Moral Hazard: Hidden Action
|
|
- Beverley Henry
- 6 years ago
- Views:
Transcription
1 Moral Hazard: Hidden Action Part of these Notes were taken (almost literally) from Rasmusen, 2007 UIB Course (UIB) MH-Hidden Actions Course / 29
2 A Principal-agent Model. The Production Game Two individuals: Principal (P) and Agent (A) P + A generate a surplus that depends on the e ort of A, namely e, and possibly on the realization of a random variable θ (a state of the world) P proposes a contract c to A, which can be accepted or refused. Accepts. A chooses an e ort and a surplus q (e, θ) is generated. A receives a payment w (c). P obtains q (e, θ) w (c). Does not accept. No surplus is generated (We could assume that A makes the o er) e 2 E R θ 2 Ω R is chosen according to a probability density f (θ). q : E Ω! R is increasing in e. (UIB) MH-Hidden Actions Course / 29
3 The preferences Satisfy the von Neumann-Morgenstern assumptions (?) Principal: Agent: V (q w) denotes her elementary utility function, de ned over her income. V 0 > 0. Increasing with income. V Risk-neutral if V 00 = 0 and risk-averse when V 00 < 0. U (w, e) denotes her elementary utility function U w (w, e) > 0. Increasing with income U e (w, e) < 0. Decreasing in e. U ww (w, e) 0. Risk-neutral if U ww = 0 and risk-averse if U ww < 0. U ee (w, e) 0. Usually we will assume separability: U (w, e) = u(w) v(e). (UIB) MH-Hidden Actions Course / 29
4 The contract, utilities and the reservation utility Veri able e ort level: c = w (q, e), where w (q) denotes the wage received by the agent exerting e ort e when the outcome is q. Unveri able e ort level: c = w (q) If two or more Principals compete to employ an agent then their equilibrium pro t equals zero (Bertrand competition). If many agents compete to work for the Principal then the agent s equilibrium utility is at least equal to what they can obtain by not accepting the job, called the reservation utility, U. (UIB) MH-Hidden Actions Course / 29
5 Production game I: Full information The Principal makes the o er. Assume that e is observed by P! c = w (q (e, θ), e) = w (e) and q (e, θ) = q e, θ 0 The problem of the Principal: max V (q (e) w) e,w s.to : U (w, e) U As V 0 (q (e) e : V 0 (q (e) w)q 0 U (w, e) (e) + λ = 0 e w (e) : V 0 U (w, e) (q (e) w) + λ = 0 w λ : λ U (w, e) U = 0, λ 0 w) > 0 and U (w,e) w > 0 we obtain λ > 0 so that U (w, e ) U = 0. (UIB) MH-Hidden Actions Course / 29
6 Thus, EFFICIENCY! 0 = V 0 (q (e ) w ) " =) MRS P e,w = q 0 (e ) = U (w,e ) e U (w,e ) w U (w (e ),e ) e U (w (e ),e ) w q 0 (e) + # = MRS A e,w The Principal must design a contract such that w (e ) = w that induces agent to choose e. There are many ways: 1 Forcing contract: w (e) = w if e = e and zero otherwise. 2 Threshold contract: w (e) = w if e e and zero otherwise. 3 Continuous contract: w (e) satisfying U (w (e ), e ) w w (e ) e + U (w (e ), e ) e = 0 SOC < 0 (UIB) MH-Hidden Actions Course / 29
7 Production game II: Full information. Agent moves rst The agent makes the o er e is observed by P! c = w (q (e)) = w (e). The problem of the Agent: The FOC yield (EFFICIENCY!) max U (w, e) e,w s.to : V (q (e) w) 0 MRS P e,w = q 0 (e ) = V (q (e ) w ) = 0 U (w (e ),e ) e U (w (e ),e ) w = MRS A e,w I.e., the contract is e cient (as before), and the Principal obtains her "reservation pro ts" of zero. (UIB) MH-Hidden Actions Course / 29
8 Production game III: A at wage under certainty Assume now that the P cannot condition the wage neither to the output nor the e ort. The outcome is obvious and (generally) ine cient. If w is such that U (w, 0) U then clearly the agent accepts the job and exerts zero e ort. So, P o ers w satisfying U (w, 0) = U if V (q (0), w ) 0 and/or ew satisfying U ( ew, 0) < U when V (q (0), w ) < 0 so that the contract is not accepted. This is a clear example of moral hazard: the agent chooses an action that goes against the interests of the Principal, as she cannot use any contract to punish him. As we will see next, a clever contract can overcome moral hazard by conditioning the wage on "something" that is observable and correlated with e ort (such as output). If there is nothing to condition the wage, however, the agency problem cannot be solved (UIB) MH-Hidden Actions Course / 29
