices, outputs,
1 Solutions to Homework 3
1 Solutions to Homework 3 1.1 163.1 (Nash equilibria of extensive games) 1. 164. (Subgames) Karl R E B H B H B H B H B H B H There are 6 proper subgames, beginning at every node where or chooses an action.
Solution Problem Set 2
ECON 282, Intro Game Theory, (Fall 2008) Christoph Luelfesmann, SFU Solution Problem Set 2 Due at the beginning of class on Tuesday, Oct. 7. Please let me know if you have problems to understand one of
Economics 101A (Lecture 21) Stefano DellaVigna
Economics 101A (Lecture 21) Stefano DellaVigna November 11, 2009 Outline 1. Oligopoly: Cournot 2. Oligopoly: Bertrand 3. Second-price Auction 4. Auctions: ebay Evidence 1 Oligopoly: Cournot Nicholson,
Answers to Microeconomics Prelim of August 24, In practice, firms often price their products by marking up a fixed percentage over (average)
Answers to Microeconomics Prelim of August 24, 2016 1. In practice, firms often price their products by marking up a fixed percentage over (average) cost. To investigate the consequences of markup pricing,
Lecture Note 3. Oligopoly
Lecture Note 3. Oligopoly 1. Competition by Quantity? Or by Price? By what do firms compete with each other? Competition by price seems more reasonable. However, the Bertrand model (by price) does not
Endogenous choice of decision variables
Endogenous choice of decision variables Attila Tasnádi MTA-BCE Lendület Strategic Interactions Research Group, Department of Mathematics, Corvinus University of Budapest June 4, 2012 Abstract In this paper
Economics 101A (Lecture 21) Stefano DellaVigna
Economics 101A (Lecture 21) Stefano DellaVigna April 14, 2015 Outline 1. Oligopoly: Cournot 2. Oligopoly: Bertrand 3. Second-price Auction 4. Auctions: ebay Evidence 1 Oligopoly: Cournot Nicholson, Ch.
Estimating Market Power in Differentiated Product Markets
Estimating Market Power in Differentiated Product Markets Metin Cakir Purdue University December 6, 2010 Metin Cakir (Purdue) Market Equilibrium Models December 6, 2010 1 / 28 Outline Outline Estimating
13.1 Infinitely Repeated Cournot Oligopoly
Chapter 13 Application: Implicit Cartels This chapter discusses many important subgame-perfect equilibrium strategies in optimal cartel, using the linear Cournot oligopoly as the stage game. For game theory
Microeconomics III. Oligopoly prefacetogametheory (Mar 11, 2012) School of Economics The Interdisciplinary Center (IDC), Herzliya
Microeconomics III Oligopoly prefacetogametheory (Mar 11, 01) School of Economics The Interdisciplinary Center (IDC), Herzliya Oligopoly is a market in which only a few firms compete with one another,
Econ 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
Mixed Motives of Simultaneous-move Games in a Mixed Duopoly. Abstract
Mixed Motives of Simultaneous-move Games in a Mixed Duopoly Kangsik Choi Graduate School of International Studies. Pusan National University Abstract This paper investigates the simultaneous-move games
Econ 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
On Forchheimer s Model of Dominant Firm Price Leadership
On Forchheimer s Model of Dominant Firm Price Leadership Attila Tasnádi Department of Mathematics, Budapest University of Economic Sciences and Public Administration, H-1093 Budapest, Fővám tér 8, Hungary
Business Strategy in Oligopoly Markets
Chapter 5 Business Strategy in Oligopoly Markets Introduction In the majority of markets firms interact with few competitors In determining strategy each firm has to consider rival s reactions strategic
Problem 3,a. ds 1 (s 2 ) ds 2 < 0. = (1+t)
Problem Set 3. Pay-off functions are given for the following continuous games, where the players simultaneously choose strategies s and s. Find the players best-response functions and graph them. Find
EconS Oligopoly - Part 3
EconS 305 - Oligopoly - Part 3 Eric Dunaway Washington State University eric.dunaway@wsu.edu December 1, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 33 December 1, 2015 1 / 49 Introduction Yesterday, we
GS/ECON 5010 Answers to Assignment 3 November 2005
GS/ECON 5010 Answers to Assignment November 005 Q1. What are the market price, and aggregate quantity sold, in long run equilibrium in a perfectly competitive market for which the demand function has the
Duopoly models Multistage games with observed actions Subgame perfect equilibrium Extensive form of a game Two-stage prisoner s dilemma
Recap Last class (September 20, 2016) Duopoly models Multistage games with observed actions Subgame perfect equilibrium Extensive form of a game Two-stage prisoner s dilemma Today (October 13, 2016) Finitely
is the best response of firm 1 to the quantity chosen by firm 2. Firm 2 s problem: Max Π 2 = q 2 (a b(q 1 + q 2 )) cq 2
Econ 37 Solution: Problem Set # Fall 00 Page Oligopoly Market demand is p a bq Q q + q.. Cournot General description of this game: Players: firm and firm. Firm and firm are identical. Firm s strategies:
Strategic Pre-Commitment
Strategic Pre-Commitment Felix Munoz-Garcia EconS 424 - Strategy and Game Theory Washington State University Strategic Commitment Limiting our own future options does not seem like a good idea. However,
Game Theory with Applications to Finance and Marketing, I
Game Theory with Applications to Finance and Marketing, I Homework 1, due in recitation on 10/18/2018. 1. Consider the following strategic game: player 1/player 2 L R U 1,1 0,0 D 0,0 3,2 Any NE can be
Econ 101A Final exam Th 15 December. Do not turn the page until instructed to.
