Comparing Allocations under Asymmetric Information: Coase Theorem Revisited
|
|
- Charity Simon
- 5 years ago
- Views:
Transcription
1 Comparing Allocations under Asymmetric Information: Coase Theorem Revisited Shingo Ishiguro Graduate School of Economics, Osaka University 1-7 Machikaneyama, Toyonaka, Osaka , Japan August 2002 Abstract This paper investigates the robustness of Coase Theorem under asymmetric information. We identify the conditions under which the same allocation is attained as an equilibrium of a bilateral trade no matter which informed or uninformed party has the bargaining power to make a contract offer. Keywords: Asymmetric Information, Coase Theorem, Principal Agent Relationship, Signaling Games JEL Classification Numbers: D80, D82 Corresponding Author. Tel: , Fax: Address: ishiguro@econ.osaka-u.ac.jp 1
2 1 Introduction Coase Theorem has been often referred to as the result that allocative efficiency of a transaction among individuals with quasi linear preferences is not affected by their bargaining powers. In this paper we investigate whether or not Coase Theorem can be extended to the environments with asymmetric information. In particular we consider a bilateral trade model where an agent has a private information (his type ) which affects both his own and the principal s benefits. Then we compare the equilibrium allocation attained in the game (called P game) in which an uninformed party (a principal) has the bargaining power to make a contract offer with that in the game (called A game) in which an informed party (an agent) has the bargaining power to do so. We say that Coase Theorem holds in this environment if the same allocation (and hence the same ex ante efficiency) is implemented as an equilibrium in both P game and A game. Since the informed party (the agent) makes a contract offer in A game, this game is known as the informed principal problem (See Maskin and Tirole (1992) for a general treatment on this issue.) Recently several papers have also examined the informed principal problem in various contractual settings. 1 However, our main focus is to compare equilibrium allocations between signaling and screening models and identify the conditions under which these coincide with each other, while the existing papers have paid little attention to such issues. 2 Our main finding is as follows: (i) The equilibrium allocation in P game can be always attained as a perfect Bayesian equilibrium (PBE) in A game when there exist some bad types of agent who never contributes to the increase of the gains from trade as compared to status quo. Put differently, the attainable efficiency (ex ante total payoffs of the principal and agent) is same in both P game and A game. Thus in this case Coase Theorem weakly holds even under asymmetric information. 3 (ii) However, there exist no PBEs in A game which attain the same equilibrium allocation in P game when the following conditions are satisfied: First, the second best allocation is distorted at the worst type agent who yields the lowest value to the principal. Second, no bunching (pooling) occurs at that type in the second best optimum as well. We also show that the former condition is satisfied under fairly general conditions (for example when the type set is finite and action is a continuous variable.) The conditions imposed in 1 See for example Chade and Silvers (2002), Inderst (2001, 2002) and Jost (1996). 2 Although Maskin and Tirole (1992) discuss the similar problem (see their Proposition 12 and 13), their model differs from ours: They assume that more than two uninformed parties compete to offer contracts in the screening model. This Bertrand competition essentially gives the informed party the bargaining power even in the screening model, which is in contrast to our bilateral monopoly model. 3 We here use the term weakly because there may exist other PBEs in A game which does not attain the same allocation in P game. 2
3 the standard mechanism design problems (so called sorting condition and monotone hazard rate condition) also results in the downward distortion and no bunching, which covers the case for our second result (ii) to hold. Therefore, we conclude that whether or not Coase Theorem holds even under asymmetric information depends on whether or not there exist some inefficient types who should be excluded from transaction. 2 The Model We will consider a bilateral trade model in which a risk neutral principal contracts with a risk neutral agent for implementing some profitable project. The principal has a quasi linear utility function, V (a; θ) t, where a A R n is an action (vector) chosen by the agent, t R a monetary transfer made from the principal to the agent, and θ Θ R m a type of agent respectively. Note that we allow both multidimensional action choices and types. V (a; θ) is assumed to be strictly concave with respect to a. The agent also has a quasi linear utility function, t ψ(a; θ), where ψ(a; θ) denotes the cost of choosing an action a. ψ(a; θ) is assumed to be strictly convex with respect to a. The reservation payoffs of both parties are normalized to zero. For simplicity, we will also assume that there exists an action a A such that V (a; θ) =ψ(a; θ) = 0 for all θ Θ. This means that there exists the contract, which specifies zero transfer and the action a, to guarantee the reservation payoffs to the contracting parties. 