9 Production game IV: An output based wage under certainty Assume that the principal cannot observe e but she can observe q and specify w (q). It is easy to check that the outcome is the same than that obtained in Production Game I. This is due to our assumption that q 0 (e) > 0 so that conditioning the wage to q is equivalent to condition it to the e ort level. Thus, the true agency problem occurs when q and e are not perfectly correlated. (UIB) MH-Hidden Actions Course / 29
10 Production game V: An output based wage under Uncertainty The Principal cannot observe e but she can observe q and speci es w (q). q (e, θ) 6= q e, θ 0 for some θ, θ 0 2 Ω and there is (e, θ), e 0, θ 0 such that q (e, θ) = q e 0, θ 0! Hidden action Remember that θ is chosen (by Nature) according to some f (θ). A given output can now be produced by several e orts. Thus, a forcing contract will not necessarily induce the desired e ort. (UIB) MH-Hidden Actions Course / 29
11 First/Second Best contracts In Production Game V Under Uncertainty and Asymmetric Information we observe a trade o : Due to uncertainty, the Principal wants to insurance the agent against risk as this will allows her to o er a lower acceptable expected wage. By doing so she reduces the incentives of the agent to put e ort, since (due to asymmetric information), e ort is not contractible. We will distinguish between two types of optimality: 1 "First-Best Contract" will be referred to the allocation that is optimal when both players have the same information sets and all variables are contractible. 2 "Second-Best Contract" will be referred to the contract that is optimal given information asymmetry and constraints in writing contracts. The di erence in welfare between the two contracts is the Cost of the Agency Problem. (UIB) MH-Hidden Actions Course / 29
12 The ICC and The PC In the PG V, the principal s objective is to maximize her utility knowing that: 1 The agent is free to reject the contract. 2 The agent is free to choose the e ort level. The constraints that guarantee that A accepts the contract and that the agent chooses the desired e ort e ort level are named the Participation constraint and the Incentive Compatibility constraint, respectively. The Principals problem is, then: max E θv (q (e, θ) e,w (q) w (q (e, θ))) ICC : e 2 arg max E θ U (w (q (e, θ)), e) e PC : E θ U (w (q (e, θ)), e) U (UIB) MH-Hidden Actions Course / 29
13 How to solve the problem Three-Step Procedure (when the Principal is risk-neutral) 1 For any e, determine the set of wage contracts that induce the agent to choose such an e ort level. 2 For any e, nd the contract which supports this e ort level at the lowest cost to the Principal. 3 Choose the e ort level that maximizes pro ts. In general, when P is not risk-neutral, we must use the First Order Approach, consisting on substituting the ICC by the FOC and the SOC of the Agent s maximization problem. When e is a discrete variable we apply a Two-Step Procedure: (2) i (3). (UIB) MH-Hidden Actions Course / 29
14 Optimal Contracts: the Broadway Game This game illustrates a peculiarity of optimal contracts: they are not necessarily monotone. There is a producer and investors. The game is as follows 1 Investors o er a wage contract w(q) as a function of the revenue q. 2 The producer either accepts or reject the contract. 3 The producer selects Embezzle or Do not Embezzle. 4 Nature chooses the state of the world to be Success or Failure with equal probability. Revenues are shown in the next table(s) (UIB) MH-Hidden Actions Course / 29