Econ 101A Final exam Th 15 December. Do not turn the page until instructed to. 1 Econ 101A Final Exam Th 15 December. Please solve Problem 1, 2, and 3 in the first blue book and Problems 4 and 5 in the
HE+ Economics Nash Equilibrium
HE+ Economics Nash Equilibrium Nash equilibrium Nash equilibrium is a fundamental concept in game theory, the study of interdependent decision making (i.e. making decisions where your decision affects
Player 2 H T T -1,1 1, -1
1 1 Question 1 Answer 1.1 Q1.a In a two-player matrix game, the process of iterated elimination of strictly dominated strategies will always lead to a pure-strategy Nash equilibrium. Answer: False, In
Advanced Microeconomics
Advanced Microeconomics Price and quantity competition Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics 1 / 92 Part C. Games and industrial organization 1
LECTURE NOTES ON GAME THEORY. Player 2 Cooperate Defect Cooperate (10,10) (-1,11) Defect (11,-1) (0,0)
LECTURE NOTES ON GAME THEORY September 11, 01 Introduction: So far we have considered models of perfect competition and monopoly which are the two polar extreme cases of market outcome. In models of monopoly,
Introduction to Game Theory
Introduction to Game Theory Part 2. Dynamic games of complete information Chapter 1. Dynamic games of complete and perfect information Ciclo Profissional 2 o Semestre / 2011 Graduação em Ciências Econômicas
IMPERFECT COMPETITION AND TRADE POLICY
IMPERFECT COMPETITION AND TRADE POLICY Once there is imperfect competition in trade models, what happens if trade policies are introduced? A literature has grown up around this, often described as strategic
Title: The Relative-Profit-Maximization Objective of Private Firms and Endogenous Timing in a Mixed Oligopoly
Working Paper Series No. 09007(Econ) China Economics and Management Academy China Institute for Advanced Study Central University of Finance and Economics Title: The Relative-Profit-Maximization Objective
PRISONER S DILEMMA. Example from P-R p. 455; also 476-7, Price-setting (Bertrand) duopoly Demand functions
ECO 300 Fall 2005 November 22 OLIGOPOLY PART 2 PRISONER S DILEMMA Example from P-R p. 455; also 476-7, 481-2 Price-setting (Bertrand) duopoly Demand functions X = 12 2 P + P, X = 12 2 P + P 1 1 2 2 2 1
M.Phil. Game theory: Problem set II. These problems are designed for discussions in the classes of Week 8 of Michaelmas term. 1
M.Phil. Game theory: Problem set II These problems are designed for discussions in the classes of Week 8 of Michaelmas term.. Private Provision of Public Good. Consider the following public good game:
ECON/MGEC 333 Game Theory And Strategy Problem Set 9 Solutions. Levent Koçkesen January 6, 2011
Koç University Department of Economics ECON/MGEC 333 Game Theory And Strategy Problem Set Solutions Levent Koçkesen January 6, 2011 1. (a) Tit-For-Tat: The behavior of a player who adopts this strategy
Solution to Assignment 3
Solution to Assignment 3 0/03 Semester I MA6 Game Theory Tutor: Xiang Sun October 5, 0. Question 5, in Tutorial set 5;. Question, in Tutorial set 6; 3. Question, in Tutorial set 7. Solution for Question
Exercise Chapter 10
Exercise 10.8.1 Where the isoprofit curves touch the gradients of the profits of Alice and Bob point in the opposite directions. Thus, increasing one agent s profit will necessarily decrease the other
Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati
Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati Module No. # 03 Illustrations of Nash Equilibrium Lecture No. # 04
Oligopoly Games and Voting Games. Cournot s Model of Quantity Competition:
Oligopoly Games and Voting Games Cournot s Model of Quantity Competition: Supposetherearetwofirms, producing an identical good. (In his 1838 book, Cournot thought of firms filling bottles with mineral
HW Consider the following game:
HW 1 1. Consider the following game: 2. HW 2 Suppose a parent and child play the following game, first analyzed by Becker (1974). First child takes the action, A 0, that produces income for the child,
By the end of this course, and having completed the Essential readings and activities, you should:
Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 013 14. The format and structure of the examination may change in future years,
