Topics in Contract Theory Lecture 1
|
|
- Caroline Richards
- 5 years ago
- Views:
Transcription
1 Leonardo Felli 7 January, 2002 Topics in Contract Theory Lecture 1 Contract Theory has become only recently a subfield of Economics. As the name suggest the main object of the analysis is a contract. Therefore the first natural question that needs to be answered is: What is a contract? 1
2 Topics in Contract Theory 2 Definition: A contract is the ruling of an economic transaction: the description of the performance that the contracting parties agree to complete at a (possibly future) date. Example: a contract for the purchase of a specific item, say a meal. It specifies: the restaurant s performance (number of courses, quality of food, cooking details, etc... ), the customer s performance (payment in full upon completion). Contracts involve not only the contracting parties, but also outsiders (enforcing agency: a court).
3 Topics in Contract Theory 3 We distinguish between implicit and explicit contracts. A contract is implicit or self-enforcing whenever the environment in which the contracting parties operate corresponds to an extensive form of a game whose (unique) subgame perfect Nash equilibrium exactly corresponds to the outcome the parties would like to implement. If you believe in Subgame Perfect equilibrium then there is no need for explicit communication. In the given environment two rational individuals will behave in the way required.
4 Topics in Contract Theory 4 If the outcome the parties would like to implement is not the subgame perfect Nash equilibrium of the environment in which they operate the parties might want to modify this environment. This is accomplished through and explicit contract. An explicit contract is a commitment device which requires: an explicit agreement between the parties, the intervention of a third party: a court. The role of the court is to force the parties to behave in a way that differs from the one that would arise in the absence of any agreement.
5 Topics in Contract Theory 5 An explicit contract therefore specifies a new extensive form corresponding to a new game for the parties. The usual way for the court to guarantee that the parties operate in this new environment is by modifying the parties payoffs, when necessary. By agreeing to bring in a court in the game the parties commit to a game that differs from the initial one they were in.
6 Topics in Contract Theory 6 To see how the presence of a court may work consider the following example: (Kreps, 1984) A buyer B and a seller S wish to trade an indivisible item at date 1. Preferences: buyer s valuation: v, seller s delivery cost: c. Let v > c trade is socially efficient.
7 Topics in Contract Theory 7 Let p be a reasonable price level (we abstract for the moment from bargaining) such that: v > p > c. B s and S s situation may be described by the following normal form: deliver not deliver pay p v p, p c p, p not pay p v, c 0, 0 The unique Nash equilibrium (dominant solvable) is: (B does not pay, S does not deliver).
8 Topics in Contract Theory 8 The situation does not change if any of the following two extensive forms are played: B pay p not pay p S S deliver not deliver not deliver deliver (v p, p c) ( p, p) (v, c) (0, 0) The unique SPE is: {B does not pay, S does not deliver at both nodes}.
9 Topics in Contract Theory 9 or deliver B B S not deliver pay p not pay p not pay p pay p (p c, v p) ( c, v) (p, p) (0, 0) The unique SPE is: {S does not deliver, B does not pay at both nodes}.
10 Topics in Contract Theory 10 Solution: to this inefficiency is an explicit contract enforced by a court that specifies (for example): the payment p that B is supposed to make contingent on S delivering the item, the punishment (implicit in the legal system) F B > p imposed by the court on B in the event that S delivers and B does not pay, the punishment (implicit in the legal system) F S > c imposed by the court on S in the event that B pays but S does not deliver.
11 Topics in Contract Theory 11 In this case the normal form describing the contracting parties problem once the contract is in place is: deliver not deliver pay p v p, p c F S p, p F S not pay p v F B, F B c 0, 0 The unique Nash equilibrium is now: (B pays p, S delivers). Notice that the particular contract considered does not require any inefficiency off-the-equilibrium-path: it is renegotiation proof. The latter property does not always hold.
12 Topics in Contract Theory 12 This example clearly shows the need for an enforcement mechanism. This mechanism may be due to: the parties being involved in a repeated relationship relationship/implicit contracting, (multiplicity might be a problem). the presence of a legal system that through a court enforces the parties agreement explicit contracting). Notice that according to this interpretation the court is essentially a commitment device available to the parties that can be used when the parties agree to call it in. An alternative interpretation is that the court itself is one of the players of the game.