4 The action a can be thought of as the status quo action in that it gives the parties the status quo payoffs, zero. The agent knows his type θ before contracting but the principal does not. Let P 0 (θ) denote the prior belief held by the principal that agent is of type θ. An allocation is defined as a mapping µ :Θ (A) which specifies for each type a probability distribution on the action set A where (A) is the set of probability distributions on A. Note that we allow random allocation. We will compare two different games depending on the bargaining powers to make a take it or leave it contract offer. One is the game called P game in which the principal (uninformed party) proposes a contract and the other is the game called A game in which the agent (informed party) does so. In P game we can apply the revelation principle and use the direct revelation mechanism without loss of generality. Let C A R denote the set of possible actions and transfers. Since the payoff functions of both the principal and agent are linear with respect to monetary transfer t, random transfer can be always replaced by nonrandom 4 More generally, we may use an alternative formulation by adding the null contract, which specifies nothing and hence ensures the reservation payoffs, to the set of possible contracts. To save notation, we will not adopt such approach. 3
4 transfer without loss of generality. 5 Let t : Θ R be a nonrandom transfer schedule. We will then consider stochastic contracts only on the part of action choice a. P game has the following timing: P game: 1. The principal offers a contract C {µ, t}, which consists of (possibly random) allocation mapping µ and transfer schedule t. Let C(θ) {µ θ,t(θ)} also denote the incentive scheme designed for type θ agent where µ θ (A). 2. The agent decides whether to accept this contract or not. 3. When accepted it, the contract is executed. On the other hand, A game proceeds with the following timing: A game: 1. The agent of type θ offers a contract C (A) R to the principal. The contract proposed by the agent also consists of (stochastic) action choice µ (A) and a transfer t R. 2. The principal decides whether to accept it or not. 3. When accepted it, the contract is executed. We first consider the full information case that the principal also knows about θ at the contracting stage. Moreover, under our assumptions, random allocation is not optimal in this first best case. Then so called Coase Theorem holds, i.e., the first best allocation a FB (θ) does not depend on which party has the bargaining power to make a contract offer. a FB (θ) is defined as a FB (θ) arg max V (a; θ) ψ(a; θ). (1) a A Note that a FB (θ) is uniquely determined. Let Π FB (θ) V (a FB (θ); θ) ψ(a FB (θ); θ) denote the first best payoff. 3 Equilibrium Allocations 3.1 Equilibrium in P Game As we noted, the equilibrium allocation in P game can be attained by using a direct revelation mechanism C(θ) ={µ θ,t(θ)} θ Θ. With slight abuse of notation, we define V (µ θ ; θ) V (a; θ)dµ θ (2) A 5 Indeed a random transfer can be replaced by its expected value without affecting the results. 4
5 and ψ(µ θ ; θ) A ψ(a; θ)dµ θ. (3) The optimization program the principal should solve at the first stage is given as follows: (P) max E[V (µ θ ; θ) t(θ)] C subject to θ arg max t(ˆθ) ψ(µˆθ; θ) for all θ Θ (I C) ˆθ t(θ) ψ(µ θ ; θ) 0 for all θ Θ (IR) where expectation E[ ] is taken over Θ. (IC) means the incentive compatibility constraint that type θ agent is induced to tell the truth. (IR) means the individual rationality constraint that each type obtains at least the reservation payoff, zero. 6 Let C (θ) {µ θ,t (θ)} be the optimal contract designed for type θ agent. Let µ also denote the equilibrium allocation attained in P game. 3.2 Equilibrium in A Game The contract proposal made by the agent becomes a signal of sending his type in A game, which is in contrast to P game. Thus we will confine our attention to the perfect Bayesian equilibrium (PBE) as follows: (i) Sequential Rationality: Each type of agent optimally offers a contract C to maximize his expected payoff. The principal optimally makes the acceptance decision, given the strategy taken by the agent and her belief about the agent s type. (ii) Belief Consistency: The principal s belief is updated according to the Bayes rule, given the above agent s strategy, whenever it is possible. Let P (θ C) denote a posterior belief of the principal after a contract C {µ, t} is offered by the agent. Then the principal chooses to accept the contract C if and only if [V (a; θ) t]dµdp (θ C) 0. (4) Θ A Let m(c) [0, 1] be a probability of the principal accepting the offered contract C, given her posterior belief P (θ C). The agent of type θ will then choose a contract C = {µ, t} to maximize the expected payoff m(c)[t ψ(µ; θ)]. (5) 6 Note that in this definition we assume all types participate in the mechanism. However, no generality is lost by this condition because when the participation of some type is not profitable for the principal she can always choose the status quo action a and zero transfer t = 0 for that type, which guarantee both herself and the agent the reservation payoffs, zero. 5