Overview Basic analysis Strategic trade policy Further topics. Overview
Robert Stehrer Version: June 19, 2013 Overview Tariffs Specific tariffs Ad valorem tariffs Non-tariff barriers Import quotas (Voluntary) Export restraints Local content requirements Subsidies Other Export
CUR 412: Game Theory and its Applications, Lecture 4
CUR 412: Game Theory and its Applications, Lecture 4 Prof. Ronaldo CARPIO March 27, 2015 Homework #1 Homework #1 will be due at the end of class today. Please check the website later today for the solutions
Chapter 11: Dynamic Games and First and Second Movers
Chapter : Dynamic Games and First and Second Movers Learning Objectives Students should learn to:. Extend the reaction function ideas developed in the Cournot duopoly model to a model of sequential behavior
Mixed strategies in PQ-duopolies
19th International Congress on Modelling and Simulation, Perth, Australia, 12 16 December 2011 http://mssanz.org.au/modsim2011 Mixed strategies in PQ-duopolies D. Cracau a, B. Franz b a Faculty of Economics
1. Players the agents ( rms, people, countries, etc.) who actively make decisions
These notes essentially correspond to chapter 13 of the text. 1 Oligopoly The key feature of the oligopoly (and to some extent, the monopolistically competitive market) market structure is that one rm
CUR 412: Game Theory and its Applications, Lecture 4
CUR 412: Game Theory and its Applications, Lecture 4 Prof. Ronaldo CARPIO March 22, 2015 Homework #1 Homework #1 will be due at the end of class today. Please check the website later today for the solutions
PAULI MURTO, ANDREY ZHUKOV
GAME THEORY SOLUTION SET 1 WINTER 018 PAULI MURTO, ANDREY ZHUKOV Introduction For suggested solution to problem 4, last year s suggested solutions by Tsz-Ning Wong were used who I think used suggested
Challenge to Hotelling s Principle of Minimum
Challenge to Hotelling s Principle of Minimum Differentiation Two conclusions 1. There is no equilibrium when sellers are too close i.e., Hotelling is wrong 2. Under a slightly modified version, get maximum
Monopoly. Johan Stennek
Monopoly Johan Stennek 1 Monopoly Q: Examples of monopoly? SJ on the route Stockholm Linköping? Pharmaceu@cal companies with patent? District hea@ng? Hemnet? 2 Monopoly Q: How do you define monopoly? Defini@on
CS364A: Algorithmic Game Theory Lecture #14: Robust Price-of-Anarchy Bounds in Smooth Games
CS364A: Algorithmic Game Theory Lecture #14: Robust Price-of-Anarchy Bounds in Smooth Games Tim Roughgarden November 6, 013 1 Canonical POA Proofs In Lecture 1 we proved that the price of anarchy (POA)
MS&E HW #1 Solutions
MS&E 341 - HW #1 Solutions 1) a) Because supply and demand are smooth, the supply curve for one competitive firm is determined by equality between marginal production costs and price. Hence, C y p y p.
Horizontal Mergers. Chapter 11: Horizontal Mergers 1
Horizontal Mergers Chapter 11: Horizontal Mergers 1 Introduction Merger mania of 1990s disappeared after 9/11/2001 But now appears to be returning Oracle/PeopleSoft AT&T/Cingular Bank of America/Fleet
Mohammad Hossein Manshaei 1394
Mohammad Hossein Manshaei manshaei@gmail.com 1394 Let s play sequentially! 1. Sequential vs Simultaneous Moves. Extensive Forms (Trees) 3. Analyzing Dynamic Games: Backward Induction 4. Moral Hazard 5.
Endogenous Price Leadership and Technological Differences
Endogenous Price Leadership and Technological Differences Maoto Yano Faculty of Economics Keio University Taashi Komatubara Graduate chool of Economics Keio University eptember 3, 2005 Abstract The present
Mixed Duopoly with Price Competition
MPRA Munich Personal RePEc Archive Mixed Duopoly with Price Competition Roy Chowdhury, Prabal Indian Statistical Institute, Delhi Center August 2009 Online at http://mpra.ub.uni-muenchen.de/9220/ MPRA
Capacity precommitment and price competition yield the Cournot outcome
Capacity precommitment and price competition yield the Cournot outcome Diego Moreno and Luis Ubeda Departamento de Economía Universidad Carlos III de Madrid This version: September 2004 Abstract We introduce
Table 10.1: Elimination and equilibrium. 1. Is there a dominant strategy for either of the two agents?