13 Topics in Contract Theory 13 It should therefore be endowed with a payoff function and an action space and should be explicitly considered in the analysis of the contractual situation (come back to it). It should be mentioned that using this line of argument one could obtain a rather extreme interpretation of a contract (a law) (Mailath, Morris and Postlewaite 2000). The view is that enforcement is the only relevant activity, a contract (a law) is at best cheap talk that allows the parties to coordinate on a particular equilibrium of the game. No new equilibrium is introduced by the parties agreeing on a contract or by the parliament passing a law.
14 Topics in Contract Theory 14 From now on we will assume that the two (or more) parties involved in the contractual relationship operate in a market economy with a well functioning legal system. Whatever contract the parties agree to it will be enforced by the court. The penalties for breaching the contract will be assumed to be sufficiently severe that no contracting party will ever consider the possibility of not honoring the contract. We will abstract from these penalties and leave the court in the background.
15 Topics in Contract Theory 15 Once we have established what a contract is and how it works the next natural question is: What could parties achieve in an economic environment in which they can costlessly negotiate a contractual agreement? The answer to this question is in an economic principle known as the Coase Theorem. Coase Theorem: (Coase 1960) In an economy where ownership rights are well defined and transacting is costless gains from trade will be exploited (a contract will be agreed upon) and efficiency achieved whatever the distribution of entitlements. That is rational agents write contracts that are individually rational and Pareto efficient.
16 Topics in Contract Theory 16 A contract is individually rational if each contracting party is not worse off by deciding to sign the contract then by deciding not to do it. This is the reflection of an other basic principle of a well functioning legal system known as: freedom of contract. This is equivalent to assume that the action space of the contracting parties always contains the option not to sign the contract. A contract is Pareto efficient if there does not exists an other feasible contract that makes at least one of the contracting party strictly better off without making any other contracting party worse off.
17 Topics in Contract Theory 17 To illustrate the Coase Theorem we consider the following simple model of a production externality. Consider two parties, labelled A and B. Party A generates revenue R A (e A ) (strictly concave) by choosing the input e A at a linear cost c e A (c > 0). A s payoff function is then: Π A (e A ) = R A (e A ) c e A Party B generate revenue R B (e B ) (strictly concave) by choosing the input e B at the linear cost c e B (c > 0). Party B also suffers from an externality γ e A (x > 0) imposed by A on B.
18 Topics in Contract Theory 18 B s payoff function is then: Π B (e B ) γ e A where Π B (e B ) = R B (e B ) c e B. Assume first that the parties choose the amounts of input e A and e B simultaneously and independently without any prior agreement. Party A s problem: max e A Π A (e A ) Party B s problem: max e B Π B (e B ) γ e A
19 Topics in Contract Theory 19 In equilibrium the amount of inputs chosen (ê A, ê B ) is such that: R A(ê A ) = c R B(ê B ) = c Consider now the social efficient amounts of input e A and e B. These solve the problem: max e A,e B Π A (e A ) + Π B (e B ) γ e A In other words (e A, e B ) are such that: R A(e A) = c + γ R B(e B) = c
20 Topics in Contract Theory 20 Comparing (ê A, ê B ) and (e A, e B ) we obtain using concavity of R A ( ): e B = ê B, e A < ê A In other words: Π A (e A)+Π B (e B) γ e A [Π A (ê A ) + Π B (ê B ) γ ê A ] = = [Π A (e A) Π A (ê A )] + γ (ê A e A) > 0 The joint surplus is reduced by the inefficiency generated by the externality. Assume now that the two contracting parties have the opportunity to get together and agree on a contract before the amounts of input are chosen.
21 Topics in Contract Theory 21 There exists strictly positive gains from trade. A reduction in the amount of input e A from ê A to e A will generate: a decrease in the net revenues from A s technology: Π A (e A) < Π A (ê A ) reduction in the negative externality γ e A < γ ê A The former effect is more than compensated by the latter one. This may create room for negotiation.
22 Topics in Contract Theory 22 Normalize for simplicity the total size of the surplus that is available to share between the two contracting parties to have size 1 (simple normalization). To establish a negotiation well defined and enforced ownership rights need to be specified. Entitlements/ownership rights define the outside option of each party to the contract. In other words it defines the payoff each party is entitled to without need for the other party to agree. Denote w A and w B the entitlements of party A, respectively B where: w A + w B < 1.
23 Topics in Contract Theory 23 We assume the following extensive form for the costless negotiation between the two parties: Infinite horizon, alternating offers bargaining game with discounting and outside options. Denote: δ the parties common discount factor, x the share of the pie to party A, (1 x) the share of the pie to party B.