6 4 Comparing Allocations under Asymmetric Information Now we will address the issue of whether or not the equilibrium allocation in P game µ can be sustained as a PBE in A game as well. We define the exclusion set as ES {θ Θ V (a; θ) ψ(a; θ) < 0 for all a a}. (6) ES is the set of agent s types who never contribute to the increase of the gains from trade as compared to the status quo. Of course, if ES, we have a FB (θ) =a for all θ ES. Then we can show the following result. Proposition 1. Suppose that ES. Then there exists a PBE in A game which attains the equilibrium allocation µ in P game. Proof. Consider the following strategies and belief: The agent of type θ proposes the contract C (θ). The principal accepts this with certainty. The principal has the posterior belief P ( C (θ)) when she is offered a contract C (θ) as follows: P (θ C (θ)) = 0 for all θ Θ \{θ Θ C (θ) =C (θ )} and P (θ C (θ)) > 0 for all other types. Moreover, the principal puts all positive weights on ES when she observes all other contracts C than {C (θ)}, i.e., P (ES C) = 1 for all C/ C {C C C = C (θ) for some θ}. It is obvious that the principal optimally accepts all contracts C C because by definition of optimal contract C we have V (µ θ ; θ) t (θ) 0 for any θ. Since C satisfies (IC), type θ agent will also offer the contract C (θ) rather than C (θ ) for θ θ, given the principal s above strategy. Suppose now that some type θ offers a contract C = {µ, t} / C. For such deviation to be profitable, t ψ(µ; θ) > 0 must be satisfied. However then V (µ; θ) t< V (µ; θ) ψ(µ; θ) < 0 for all θ ES. Given her belief that P (ES C) =1 for all C / C, the principal will then reject such deviation offer. Thus the agent cannot gain by the deviation. Q.E.D. Proposition 1 states that Coase Theorem weakly holds under asymmetric information in the sense that the same allocation can be an equilibrium, no matter how bargaining power to make a contract offer is allocated to an informed party or an uninformed party. Thus the same ex ante efficiency can be attained in both P game and A game. The intuition for this result to hold is simple: The original (IC) means that each type does not mimic the other types. Thus in order to sustain µ as a PBE in A game it is sufficient to construct off the path belief for observing other contracts C/ {C (θ)} θ Θ. If ES, this is easily done by putting all positive probabilities on the exclusion set ES when having observed such deviation contracts. 6
7 The condition stated in Proposition 1 means that some inefficient types are excluded from transaction. If this condition does not hold, Coase Theorem may not be extended to the cases of asymmetric information. Such issue will be addressed in the following proposition. To this end, we assume the existence of the worst type of agent, denoted θ, which satisfies V (a; θ) V (a; θ) for all θ θ and a A. This condition is satisfied when V (a; ) is monotone with respect to θ. Proposition 2. Suppose that µ θ µ θ for any θ θ and also that µ θ does not put mass one to a FB (θ). Then there exist no PBEs in A game which attain the equilibrium allocation µ in P game. Proof. Since µ θ does not put mass one to afb (θ), a FB (θ) a must hold. This is because, if a FB (θ) =a in the first best, then this must be also the case in the second best, 7 which contradicts the stated condition. Suppose, contrary to the claim, that there exists a PBE in which the allocation µ can be attained in A game. Then type θ agent must offer the contract Ĉ(θ) {µ θ, ˆt(θ)} in that PBE, which attains the allocation µ. In particular there must exist no θ θ such that Ĉ(θ) =Ĉ(θ), because µ θ µ θ by assumption. Now consider the deviation by type θ agent such that C {a FB (θ),t } is offered where t satisfies V (a FB (θ); θ) t >V(µ θ; θ) ˆt(θ) (7) t ψ(a FB (θ); θ) > ˆt(θ) ψ(µ θ; θ) (8) where the right hand sides of (7) and (8) represent the equilibrium payoffs of the principal and type θ agent respectively when Ĉ(θ) is offered. Note here that the principal s posterior belief P ( Ĉ(θ)) after Ĉ(θ) was offered must be P (θ Ĉ(θ)) = 1 in the PBE because Ĉ(θ) Ĉ(θ) for all θ θ. In fact such transfer t exists because µ θ does not put mass one to afb (θ) by assumption and hence this implies V (a FB (θ); θ) ψ(a FB (θ); θ) >V(µ θ; θ) ψ(µ θ; θ). (9) Moreover, since V (µ θ ; θ) ψ(µ θ ; θ) 0, the principal will accept the contract C with certainty: E[V (a FB (θ); θ) C ] t V (a FB (θ); θ) t >V(µ θ; θ) ψ(µ θ; θ) 0 7 Since V (µ θ; θ) t (θ) V (µ θ; θ) ψ(µ θ; θ) V (a FB (θ); θ) ψ(a FB (θ); θ) =V (a; θ) ψ(a; θ) = 0, we must have µ θ({a}) = 1 and t (θ) = 0 due to the optimality of C (θ). 7
8 where E[ C ] denotes the expectation over Θ conditional on the deviation offer C. Here the first inequality follows from the assumption that V (a; θ) V (a; θ) for all θ θ and a A. This argument shows that the worst type agent θ will deviate from the equilibrium contract C (θ) toc, anticipating that the principal surely accepts such contract, which is a contradiction. Q.E.D. Proposition 2 states that Coase Theorem may not be extended to the case of asymmetric information when the first best action for the worst type is not implemented in the second best. This is because if some distortion arises at the bottom (the worst type) in the allocation µ the worst type always has the incentive to offer the contract which includes the first best action a FB (θ) in A game: Such contract offer attracts the principal and hence no PBEs exist for µ to be achieved. All the conditions stated in Proposition 2 are satisfied in the standard mechanism design problems which assume so called Sorting Condition 8 and monotone hazard rate condition are satisfied. These conditions result in the monotonicity of action choice and its downward distortion except for the most efficient type. However, even when these standard conditions are not met, we will show that some distortion always arises at the worst type when the following certain conditions hold. Assumption 1. (i) Θ is finite. (ii) P 0 (θ) > 0 for some θ θ. (iii) A is a closed interval in R. (iv) V (a; θ) and ψ(a; θ) are differentiable with respect to a A Assumption 2. (i) ψ(a; θ) ψ(a; θ) for all θ θ and a A. (ii) ψ a (a FB (θ); θ) >ψ a (a FB (θ); θ) for θ θ. Assumption 1 (i) and (ii) say that the type set is finite and prior belief puts some positive weight on other types than the worst one. The remaining conditions of Assumption 1 mean that we restrict attention to the smooth environment. Assumption 2 simply means that type θ agent is the worst in the sense that his action cost is the highest as well as he gives the principal the lowest value. Assumption 2 (ii) is weaker than the standard sorting condition, which requires ψ a is monotone with θ for all a. Proposition 3. Suppose that a FB (θ) a and Assumption 1 2 are satisfied. Then the optimal contract which solves the problem (P) does not induce the worst type θ agent to choose the first best action a FB (θ) with certainty. 