15 The Broadway Game I Conditional probabilities: F (1/2) S(1/2) E DNE =) E 1/2 1/2 0 DNE 1/2 0 1/2 Payo s: The producer is risk-averse and the investors are risk-neutral. U (w (q) + 50) if E U p = U (w (q)) if DNE, U p = q w (q), U = U (100) Contracts: Investors only observe q so the possible contracts are c = (w ( 100), w (100), w (500)). (UIB) MH-Hidden Actions Course / 29
16 The Broadway Game I Expected utility of the producer (A): 1 U p = 2 U (w ( 100) + 50) U (w (+100) + 50) if E 1 2 U (w ( 100)) U (w (+500)) if DNE The ICC is: 1 2 U (w ( 100)) + 1 U (w (+500)) U (w ( 100) + 50) + 1 U (w (+100) + 50) 2 The PC is: 1 2 U (w ( 100)) + 1 U (w (+500)) U (100) 2 (UIB) MH-Hidden Actions Course / 29
17 The Broadway Game I Since investors want to impose as little risk as possible to A (allows to reduce the expected wage) they will ideally select w ( 100) = w (+500) satisfying the PC with equality, which provides full insurance. In general, this may go against incentives. However, as Pr (+100jDNE ) = 0 and Pr (+100jE ) > 0 this is not the case and the optimal solution of investors is easily achieved by selecting This yields so that it is pro table. w ( 100) = w (+500) = 100 w (+100) = Up e = 1 2 ( 100) + 1 (+500) 100 = 100 > 0 2 (UIB) MH-Hidden Actions Course / 29
18 The Broadway Game I This contract illustrates the idea that the principal rewards inputs, not output. If the contract was monotone with respect to output, this would mean that she rewards Nature, not the agent. Thus, the optimal wage structure would depend on the information about the choice of the agent that can be inferred by observing the outcome. Sometimes, as in the previous example, there is a su cient statistic to exactly infer the agent s choice (if +100 is observed, it means E). In general, when there is no su cient statistic for wrong actions, (i) the rst best cannot be achieved and (ii) such an extreme boiling-in-oil contract cannot be used. However, when the e orts level alters the distribution of the outcomes, the optimal contracts would also include such a dependence. Consequently, the contract is not necessarily monotone. (UIB) MH-Hidden Actions Course / 29
19 The Broadway Game II =) F (0.5) ms(0.3) MS(0.2) E DNE E DNE w ( 100) = w (+450) = w (+575) = 100 and w (+400) = (or smaller than...) (UIB) MH-Hidden Actions Course / 29
20 The Broadway Game III. How Public Information may hurt both players Assume that before the agent takes his action both players can tell whether the show will be a major success or not. I.e., they know that they will be either in scenario A or B given below: A : B : F (0.625) ms(0.375) E DNE MS(1) E +400 DNE +575 Expected pro ts if DNE: ( ) (0.625 ( 100) ). However, in case A the agent will choose E... (UIB) MH-Hidden Actions Course / 29
21 A nite set of outcome and two e ort levels X = fx 1,...x n g e 2 e H, e L, that induce p i e H = p H i and p i e L = p L i. v e H > v e L U (w, e) = u(w) v(e) Constraints of P when selecting c = (w 1,..., w n ) in order to induce e L 1 Participation: n i =1 p i (e L )u(w i ) v(e L ) U. 2 Incentives: n i =1 p i (e L )u(w i ) v(e L ) n i =1 p i (e H )u(w i ) v(e H ). To induce e L is simple. Any xed wage satisfying PC would. (MAYBE IT IS NOT OPTIMAL!!) Di culties appear when P wants to induce e H. (UIB) MH-Hidden Actions Course / 29
22 Inducing a high e ort L(w 1,..., w n, λ, µ) = n i=1 pi H B(x i w i ) +λ n i=1 pi H u(w i ) v(e H ) U +µ n i=1 p H i pi L u(wi ) v(e H ) + v(e L ), FOC: 1 pi H B 0 (x i w i ) + λpi H u 0 (w i ) + µ pi H pi L u 0 (w i ) = 0 for all i = 1,..., n 2 0 = λ n i=1 pi H u(w i ) v(e H ) U, λ = µ n i=1 p H i u(wi ) v(e H ) + v(e L ), µ 0. p L i (UIB) MH-Hidden Actions Course / 29