24 Odd periods: Topics in Contract Theory 24 Stage I A makes an offer x A to B, Stage II B observes the offer and has three alternative choices: he can accept the offer, then x = x A and the game terminates; he can reject the offer and take his outside option w B and the game terminates; he can reject the offer and do not take his outside option, then the game moves to Stage I of the following period.
25 Even periods: Topics in Contract Theory 25 Stage I B makes an offer x B to A, Stage II A observes the offer and ha three alternative choices: he can accept the offer, then x = x B and the game terminates; he can reject the offer and take his outside option w A and the game terminates; he can reject the offer and do not take his outside option, then the game moves to Stage I of the following period.
26 Topics in Contract Theory 26 Payoffs: If parties agree on x in period n + 1: π A (σ A, σ B ) = δ n x, π B (σ A, σ B ) = δ n (1 x), If they do not agree and either party takes his outside option in period n + 1: π A (σ A, σ B ) = δ n w A, π B (σ A, σ B ) = δ n w B. Result 1. (Deal Me Out) For any discount factor δ < 1, and any pair (w A, w B ), w A + w B < 1, the bargaining game has a unique subgame perfect equilibrium, where agreement between the parties is immediate and the outside options are never exercised.
27 Topics in Contract Theory 27 Proof: (sketch) Denote x H i, respectively xl i, i {A, B}, the highest, respectively the lowest, possible share that A can receive in a subgame that starts with i making the offer. We then have that: x H B max{w A, δ x H A } 1 x L A max{w B, δ ( 1 x L B) } Moreover: x L B max{w A, δ x L A}, 1 x H A max{w B, δ ( 1 x H B) }
28 Topics in Contract Theory 28 Solving these inequalities we obtain: x H A = x L A = x A, x H B = x L B = x B We also obtain that: If then w A δ 1 + δ, w B δ 1 + δ x A = δ, x B = δ 1 + δ If then w A δ 1 + δ, w B δ(1 w A ) x A = 1 δ(1 w A ), x B = w A
29 Topics in Contract Theory 29 If then w A δ(1 w B ), w B δ 1 + δ x A = 1 w B, x B = δ(1 w B ) If w A δ(1 w B ), w B δ(1 w A ) then x A = 1 w B, x B = w A These offers characterize a pair of strategies (σ A, σ B ). It is easy to show that these strategies constitute the unique subgame perfect equilibrium of the bargaining game.
30 Topics in Contract Theory 30 Notice that the efficient agreement is reached independently of the size of the entitlements. In particular if each party is entitle to the choice of his input, then: Π A (ê A ) w A = Π A (e A ) + Π B(e B ) γ e A w B = Π B (ê B ) γ ê A Π A (e A ) + Π B(e B ) γ e A If instead party B is entitled to preclude party A from operating his technology, then: w A = 0, w B = Π B (ê B ) Π A (e A ) + Π B(e B ) γ e A
31 Topics in Contract Theory 31 In either case the result above implies that we would get the efficient outcome: (e A, e B ). However, the share that accrue to each party depends on the entitlements w A and w B. The equilibrium contract specifies a transfer between the two parties and A s choice of input e A. Also the transfer depend on the entitlements w A and w B.
EC487 Advanced Microeconomics, Part I: Lecture 9
EC487 Advanced Microeconomics, Part I: Lecture 9 Leonardo Felli 32L.LG.04 24 November 2017 Bargaining Games: Recall Two players, i {A, B} are trying to share a surplus. The size of the surplus is normalized
More informationTopics in Contract Theory Lecture 3
Leonardo Felli 9 January, 2002 Topics in Contract Theory Lecture 3 Consider now a different cause for the failure of the Coase Theorem: the presence of transaction costs. Of course for this to be an interesting
More informationEC476 Contracts and Organizations, Part III: Lecture 3
EC476 Contracts and Organizations, Part III: Lecture 3 Leonardo Felli 32L.G.06 26 January 2015 Failure of the Coase Theorem Recall that the Coase Theorem implies that two parties, when faced with a potential
More informationTopics in Contract Theory Lecture 5. Property Rights Theory. The key question we are staring from is: What are ownership/property rights?