8 Roughly speaking this condition ensures that the indifference curves of different type agents cross each other only once in the plane of action and transfer. 8
9 Proof. Suppose contrary to the claim that µ θ puts mass one to afb (θ). Since the following inequalities must be satisfied: t (θ) ψ(µ θ; θ) t (θ) ψ(µ θ; θ) t (θ) ψ(µ θ; θ) 0 due to (IC), Assumption 2 (i) and (IR), the relevant (IR) is only for the worst type θ. Thus (IR) must be binding at θ because of the optimality of µ θ, i.e., t (θ) =ψ(a FB (θ); θ). Now consider the change of the optimal contract as follows: Pick a contract C {a,t } such that t ψ(a ; θ) =t (θ) ψ(a FB (θ); θ) = 0, with a a FB (θ) ɛ for small ɛ>0, and offer such contract to the agent who reported he is of the worst type θ. Moreover, the contracts offered to other types θ θ are modified as C ɛ (θ) {µ θ,t (θ) αɛ} where α>0 and ɛ>0 is sufficiently small (See below for the specification of α). Note that all types θ θ do not mimic the other types θ θ because transfer is only modified for those types by subtracting the same constant αɛ. The worst type also does not have the incentive to mimic other types because t ψ(a ; θ) = 0 t (θ) ψ(µ θ; θ) > t (θ) αɛ ψ(µ θ ; θ) where the first inequality follows from the original (IC). Then we will check that every type θ θ also has no incentive to mimic the worst type θ. This constraint can be written by t (θ) αɛ ψ(µ θ ; θ) t ψ(a ; θ) = ψ(a ; θ) ψ(a ; θ) = ψ(a FB (θ) ɛ; θ) ψ(a FB (θ) ɛ; θ). Let L(ɛ) and R(ɛ) denote the first left hand and last right hand expressions of the above inequalities respectively. By the original (IC), we have L(0) R(0). Moreover, L (ɛ) = α and R (0) = ψ a (a FB (θ); θ) ψ a (a FB (θ); θ) < 0 by Assumption 2 (ii). Thus the above incentive compatibility constraint will be satisfied by taking small ɛ and α<min {ψ a(a FB (θ); θ) ψ a (a FB (θ); θ)}. θ θ Finally we show that the above modified contract improves the principal s expected payoff, which contradicts the optimality of {C (θ)} θ Θ. Under the modified contract, the principal obtains the following expected payoff Π(ɛ) θ θ P 0 (θ)[v (µ θ ; θ) t (θ)+αɛ]+p 0 (θ)[v (a FB (θ) ɛ; θ) ψ(a FB (θ) ɛ; θ)]. 9
10 Differentiating this with respect to ɛ and taking ɛ +0, we obtain Π (0) = α θ θ P 0 (θ) P 0 (θ)[v a (a FB (θ); θ) ψ a (a FB (θ); θ)]. Since the second term in the above expression becomes zero due to the optimality of a FB (θ) and its first order condition, we have Π (0) = α θ θ P 0 (θ) > 0 by Assumption 1 (ii), which is the desired contradiction. Q.E.D. Combining Proposition 2 and 3, we conclude that the equilibrium allocation µ in P game cannot be attained as a PBE in A game under fairly general conditions (Assumption 1 and 2), when the worst type is productive in the sense that a FB (θ) a and no bunching occurs at that type in the second best optimum. References [1] Chade, H., Silvers, R., Informed Principal, Moral Hazard, and the Value of a More Informative Technology, Economics Letters 74, [2] Inderst, R., Contractual Signaling in a Market Environment, Games and Economic Behavior 40, [3] Inderst, R., Incentive Schemes As a Signaling Device, Journal of Economic Behavior and Organization 44, [4] Jost, P-J., On the Role of Commitment in a Principal Agent Relationship with an Informed Principal, Journal of Economic Theory 68, [5] Maskin, E., Tirole, J., The Principal Agent Relationship with an Informed Principal II: Common Values, Econometrica 60,
Comparing allocations under asymmetric information: Coase Theorem revisited
Economics Letters 80 (2003) 67 71 www.elsevier.com/ locate/ econbase Comparing allocations nder asymmetric information: Coase Theorem revisited Shingo Ishigro* Gradate School of Economics, Osaka University,
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 informationKIER DISCUSSION PAPER SERIES
KIER DISCUSSION PAPER SERIES KYOTO INSTITUTE OF ECONOMIC RESEARCH http://www.kier.kyoto-u.ac.jp/index.html Discussion Paper No. 657 The Buy Price in Auctions with Discrete Type Distributions Yusuke Inami
More informationMONOPOLY (2) Second Degree Price Discrimination
1/22 MONOPOLY (2) Second Degree Price Discrimination May 4, 2014 2/22 Problem The monopolist has one customer who is either type 1 or type 2, with equal probability. How to price discriminate between the
More informationCompetition and Moral Hazard
Competition and Moral Hazard Shingo Ishiguro Graduate School of Economics Osaka University February 2004 Abstract This paper investigates the equilibrium consequences of a contractual market with moral
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 informationLoss-leader pricing and upgrades
Loss-leader pricing and upgrades Younghwan In and Julian Wright This version: August 2013 Abstract A new theory of loss-leader pricing is provided in which firms advertise low below cost) prices for certain
More informationAdverse Selection: The Market for Lemons