23 Risk neutral Principal: B 00 () = 0 We have that h pi H + λpi H u 0 (w i ) + µ pi H p L i i u 0 (w i ) = 0 for all i = 1,..., n or, (we know that u 0 (w i ) > 0), pi H h u 0 (w i ) = λph i + µ pi H Adding up all these n FOC we obtain p L i i for all i = 1,..., n which implies That is, PC is binding. λ = n i=1 p H i u 0 (w i ) > 0 n pi H u(w i ) v(e H ) U = 0 i=1 (UIB) MH-Hidden Actions Course / 29
24 From we also obtain pi H h u 0 (w i ) = λph i + µ pi H 1 u 0 (w i ) = λ + µ 1 pi L pi H p L i i for all i = 1,..., n for all i = 1,..., n Can we have µ = 0? When u 00 = 0 it is possible. If u 00 < 0, this would imply that w i is constant =) e = e L. Thus, µ = 0 and ICC (for e H ) cannot be simultaneously satis ed, which implies that µ > 0. In these cases, the wages w i do not depend directly on x i but on p L i /ph i, referred as the Likelihood ratio. higher p L i /ph i =) higher u 0 (w i ) =) lower w i. (UIB) MH-Hidden Actions Course / 29
25 The likelihood ratio Pr x i j e L Pr (x i j e H ) = pl i p H i = Pr eh Pr (e L ) Pr el, x i Pr (e H, x i ) = Φ Pr el, x i Pr (e H, x i ) It means that Pr e L, x i / Pr e H, x i increases with the likelihood ratio. Thus, for any x i, as high is the likelihood ratio as low is the relative probability that e ort is e H and therefore as low is the wage. (UIB) MH-Hidden Actions Course / 29
26 Example so that crop A e L e H pi L/pH i x 1 2/3 1/3 2 x 2 1/3 2/3 0.5 crop B e L e H pi L/pH i x 1 4/5 1/5 4 x 2 1/5 4/ p1 L(B) p1 H (B) > pl 1 (A) p1 H (A) > pl 2 (A) p2 H (A) > pl 2 (B) p2 H (B) w B 1 < w A 1 < w A 2 < w B 2. A good crop receives more reward in case B than in case A. in case B, if the agent puts high e ort he obtains a good crop with probability 4/5 = 80% In case A this probability is only 2/3 = 67% =) obtaining a good crop in B reveals that it is highly probable that the e ort has been high. (UIB) MH-Hidden Actions Course / 29
27 Example. Non-monotone contracts e L e H pi L/pH i x 1 1/6 1/3 1/2 x 2 2/3 1/3 2 x 3 1/6 1/3 1/2 =) w 1 = w 3 > w 2 Stochastic dominance does not imply monotone contracts, too. Consider, for instance l (e 1 ) = (x 1, x 2, x 3 ; 1/4, 1/4, 1/2) l (e 2 ) = (x 1, x 2, x 3 ; 1/8, 3/8, 1/2) so that l (e 1 ) 1 l (e 2 ). The likelihood ratios are (2, 2/3, 1) and therefore w 2 > w 3 > w 1. (UIB) MH-Hidden Actions Course / 29
28 Optimal contracts: 4 generic cases 1 B 00 = 0, u 00 < 0! c? 2 B 00 = 0, u 00 = 0! c? 3 B 00 < 0, u 00 < 0! c? 4 B 00 < 0, u 00 = 0! c? Problem Find an example of optimal contracts for any of the previous situations when v(e) = e, U = 1 and the conditional probabilities are given next x 1 = 10 x 2 = 100 e L = e H = (UIB) MH-Hidden Actions Course / 29
29 Bibliography E. Rasmusen (2007), "Games and Information: An Introduction to Game Theory", chapter 7. Blackwell Publishing. D. Cardona (2012), "Apunts d Economia de la Informació (20619)". Arxius/Assignatures/EI/Apunts-EI-2013.pdf (UIB) MH-Hidden Actions Course / 29
Game Theory and Economics of Contracts Lecture 5 Static Single-agent Moral Hazard Model
Game Theory and Economics of Contracts Lecture 5 Static Single-agent Moral Hazard Model Yu (Larry) Chen School of Economics, Nanjing University Fall 2015 Principal-Agent Relationship Principal-agent relationship
More informationMoral Hazard. Felix Munoz-Garcia. Advanced Microeconomics II - Washington State University
Moral Hazard Felix Munoz-Garcia Advanced Microeconomics II - Washington State University Moral Hazard Reading materials: Start with Prajit Dutta, Chapter 19. MWG, Chapter 14 Macho-Stadler and Perez-Castrillo,
More informationThis is designed for one 75-minute lecture using Games and Information. October 3, 2006
This is designed for one 75-minute lecture using Games and Information. October 3, 2006 1 7 Moral Hazard: Hidden Actions PRINCIPAL-AGENT MODELS The principal (or uninformed player) is the player who has
More informationMoral Hazard. EC202 Lectures XV & XVI. Francesco Nava. February London School of Economics. Nava (LSE) EC202 Lectures XV & XVI Feb / 19