Leonardo Felli 15 January, 2002 Topics in Contract Theory Lecture 5 Property Rights Theory The key question we are staring from is: What are ownership/property rights? For an answer we need to distinguish
More informationIntroduction to Game Theory Lecture Note 5: Repeated Games
Introduction to Game Theory Lecture Note 5: Repeated Games Haifeng Huang University of California, Merced Repeated games Repeated games: given a simultaneous-move game G, a repeated game of G is an extensive
More informationFinitely repeated simultaneous move game.
Finitely repeated simultaneous move game. Consider a normal form game (simultaneous move game) Γ N which is played repeatedly for a finite (T )number of times. The normal form game which is played repeatedly
More informationG5212: Game Theory. Mark Dean. Spring 2017
G5212: Game Theory Mark Dean Spring 2017 Bargaining We will now apply the concept of SPNE to bargaining A bit of background Bargaining is hugely interesting but complicated to model It turns out that the
More informationPrisoner s dilemma with T = 1
REPEATED GAMES Overview Context: players (e.g., firms) interact with each other on an ongoing basis Concepts: repeated games, grim strategies Economic principle: repetition helps enforcing otherwise unenforceable
More informationIntroduction 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
More informationThe Nash equilibrium of the stage game is (D, R), giving payoffs (0, 0). Consider the trigger strategies:
Problem Set 4 1. (a). Consider the infinitely repeated game with discount rate δ, where the strategic fm below is the stage game: B L R U 1, 1 2, 5 A D 2, 0 0, 0 Sketch a graph of the players payoffs.
More informationSimon Fraser University Spring 2014
Simon Fraser University Spring 2014 Econ 302 D200 Final Exam Solution This brief solution guide does not have the explanations necessary for full marks. NE = Nash equilibrium, SPE = subgame perfect equilibrium,
More informationGame Theory. Wolfgang Frimmel. Repeated Games
Game Theory Wolfgang Frimmel Repeated Games 1 / 41 Recap: SPNE The solution concept for dynamic games with complete information is the subgame perfect Nash Equilibrium (SPNE) Selten (1965): A strategy
More informationLecture 5 Leadership and Reputation
Lecture 5 Leadership and Reputation Reputations arise in situations where there is an element of repetition, and also where coordination between players is possible. One definition of leadership is that
More informationMicroeconomic Theory II Preliminary Examination Solutions
Microeconomic Theory II Preliminary Examination Solutions 1. (45 points) Consider the following normal form game played by Bruce and Sheila: L Sheila R T 1, 0 3, 3 Bruce M 1, x 0, 0 B 0, 0 4, 1 (a) Suppose
More informationOutline for Dynamic Games of Complete Information
Outline for Dynamic Games of Complete Information I. Examples of dynamic games of complete info: A. equential version of attle of the exes. equential version of Matching Pennies II. Definition of subgame-perfect
More informationProblem 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]
More informationRepeated Games. EC202 Lectures IX & X. Francesco Nava. January London School of Economics. Nava (LSE) EC202 Lectures IX & X Jan / 16
Repeated Games EC202 Lectures IX & X Francesco Nava London School of Economics January 2011 Nava (LSE) EC202 Lectures IX & X Jan 2011 1 / 16 Summary Repeated Games: Definitions: Feasible Payoffs Minmax
More informationMicroeconomic Theory II Preliminary Examination Solutions Exam date: June 5, 2017
Microeconomic Theory II Preliminary Examination Solutions Exam date: June 5, 07. (40 points) Consider a Cournot duopoly. The market price is given by q q, where q and q are the quantities of output produced
More informationIn reality; some cases of prisoner s dilemma end in cooperation. Game Theory Dr. F. Fatemi Page 219
Repeated Games Basic lesson of prisoner s dilemma: In one-shot interaction, individual s have incentive to behave opportunistically Leads to socially inefficient outcomes In reality; some cases of prisoner
More informationA Theory of Value Distribution in Social Exchange Networks
A Theory of Value Distribution in Social Exchange Networks Kang Rong, Qianfeng Tang School of Economics, Shanghai University of Finance and Economics, Shanghai 00433, China Key Laboratory of Mathematical
More informationM.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:
More informationTopics in Contract Theory Lecture 6. Separation of Ownership and Control
Leonardo Felli 16 January, 2002 Topics in Contract Theory Lecture 6 Separation of Ownership and Control The definition of ownership considered is limited to an environment in which the whole ownership
More informationA Theory of Value Distribution in Social Exchange Networks
A Theory of Value Distribution in Social Exchange Networks Kang Rong, Qianfeng Tang School of Economics, Shanghai University of Finance and Economics, Shanghai 00433, China Key Laboratory of Mathematical
More informationRepeated Games with Perfect Monitoring
Repeated Games with Perfect Monitoring Mihai Manea MIT Repeated Games normal-form stage game G = (N, A, u) players simultaneously play game G at time t = 0, 1,... at each date t, players observe all past
More informationGame Theory. Important Instructions
Prof. Dr. Anke Gerber Game Theory 2. Exam Summer Term 2012 Important Instructions 1. There are 90 points on this 90 minutes exam. 2. You are not allowed to use any material (books, lecture notes etc.).