Chapter 10 Strategic Behaviour Exercise 10.1 Table 10.1 is the strategic form representation of a simultaneous move game in which strategies are actions. s b 1 s b 2 s b 3 s a 1 0, 2 3, 1 4, 3 s a 2 2,
Chapter 10: Price Competition Learning Objectives Suggested Lecture Outline: Lecture 1: Lecture 2: Suggestions for the Instructor:
Chapter 0: Price Competition Learning Objectives Students should learn to:. Understand the logic behind the ertrand model of price competition, the idea of discontinuous reaction functions, how to solve
In Class Exercises. Problem 1
In Class Exercises Problem 1 A group of n students go to a restaurant. Each person will simultaneously choose his own meal but the total bill will be shared amongst all the students. If a student chooses
I. Introduction and definitions
Economics 335 March 7, 1999 Notes 7: Noncooperative Oligopoly Models I. Introduction and definitions A. Definition A noncooperative oligopoly is a market where a small number of firms act independently,
6.207/14.15: Networks Lecture 10: Introduction to Game Theory 2
6.207/14.15: Networks Lecture 10: Introduction to Game Theory 2 Daron Acemoglu and Asu Ozdaglar MIT October 14, 2009 1 Introduction Outline Review Examples of Pure Strategy Nash Equilibria Mixed Strategies
The Timing of Endogenous Wage Setting under Bertrand Competition in a Unionized Mixed Duopoly
MPRA Munich Personal RePEc Archive The Timing of Endogenous Wage Setting under Bertrand Competition in a Unionized Mixed Duopoly Choi, Kangsik 22. January 2010 Online at http://mpra.ub.uni-muenchen.de/20205/
Problem 3 Solutions. l 3 r, 1
. Economic Applications of Game Theory Fall 00 TA: Youngjin Hwang Problem 3 Solutions. (a) There are three subgames: [A] the subgame starting from Player s decision node after Player s choice of P; [B]
Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati
Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati Module No. # 03 Illustrations of Nash Equilibrium Lecture No. # 02
Repeated Games. Econ 400. University of Notre Dame. Econ 400 (ND) Repeated Games 1 / 48
Repeated Games Econ 400 University of Notre Dame Econ 400 (ND) Repeated Games 1 / 48 Relationships and Long-Lived Institutions Business (and personal) relationships: Being caught cheating leads to punishment
Microeconomic Theory II Preliminary Examination Solutions Exam date: August 7, 2017
Microeconomic Theory II Preliminary Examination Solutions Exam date: August 7, 017 1. Sheila moves first and chooses either H or L. Bruce receives a signal, h or l, about Sheila s behavior. The distribution
UC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2016
UC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2016 More on strategic games and extensive games with perfect information Block 2 Jun 11, 2017 Auctions results Histogram of
In the Name of God. Sharif University of Technology. Graduate School of Management and Economics
In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics (for MBA students) 44111 (1393-94 1 st term) - Group 2 Dr. S. Farshad Fatemi Game Theory Game:
Problem Set 2 - SOLUTIONS
Problem Set - SOLUTONS 1. Consider the following two-player game: L R T 4, 4 1, 1 B, 3, 3 (a) What is the maxmin strategy profile? What is the value of this game? Note, the question could be solved like
FIRST PUBLIC EXAMINATION
A10282W1 FIRST PUBLIC EXAMINATION Preliminary Examination for Philosophy, Politics and Economics Preliminary Examination for Economics and Management Preliminary Examination for History and Economics SECOND
EconS Games with Incomplete Information II and Auction Theory
EconS 424 - Games with Incomplete Information II and Auction Theory Félix Muñoz-García Washington State University fmunoz@wsu.edu April 28, 2014 Félix Muñoz-García (WSU) EconS 424 - Recitation 9 April
Microeconomics I Lent Term
Microeconomics I Lent Term Matthew Chesnes The London School of Economics March 22, 2002 1 Week 1: 14 Jan - 18 Jan 1.1 Introduction to John Sutton s Lectures Last term we studied perfect competition type
VERTICAL RELATIONS AND DOWNSTREAM MARKET POWER by. Ioannis Pinopoulos 1. May, 2015 (PRELIMINARY AND INCOMPLETE) Abstract
VERTICAL RELATIONS AND DOWNSTREAM MARKET POWER by Ioannis Pinopoulos 1 May, 2015 (PRELIMINARY AND INCOMPLETE) Abstract A well-known result in oligopoly theory regarding one-tier industries is that the
PROBLEM SET 7 ANSWERS: Answers to Exercises in Jean Tirole s Theory of Industrial Organization
PROBLEM SET 7 ANSWERS: Answers to Exercises in Jean Tirole s Theory of Industrial Organization 12 December 2006. 0.1 (p. 26), 0.2 (p. 41), 1.2 (p. 67) and 1.3 (p.68) 0.1** (p. 26) In the text, it is assumed