Andrew McLennan September 4, 2014 I. Introduction Economics 6030/8030 Microeconomics B Second Semester 2014 Lecture 6 Adverse Selection: The Market for Lemons A. One of the most famous and influential
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 informationOn 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
More informationAdverse Selection and Moral Hazard with Multidimensional Types
6631 2017 August 2017 Adverse Selection and Moral Hazard with Multidimensional Types Suehyun Kwon Impressum: CESifo Working Papers ISSN 2364 1428 (electronic version) Publisher and distributor: Munich
More informationEvaluating Strategic Forecasters. Rahul Deb with Mallesh Pai (Rice) and Maher Said (NYU Stern) Becker Friedman Theory Conference III July 22, 2017
Evaluating Strategic Forecasters Rahul Deb with Mallesh Pai (Rice) and Maher Said (NYU Stern) Becker Friedman Theory Conference III July 22, 2017 Motivation Forecasters are sought after in a variety of
More informationBargaining and Competition Revisited Takashi Kunimoto and Roberto Serrano
Bargaining and Competition Revisited Takashi Kunimoto and Roberto Serrano Department of Economics Brown University Providence, RI 02912, U.S.A. Working Paper No. 2002-14 May 2002 www.econ.brown.edu/faculty/serrano/pdfs/wp2002-14.pdf
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 informationPractice Problems 2: Asymmetric Information
Practice Problems 2: Asymmetric Information November 25, 2013 1 Single-Agent Problems 1. Nonlinear Pricing with Two Types Suppose a seller of wine faces two types of customers, θ 1 and θ 2, where θ 2 >
More informationThe Value of Information in an Agency Model with Moral Hazard
Faculty of Business and Law SCHOOL OF ACCOUNTING, ECONOMICS AND FINANCE School Working Paper - Economic Series 2006 SWP 2006/22 The Value of Information in an Agency Model with Moral Hazard Randy Silvers
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics May 29, 2015 Instructions This exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationUnraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets
Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren October, 2013 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that
More informationEffects of Wealth and Its Distribution on the Moral Hazard Problem
Effects of Wealth and Its Distribution on the Moral Hazard Problem Jin Yong Jung We analyze how the wealth of an agent and its distribution affect the profit of the principal by considering the simple
More informationDiscussion Papers In Economics And Business
Discussion Papers In Economics And Business Moral Hazard and Target Budgets Shingo Ishiguro, Yosuke Yasuda Discussion Paper 18-03 Graduate School of Economics and Osaka School of International Public Policy
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 informationWhere do securities come from
Where do securities come from We view it as natural to trade common stocks WHY? Coase s policemen Pricing Assumptions on market trading? Predictions? Partial Equilibrium or GE economies (risk spanning)
More informationSequential Investment, Hold-up, and Strategic Delay
Sequential Investment, Hold-up, and Strategic Delay Juyan Zhang and Yi Zhang February 20, 2011 Abstract We investigate hold-up in the case of both simultaneous and sequential investment. We show that if
More informationAuctions That Implement Efficient Investments
Auctions That Implement Efficient Investments Kentaro Tomoeda October 31, 215 Abstract This article analyzes the implementability of efficient investments for two commonly used mechanisms in single-item
More informationGraduate Microeconomics II Lecture 7: Moral Hazard. Patrick Legros
Graduate Microeconomics II Lecture 7: Moral Hazard Patrick Legros 1 / 25 Outline Introduction 2 / 25 Outline Introduction A principal-agent model The value of information 3 / 25 Outline Introduction A
More informationHomework 3: Asymmetric Information
Homework 3: Asymmetric Information 1. Public Goods Provision A firm is considering building a public good (e.g. a swimming pool). There are n agents in the economy, each with IID private value θ i [0,
More informationOn the 'Lock-In' Effects of Capital Gains Taxation
May 1, 1997 On the 'Lock-In' Effects of Capital Gains Taxation Yoshitsugu Kanemoto 1 Faculty of Economics, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113 Japan Abstract The most important drawback
More informationECONS 424 STRATEGY AND GAME THEORY HANDOUT ON PERFECT BAYESIAN EQUILIBRIUM- III Semi-Separating equilibrium
ECONS 424 STRATEGY AND GAME THEORY HANDOUT ON PERFECT BAYESIAN EQUILIBRIUM- III Semi-Separating equilibrium Let us consider the following sequential game with incomplete information. Two players are playing
More informationAn Incomplete Contracts Approach to Financial Contracting
Ph.D. Seminar in Corporate Finance Lecture 4 An Incomplete Contracts Approach to Financial Contracting (Aghion-Bolton, Review of Economic Studies, 1982) S. Viswanathan The paper analyzes capital structure
More information4. Adverse Selection
4. Adverse Selection Klaus M. Schmidt LMU Munich Contract Theory, Summer 2010 Klaus M. Schmidt (LMU Munich) 4. Adverse Selection Contract Theory, Summer 2010 1 / 51 Basic Readings Basic Readings Textbooks:
More informationCompeting Mechanisms with Limited Commitment
Competing Mechanisms with Limited Commitment Suehyun Kwon CESIFO WORKING PAPER NO. 6280 CATEGORY 12: EMPIRICAL AND THEORETICAL METHODS DECEMBER 2016 An electronic version of the paper may be downloaded
More informationECONOMICS SERIES SWP 2006/23. The Value of Information in a Principal-Agent Model with Moral Hazard: The Ex Ante Contracting Case.