More informationMicroeconomics II. CIDE, MsC Economics. List of Problems
Microeconomics II CIDE, MsC Economics List of Problems 1. There are three people, Amy (A), Bart (B) and Chris (C): A and B have hats. These three people are arranged in a room so that B can see everything
More informationFDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.
FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 2 1. Consider a zero-sum game, where
More informationFDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.
FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 3 1. Consider the following strategic
More informationMA200.2 Game Theory II, LSE
MA200.2 Game Theory II, LSE Answers to Problem Set [] In part (i), proceed as follows. Suppose that we are doing 2 s best response to. Let p be probability that player plays U. Now if player 2 chooses
More informationECE 586BH: Problem Set 5: Problems and Solutions Multistage games, including repeated games, with observed moves
University of Illinois Spring 01 ECE 586BH: Problem Set 5: Problems and Solutions Multistage games, including repeated games, with observed moves Due: Reading: Thursday, April 11 at beginning of class
More informationCHAPTER 14: REPEATED PRISONER S DILEMMA
CHAPTER 4: REPEATED PRISONER S DILEMMA In this chapter, we consider infinitely repeated play of the Prisoner s Dilemma game. We denote the possible actions for P i by C i for cooperating with the other
More informationGame Theory Fall 2006
Game Theory Fall 2006 Answers to Problem Set 3 [1a] Omitted. [1b] Let a k be a sequence of paths that converge in the product topology to a; that is, a k (t) a(t) for each date t, as k. Let M be the maximum
More informationCOSTLY BARGAINING AND RENEGOTIATION
COSTLY BARGAINING AND RENEGOTIATION Luca Anderlini (Southampton University) Leonardo Felli (London School of Economics) September 1998 Revised January 2000 Abstract. We identify the inefficiencies that
More informationAnswers 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,
More informationGAME THEORY. Department of Economics, MIT, Follow Muhamet s slides. We need the following result for future reference.
14.126 GAME THEORY MIHAI MANEA Department of Economics, MIT, 1. Existence and Continuity of Nash Equilibria Follow Muhamet s slides. We need the following result for future reference. Theorem 1. Suppose
More informationAnswer Key: Problem Set 4
Answer Key: Problem Set 4 Econ 409 018 Fall A reminder: An equilibrium is characterized by a set of strategies. As emphasized in the class, a strategy is a complete contingency plan (for every hypothetical
More informationCUR 412: Game Theory and its Applications, Lecture 12
CUR 412: Game Theory and its Applications, Lecture 12 Prof. Ronaldo CARPIO May 24, 2016 Announcements Homework #4 is due next week. Review of Last Lecture In extensive games with imperfect information,
More informationEconomics 209A Theory and Application of Non-Cooperative Games (Fall 2013) Repeated games OR 8 and 9, and FT 5
Economics 209A Theory and Application of Non-Cooperative Games (Fall 2013) Repeated games OR 8 and 9, and FT 5 The basic idea prisoner s dilemma The prisoner s dilemma game with one-shot payoffs 2 2 0
More informationIn 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:
More information14.12 Game Theory Midterm II 11/15/ Compute all the subgame perfect equilibria in pure strategies for the following game:
4. Game Theory Midterm II /5/7 Prof. Muhamet Yildiz Instructions. This is an open book exam; you can use any written material. You have one hour and minutes. Each question is 5 points. Good luck!. Compute
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationIntroduction 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,
More informationpreferences of the individual players over these possible outcomes, typically measured by a utility or payoff function.