Faculty of Business and Law School of Accounting, Economics and Finance ECONOMICS SERIES SWP 2006/23 The Value of Information in a Principal-Agent Model with Moral Hazard: The Ex Ante Contracting Case
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 informationAll Equilibrium Revenues in Buy Price Auctions
All Equilibrium Revenues in Buy Price Auctions Yusuke Inami Graduate School of Economics, Kyoto University This version: January 009 Abstract This note considers second-price, sealed-bid auctions with
More informationSequential versus Static Screening: An equivalence result
Sequential versus Static Screening: An equivalence result Daniel Krähmer and Roland Strausz First version: February 12, 215 This version: March 12, 215 Abstract We show that the sequential screening model
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 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 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 informationSequential Investment, Hold-up, and Strategic Delay
Sequential Investment, Hold-up, and Strategic Delay Juyan Zhang and Yi Zhang December 20, 2010 Abstract We investigate hold-up with simultaneous and sequential investment. We show that if the encouragement
More informationHomework 2: Dynamic Moral Hazard
Homework 2: Dynamic Moral Hazard Question 0 (Normal learning model) Suppose that z t = θ + ɛ t, where θ N(m 0, 1/h 0 ) and ɛ t N(0, 1/h ɛ ) are IID. Show that θ z 1 N ( hɛ z 1 h 0 + h ɛ + h 0m 0 h 0 +
More informationInformation and Evidence in Bargaining
Information and Evidence in Bargaining Péter Eső Department of Economics, University of Oxford peter.eso@economics.ox.ac.uk Chris Wallace Department of Economics, University of Leicester cw255@leicester.ac.uk
More informationWeb Appendix: Proofs and extensions.
B eb Appendix: Proofs and extensions. B.1 Proofs of results about block correlated markets. This subsection provides proofs for Propositions A1, A2, A3 and A4, and the proof of Lemma A1. Proof of Proposition
More informationFinite Memory and Imperfect Monitoring
Federal Reserve Bank of Minneapolis Research Department Finite Memory and Imperfect Monitoring Harold L. Cole and Narayana Kocherlakota Working Paper 604 September 2000 Cole: U.C.L.A. and Federal Reserve
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 informationMA300.2 Game Theory 2005, LSE
MA300.2 Game Theory 2005, LSE Answers to Problem Set 2 [1] (a) This is standard (we have even done it in class). The one-shot Cournot outputs can be computed to be A/3, while the payoff to each firm can
More informationCHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION
CHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION Szabolcs Sebestyén szabolcs.sebestyen@iscte.pt Master in Finance INVESTMENTS Sebestyén (ISCTE-IUL) Choice Theory Investments 1 / 65 Outline 1 An Introduction
More informationFinancial Economics Field Exam August 2011
Financial Economics Field Exam August 2011 There are two questions on the exam, representing Macroeconomic Finance (234A) and Corporate Finance (234C). Please answer both questions to the best of your
More informationDARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 21. Dartmouth College, Department of Economics: Economics 21, Summer 02. Topic 5: Information
Dartmouth College, Department of Economics: Economics 21, Summer 02 Topic 5: Information Economics 21, Summer 2002 Andreas Bentz Dartmouth College, Department of Economics: Economics 21, Summer 02 Introduction
More information(1 p)(1 ε)+pε p(1 ε)+(1 p)ε. ε ((1 p)(1 ε) + pε). This is indeed the case since 1 ε > ε (in turn, since ε < 1/2). QED
July 2008 Philip Bond, David Musto, Bilge Yılmaz Supplement to Predatory mortgage lending The key assumption in our model is that the incumbent lender has an informational advantage over the borrower.
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 informationProblem Set 2. Theory of Banking - Academic Year Maria Bachelet March 2, 2017
Problem Set Theory of Banking - Academic Year 06-7 Maria Bachelet maria.jua.bachelet@gmai.com March, 07 Exercise Consider an agency relationship in which the principal contracts the agent, whose effort
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 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 informationProblem Set: Contract Theory
Problem Set: Contract Theory Problem 1 A risk-neutral principal P hires an agent A, who chooses an effort a 0, which results in gross profit x = a + ε for P, where ε is uniformly distributed on [0, 1].
More informationWhen does strategic information disclosure lead to perfect consumer information?
When does strategic information disclosure lead to perfect consumer information? Frédéric Koessler Régis Renault April 7, 2010 (Preliminary) Abstract A firm chooses a price and how much information to
More informationOnline Appendix for Military Mobilization and Commitment Problems
Online Appendix for Military Mobilization and Commitment Problems Ahmer Tarar Department of Political Science Texas A&M University 4348 TAMU College Station, TX 77843-4348 email: ahmertarar@pols.tamu.edu
More informationHomework 1: Basic Moral Hazard
Homework 1: Basic Moral Hazard October 10, 2011 Question 1 (Normal Linear Model) The following normal linear model is regularly used in applied models. Given action a R, output is q = a + x, where x N(0,
More informationAn optimal board system : supervisory board vs. management board
An optimal board system : supervisory board vs. management board Tomohiko Yano Graduate School of Economics, The University of Tokyo January 10, 2006 Abstract We examine relative effectiveness of two kinds
More informationTopics in Contract Theory Lecture 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
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 informationDynamic signaling and market breakdown
Journal of Economic Theory ( ) www.elsevier.com/locate/jet Dynamic signaling and market breakdown Ilan Kremer, Andrzej Skrzypacz Graduate School of Business, Stanford University, Stanford, CA 94305, USA
More informationd. Find a competitive equilibrium for this economy. Is the allocation Pareto efficient? Are there any other competitive equilibrium allocations?
Answers to Microeconomics Prelim of August 7, 0. Consider an individual faced with two job choices: she can either accept a position with a fixed annual salary of x > 0 which requires L x units of labor
More informationTHE MIRRLEES APPROACH TO MECHANISM DESIGN WITH RENEGOTIATION (WITH APPLICATIONS TO HOLD-UP AND RISK SHARING) By Ilya Segal and Michael D.
Econometrica, Vol. 70, No. 1 (January, 2002), 1 45 THE MIRRLEES APPROACH TO MECHANISM DESIGN WITH RENEGOTIATION (WITH APPLICATIONS TO HOLD-UP AND RISK SHARING) By Ilya Segal and Michael D. Whinston 1 The
More informationReputation and Signaling in Asset Sales: Internet Appendix
Reputation and Signaling in Asset Sales: Internet Appendix Barney Hartman-Glaser September 1, 2016 Appendix D. Non-Markov Perfect Equilibrium In this appendix, I consider the game when there is no honest-type
More informationDefinition of Incomplete Contracts
Definition of Incomplete Contracts Susheng Wang 1 2 nd edition 2 July 2016 This note defines incomplete contracts and explains simple contracts. Although widely used in practice, incomplete contracts have
More informationFinite Memory and Imperfect Monitoring
Federal Reserve Bank of Minneapolis Research Department Staff Report 287 March 2001 Finite Memory and Imperfect Monitoring Harold L. Cole University of California, Los Angeles and Federal Reserve Bank
More informationDynamic games with incomplete information
Dynamic games with incomplete information Perfect Bayesian Equilibrium (PBE) We have now covered static and dynamic games of complete information and static games of incomplete information. The next step
More informationProblem Set: Contract Theory
Problem Set: Contract Theory Problem 1 A risk-neutral principal P hires an agent A, who chooses an effort a 0, which results in gross profit x = a + ε for P, where ε is uniformly distributed on [0, 1].
More informationBest-Reply Sets. Jonathan Weinstein Washington University in St. Louis. This version: May 2015
Best-Reply Sets Jonathan Weinstein Washington University in St. Louis This version: May 2015 Introduction The best-reply correspondence of a game the mapping from beliefs over one s opponents actions to
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 informationIn Diamond-Dybvig, we see run equilibria in the optimal simple contract.
Ennis and Keister, "Run equilibria in the Green-Lin model of financial intermediation" Journal of Economic Theory 2009 In Diamond-Dybvig, we see run equilibria in the optimal simple contract. When the
More informationLecture 3: Information in Sequential Screening
Lecture 3: Information in Sequential Screening NMI Workshop, ISI Delhi August 3, 2015 Motivation A seller wants to sell an object to a prospective buyer(s). Buyer has imperfect private information θ about
More informationProblem Set 3: Suggested Solutions
Microeconomics: Pricing 3E00 Fall 06. True or false: Problem Set 3: Suggested Solutions (a) Since a durable goods monopolist prices at the monopoly price in her last period of operation, the prices must
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 informationNon-Exclusive Competition in the Market for Lemons
Non-Exclusive Competition in the Market for Lemons Andrea Attar Thomas Mariotti François Salanié October 2007 Abstract In order to check the impact of the exclusivity regime on equilibrium allocations,
More informationSupplementary Material for: Belief Updating in Sequential Games of Two-Sided Incomplete Information: An Experimental Study of a Crisis Bargaining
Supplementary Material for: Belief Updating in Sequential Games of Two-Sided Incomplete Information: An Experimental Study of a Crisis Bargaining Model September 30, 2010 1 Overview In these supplementary
More informationTwo-Dimensional Bayesian Persuasion
Two-Dimensional Bayesian Persuasion Davit Khantadze September 30, 017 Abstract We are interested in optimal signals for the sender when the decision maker (receiver) has to make two separate decisions.