Leigh Tesfatsion 26 January 2009 Game Theory: Basic Concepts and Terminology A GAME consists of: a collection of decision-makers, called players; the possible information states of each player at each
More informationTransaction Costs and the Robustness of the Coase Theorem
Transaction Costs and the Robustness of the Coase Theorem Luca Anderlini (Southampton University and Georgetown University) Leonardo Felli (London School of Economics) June 2001 Abstract. This paper explores
More informationGame theory and applications: Lecture 1
Game theory and applications: Lecture 1 Adam Szeidl September 20, 2018 Outline for today 1 Some applications of game theory 2 Games in strategic form 3 Dominance 4 Nash equilibrium 1 / 8 1. Some applications
More informationCMSC 474, Introduction to Game Theory 16. Behavioral vs. Mixed Strategies
CMSC 474, Introduction to Game Theory 16. Behavioral vs. Mixed Strategies Mohammad T. Hajiaghayi University of Maryland Behavioral Strategies In imperfect-information extensive-form games, we can define
More informationUniversity at Albany, State University of New York Department of Economics Ph.D. Preliminary Examination in Microeconomics, June 20, 2017
University at Albany, State University of New York Department of Economics Ph.D. Preliminary Examination in Microeconomics, June 0, 017 Instructions: Answer any three of the four numbered problems. Justify
More informationRepeated Games. September 3, Definitions: Discounting, Individual Rationality. Finitely Repeated Games. Infinitely Repeated Games
Repeated Games Frédéric KOESSLER September 3, 2007 1/ Definitions: Discounting, Individual Rationality Finitely Repeated Games Infinitely Repeated Games Automaton Representation of Strategies The One-Shot
More information1 Two Period Exchange Economy
University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Handout # 2 1 Two Period Exchange Economy We shall start our exploration of dynamic economies with
More informationRelational Incentive Contracts
Relational Incentive Contracts Jonathan Levin May 2006 These notes consider Levin s (2003) paper on relational incentive contracts, which studies how self-enforcing contracts can provide incentives in
More informationMicroeconomics of Banking: Lecture 5
Microeconomics of Banking: Lecture 5 Prof. Ronaldo CARPIO Oct. 23, 2015 Administrative Stuff Homework 2 is due next week. Due to the change in material covered, I have decided to change the grading system
More informationDirected Search and the Futility of Cheap Talk
Directed Search and the Futility of Cheap Talk Kenneth Mirkin and Marek Pycia June 2015. Preliminary Draft. Abstract We study directed search in a frictional two-sided matching market in which each seller
More informationRegret Minimization and Security Strategies
Chapter 5 Regret Minimization and Security Strategies Until now we implicitly adopted a view that a Nash equilibrium is a desirable outcome of a strategic game. In this chapter we consider two alternative
More informationTHE PENNSYLVANIA STATE UNIVERSITY. Department of Economics. January Written Portion of the Comprehensive Examination for
THE PENNSYLVANIA STATE UNIVERSITY Department of Economics January 2014 Written Portion of the Comprehensive Examination for the Degree of Doctor of Philosophy MICROECONOMIC THEORY Instructions: This examination
More informationEconomics 502 April 3, 2008
Second Midterm Answers Prof. Steven Williams Economics 502 April 3, 2008 A full answer is expected: show your work and your reasoning. You can assume that "equilibrium" refers to pure strategies unless
More informationCUR 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
More informationMS&E 246: Lecture 5 Efficiency and fairness. Ramesh Johari
MS&E 246: Lecture 5 Efficiency and fairness Ramesh Johari A digression In this lecture: We will use some of the insights of static game analysis to understand efficiency and fairness. Basic setup N players
More informationGame Theory. Lecture Notes By Y. Narahari. Department of Computer Science and Automation Indian Institute of Science Bangalore, India October 2012
Game Theory Lecture Notes By Y. Narahari Department of Computer Science and Automation Indian Institute of Science Bangalore, India October 22 COOPERATIVE GAME THEORY Correlated Strategies and Correlated
More informationFinal Examination December 14, Economics 5010 AF3.0 : Applied Microeconomics. time=2.5 hours
YORK UNIVERSITY Faculty of Graduate Studies Final Examination December 14, 2010 Economics 5010 AF3.0 : Applied Microeconomics S. Bucovetsky time=2.5 hours Do any 6 of the following 10 questions. All count
More informationMicroeconomic Theory August 2013 Applied Economics. Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY. Applied Economics Graduate Program
Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY Applied Economics Graduate Program August 2013 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationCS364A: 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)
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationSequential-move games with Nature s moves.