More informationUniversidade de Aveiro Departamento de Economia, Gestão e Engenharia Industrial. Documentos de Trabalho em Economia Working Papers in Economics
Universidade de Aveiro Departamento de Economia, Gestão e Engenharia Industrial Documentos de Trabalho em Economia Working Papers in Economics ÈUHD&LHQWtILFDGHFRQRPLD Qž 7KHVLPSOHDQDO\WLFVRILQIRUPDWLRQ
More informationEconometrica Supplementary Material
Econometrica Supplementary Material PUBLIC VS. PRIVATE OFFERS: THE TWO-TYPE CASE TO SUPPLEMENT PUBLIC VS. PRIVATE OFFERS IN THE MARKET FOR LEMONS (Econometrica, Vol. 77, No. 1, January 2009, 29 69) BY
More informationMicroeconomic Theory (501b) Comprehensive Exam
Dirk Bergemann Department of Economics Yale University Microeconomic Theory (50b) Comprehensive Exam. (5) Consider a moral hazard model where a worker chooses an e ort level e [0; ]; and as a result, either
More informationIncentive Compatibility: Everywhere vs. Almost Everywhere
Incentive Compatibility: Everywhere vs. Almost Everywhere Murali Agastya Richard T. Holden August 29, 2006 Abstract A risk neutral buyer observes a private signal s [a, b], which informs her that the mean
More informationSCREENING BY THE COMPANY YOU KEEP: JOINT LIABILITY LENDING AND THE PEER SELECTION EFFECT
SCREENING BY THE COMPANY YOU KEEP: JOINT LIABILITY LENDING AND THE PEER SELECTION EFFECT Author: Maitreesh Ghatak Presented by: Kosha Modi February 16, 2017 Introduction In an economic environment where
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 informationOnline Appendix. Bankruptcy Law and Bank Financing
Online Appendix for Bankruptcy Law and Bank Financing Giacomo Rodano Bank of Italy Nicolas Serrano-Velarde Bocconi University December 23, 2014 Emanuele Tarantino University of Mannheim 1 1 Reorganization,
More informationLiability, Insurance and the Incentive to Obtain Information About Risk. Vickie Bajtelsmit * Colorado State University
\ins\liab\liabinfo.v3d 12-05-08 Liability, Insurance and the Incentive to Obtain Information About Risk Vickie Bajtelsmit * Colorado State University Paul Thistle University of Nevada Las Vegas December
More informationMicroeconomics Qualifying Exam
Summer 2018 Microeconomics Qualifying Exam There are 100 points possible on this exam, 50 points each for Prof. Lozada s questions and Prof. Dugar s questions. Each professor asks you to do two long questions
More informationBACKGROUND RISK IN THE PRINCIPAL-AGENT MODEL. James A. Ligon * University of Alabama. and. Paul D. Thistle University of Nevada Las Vegas
mhbr\brpam.v10d 7-17-07 BACKGROUND RISK IN THE PRINCIPAL-AGENT MODEL James A. Ligon * University of Alabama and Paul D. Thistle University of Nevada Las Vegas Thistle s research was supported by a grant
More informationTitleMoral Hazard and Renegotiation with. Citation Review of Economic Studies, 68(1):
TitleMoral Hazard and Renegotiation with Author(s) Ishiguro, Shingo; Itoh, Hideshi Citation Review of Economic Studies, 68(1): Issue 2001-01 Date Type Journal Article Text Version author URL http://hdl.handle.net/10086/14116
More informationMartingale Pricing Theory in Discrete-Time and Discrete-Space Models
IEOR E4707: Foundations of Financial Engineering c 206 by Martin Haugh Martingale Pricing Theory in Discrete-Time and Discrete-Space Models These notes develop the theory of martingale pricing in a discrete-time,
More informationPersuasion in Global Games with Application to Stress Testing. Supplement
Persuasion in Global Games with Application to Stress Testing Supplement Nicolas Inostroza Northwestern University Alessandro Pavan Northwestern University and CEPR January 24, 208 Abstract This document
More informationPractice Problems 1: Moral Hazard
Practice Problems 1: Moral Hazard December 5, 2012 Question 1 (Comparative Performance Evaluation) Consider the same normal linear model as in Question 1 of Homework 1. This time the principal employs
More informationMANAGEMENT SCIENCE doi /mnsc ec
MANAGEMENT SCIENCE doi 10.1287/mnsc.1110.1334ec e-companion ONLY AVAILABLE IN ELECTRONIC FORM informs 2011 INFORMS Electronic Companion Trust in Forecast Information Sharing by Özalp Özer, Yanchong Zheng,
More informationAdverse Selection When Agents Envy Their Principal. KANGSIK CHOI June 7, 2004
THE INSTITUTE OF ECONOMIC RESEARCH Working Paper Series No. 92 Adverse Selection When Agents Envy Their Principal KANGSIK CHOI June 7, 2004 KAGAWA UNIVERSITY Takamatsu, Kagawa 760-8523 JAPAN Adverse Selection
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 information1 The principal-agent problems
1 The principal-agent problems The principal-agent problems are at the heart of modern economic theory. One of the reasons for this is that it has widespread applicability. We start with some eamples.
More informationHedonic Equilibrium. December 1, 2011
Hedonic Equilibrium December 1, 2011 Goods have characteristics Z R K sellers characteristics X R m buyers characteristics Y R n each seller produces one unit with some quality, each buyer wants to buy
More informationFundamental Theorems of Welfare Economics
Fundamental Theorems of Welfare Economics Ram Singh October 4, 015 This Write-up is available at photocopy shop. Not for circulation. In this write-up we provide intuition behind the two fundamental theorems
More informationUp till now, we ve mostly been analyzing auctions under the following assumptions:
Econ 805 Advanced Micro Theory I Dan Quint Fall 2007 Lecture 7 Sept 27 2007 Tuesday: Amit Gandhi on empirical auction stuff p till now, we ve mostly been analyzing auctions under the following assumptions:
More informationPrice Setting with Interdependent Values
Price Setting with Interdependent Values Artyom Shneyerov Concordia University, CIREQ, CIRANO Pai Xu University of Hong Kong, Hong Kong December 11, 2013 Abstract We consider a take-it-or-leave-it price
More informationAuctions in the wild: Bidding with securities. Abhay Aneja & Laura Boudreau PHDBA 279B 1/30/14
Auctions in the wild: Bidding with securities Abhay Aneja & Laura Boudreau PHDBA 279B 1/30/14 Structure of presentation Brief introduction to auction theory First- and second-price auctions Revenue Equivalence
More information