Econ 221 Fall, 2018 Li, Hao UBC CHAPTER 3. GAMES WITH SEQUENTIAL MOVES Game trees. Sequential-move games with finite number of decision notes. Sequential-move games with Nature s moves. 1 Strategies in
More informationLecture Notes on Adverse Selection and Signaling
Lecture Notes on Adverse Selection and Signaling Debasis Mishra April 5, 2010 1 Introduction In general competitive equilibrium theory, it is assumed that the characteristics of the commodities are observable
More informationMicroeconomic 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
More informationEfficiency in Decentralized Markets with Aggregate Uncertainty
Efficiency in Decentralized Markets with Aggregate Uncertainty Braz Camargo Dino Gerardi Lucas Maestri December 2015 Abstract We study efficiency in decentralized markets with aggregate uncertainty and
More informationNot 0,4 2,1. i. Show there is a perfect Bayesian equilibrium where player A chooses to play, player A chooses L, and player B chooses L.
Econ 400, Final Exam Name: There are three questions taken from the material covered so far in the course. ll questions are equally weighted. If you have a question, please raise your hand and I will come
More informationGame Theory Fall 2003
Game Theory Fall 2003 Problem Set 5 [1] Consider an infinitely repeated game with a finite number of actions for each player and a common discount factor δ. Prove that if δ is close enough to zero then
More informationAppendix: Common Currencies vs. Monetary Independence
Appendix: Common Currencies vs. Monetary Independence A The infinite horizon model This section defines the equilibrium of the infinity horizon model described in Section III of the paper and characterizes
More information6.254 : Game Theory with Engineering Applications Lecture 3: Strategic Form Games - Solution Concepts
6.254 : Game Theory with Engineering Applications Lecture 3: Strategic Form Games - Solution Concepts Asu Ozdaglar MIT February 9, 2010 1 Introduction Outline Review Examples of Pure Strategy Nash Equilibria
More informationCUR 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,
More informationExternality and Corrective Measures
Externality and Corrective Measures Ram Singh Microeconomic Theory Lecture 20 Ram Singh: (DSE) Market Failure Lecture 20 1 / 25 Questions Question What is an externality? What corrective measures are available
More informationLectures on Externalities
Lectures on Externalities An externality is present whenever the well-being of a consumer or the production possibilities of a firm are directly affected by the actions of another agent in the economy.
More informationBargaining Theory and Solutions
Bargaining Theory and Solutions Lin Gao IERG 3280 Networks: Technology, Economics, and Social Interactions Spring, 2014 Outline Bargaining Problem Bargaining Theory Axiomatic Approach Strategic Approach
More informationComparing Allocations under Asymmetric Information: Coase Theorem Revisited
Comparing Allocations under Asymmetric Information: Coase Theorem Revisited Shingo Ishiguro Graduate School of Economics, Osaka University 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan August 2002
More informationRepeated 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
More informationExercises Solutions: Game Theory
Exercises Solutions: Game Theory Exercise. (U, R).. (U, L) and (D, R). 3. (D, R). 4. (U, L) and (D, R). 5. First, eliminate R as it is strictly dominated by M for player. Second, eliminate M as it is strictly
More informationEXTENSIVE AND NORMAL FORM GAMES
EXTENSIVE AND NORMAL FORM GAMES Jörgen Weibull February 9, 2010 1 Extensive-form games Kuhn (1950,1953), Selten (1975), Kreps and Wilson (1982), Weibull (2004) Definition 1.1 A finite extensive-form game
More informationSF2972 GAME THEORY Infinite games
SF2972 GAME THEORY Infinite games Jörgen Weibull February 2017 1 Introduction Sofar,thecoursehasbeenfocusedonfinite games: Normal-form games with a finite number of players, where each player has a finite
More informationProblem Set 2 Answers
Problem Set 2 Answers BPH8- February, 27. Note that the unique Nash Equilibrium of the simultaneous Bertrand duopoly model with a continuous price space has each rm playing a wealy dominated strategy.
More informationSimple Efficient Contracts in Complex Environments
Simple Efficient Contracts in Complex Environments 5REHUW(YDQV 0DUFK &:3( 1RWWREHTXRWHGZLWKRXWSHUPLVVLRQ Simple Efficient Contracts in Complex Environments Robert Evans St. John s College, Cambridge, UK.
More informationMicroeconomics Comprehensive Exam
Microeconomics Comprehensive Exam June 2009 Instructions: (1) Please answer each of the four questions on separate pieces of paper. (2) When finished, please arrange your answers alphabetically (in the
More informationAlternating-Offer Games with Final-Offer Arbitration
Alternating-Offer Games with Final-Offer Arbitration Kang Rong School of Economics, Shanghai University of Finance and Economic (SHUFE) August, 202 Abstract I analyze an alternating-offer model that integrates
More informationOnline Appendix for Debt Contracts with Partial Commitment by Natalia Kovrijnykh
Online Appendix for Debt Contracts with Partial Commitment by Natalia Kovrijnykh Omitted Proofs LEMMA 5: Function ˆV is concave with slope between 1 and 0. PROOF: The fact that ˆV (w) is decreasing in
More information13.1 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
More information1 Theory of Auctions. 1.1 Independent Private Value Auctions
1 Theory of Auctions 1.1 Independent Private Value Auctions for the moment consider an environment in which there is a single seller who wants to sell one indivisible unit of output to one of n buyers
More informationPreliminary Notions in Game Theory
Chapter 7 Preliminary Notions in Game Theory I assume that you recall the basic solution concepts, namely Nash Equilibrium, Bayesian Nash Equilibrium, Subgame-Perfect Equilibrium, and Perfect Bayesian
More informationMANAGEMENT SCIENCE doi /mnsc ec pp. ec1 ec23
MANAGEMENT SCIENCE doi 101287/mnsc10800894ec pp ec1 ec23 e-companion ONLY AVAILABLE IN ELECTRONIC FORM informs 2008 INFORMS Electronic Companion Strategic Inventories in Vertical Contracts by Krishnan
More informationOther Regarding Preferences
Other Regarding Preferences Mark Dean Lecture Notes for Spring 015 Behavioral Economics - Brown University 1 Lecture 1 We are now going to introduce two models of other regarding preferences, and think
More informationFebruary 23, An Application in Industrial Organization
An Application in Industrial Organization February 23, 2015 One form of collusive behavior among firms is to restrict output in order to keep the price of the product high. This is a goal of the OPEC oil
More informationRelational Incentive Contracts with Persistent Private Information
Relational Incentive Contracts with Persistent Private Information James M. Malcomson CESIFO WORKING PAPER NO. 5462 CATEGORY 12: EMPIRICAL AND THEORETICAL METHODS JULY 2015 An electronic version of the
More informationSo we turn now to many-to-one matching with money, which is generally seen as a model of firms hiring workers
Econ 805 Advanced Micro Theory I Dan Quint Fall 2009 Lecture 20 November 13 2008 So far, we ve considered matching markets in settings where there is no money you can t necessarily pay someone to marry
More informationA Decentralized Learning Equilibrium
Paper to be presented at the DRUID Society Conference 2014, CBS, Copenhagen, June 16-18 A Decentralized Learning Equilibrium Andreas Blume University of Arizona Economics ablume@email.arizona.edu April
More informationBeliefs and Sequential Rationality
Beliefs and Sequential Rationality A system of beliefs µ in extensive form game Γ E is a specification of a probability µ(x) [0,1] for each decision node x in Γ E such that x H µ(x) = 1 for all information
More informationBargaining Order and Delays in Multilateral Bargaining with Asymmetric Sellers
WP-2013-015 Bargaining Order and Delays in Multilateral Bargaining with Asymmetric Sellers Amit Kumar Maurya and Shubhro Sarkar Indira Gandhi Institute of Development Research, Mumbai August 2013 http://www.igidr.ac.in/pdf/publication/wp-2013-015.pdf
More informationUCLA Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory
UCLA Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory (SPRING 2016) Instructions: You have 4 hours for the exam Answer any 5 out of the 6 questions. All questions are weighted equally.
More informationGame 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
More informationCounterfeiting substitute media-of-exchange: a threat to monetary systems
Counterfeiting substitute media-of-exchange: a threat to monetary systems Tai-Wei Hu Penn State University June 2008 Abstract One justification for cash-in-advance equilibria is the assumption that the
More informationExtensive-Form Games with Imperfect Information
May 6, 2015 Example 2, 2 A 3, 3 C Player 1 Player 1 Up B Player 2 D 0, 0 1 0, 0 Down C Player 1 D 3, 3 Extensive-Form Games With Imperfect Information Finite No simultaneous moves: each node belongs to
More informationOn Existence of Equilibria. Bayesian Allocation-Mechanisms
On Existence of Equilibria in Bayesian Allocation Mechanisms Northwestern University April 23, 2014 Bayesian Allocation Mechanisms In allocation mechanisms, agents choose messages. The messages determine
More information