Moral Hazard EC202 Lectures XV & XVI Francesco Nava London School of Economics February 2011 Nava (LSE) EC202 Lectures XV & XVI Feb 2011 1 / 19 Summary Hidden Action Problem aka: 1 Moral Hazard Problem
More informationScreening. Diego Moreno Universidad Carlos III de Madrid. Diego Moreno () Screening 1 / 1
Screening Diego Moreno Universidad Carlos III de Madrid Diego Moreno () Screening 1 / 1 The Agency Problem with Adverse Selection A risk neutral principal wants to o er a menu of contracts to be o ered
More informationGame Theory, Information, Incentives
Game Theory, Information, Incentives Ronald Wendner Department of Economics Graz University, Austria Course # 320.501: Analytical Methods (part 6) The Moral Hazard Problem Moral hazard as a problem of
More informationSome Notes on Moral Hazard
Some Notes on Moral Hazard John Morgan University of California at Berkeley Preliminaries Up until this point, we have been concerned mainly with the problem of private information on the part of the agent,
More informationTeoria das organizações e contratos
Teoria das organizações e contratos Chapter 6: Adverse Selection with two types Mestrado Profissional em Economia 3 o trimestre 2015 EESP (FGV) Teoria das organizações e contratos 3 o trimestre 2015 1
More informationEconS Microeconomic Theory II Midterm Exam #2 - Answer Key
EconS 50 - Microeconomic Theory II Midterm Exam # - Answer Key 1. Revenue comparison in two auction formats. Consider a sealed-bid auction with bidders. Every bidder i privately observes his valuation
More informationMinimum Wages and Excessive E ort Supply
Minimum Wages and Excessive E ort Supply Matthias Kräkel y Anja Schöttner z Abstract It is well-known that, in static models, minimum wages generate positive worker rents and, consequently, ine ciently
More informationHidden information. Principal s payoff: π (e) w,
Hidden information Section 14.C. in MWG We still consider a setting with information asymmetries between the principal and agent. However, the effort is now perfectly observable. What is unobservable?
More informationMicroeconomic Theory (501b) Problem Set 10. Auctions and Moral Hazard Suggested Solution: Tibor Heumann
Dirk Bergemann Department of Economics Yale University Microeconomic Theory (50b) Problem Set 0. Auctions and Moral Hazard Suggested Solution: Tibor Heumann 4/5/4 This problem set is due on Tuesday, 4//4..
More informationEC476 Contracts and Organizations, Part III: Lecture 2
EC476 Contracts and Organizations, Part III: Lecture 2 Leonardo Felli 32L.G.06 19 January 2015 Moral Hazard: Consider the contractual relationship between two agents (a principal and an agent) The principal
More informationLecture Notes - Dynamic Moral Hazard
Lecture Notes - Dynamic Moral Hazard Simon Board and Moritz Meyer-ter-Vehn October 27, 2011 1 Marginal Cost of Providing Utility is Martingale (Rogerson 85) 1.1 Setup Two periods, no discounting Actions
More informationLecture Notes - Dynamic Moral Hazard
Lecture Notes - Dynamic Moral Hazard Simon Board and Moritz Meyer-ter-Vehn October 23, 2012 1 Dynamic Moral Hazard E ects Consumption smoothing Statistical inference More strategies Renegotiation Non-separable
More informationNotes on Mechanism Designy
Notes on Mechanism Designy ECON 20B - Game Theory Guillermo Ordoñez UCLA February 0, 2006 Mechanism Design. Informal discussion. Mechanisms are particular types of games of incomplete (or asymmetric) information
More informationLinear Contracts. Ram Singh. February 23, Department of Economics. Ram Singh (Delhi School of Economics) Moral Hazard February 23, / 22
Ram Singh Department of Economics February 23, 2015 Ram Singh (Delhi School of Economics) Moral Hazard February 23, 2015 1 / 22 SB: Linear Contracts I Linear Contracts Assumptions: q(e, ɛ) = e + ɛ, where
More informationNotes on the Thomas and Worrall paper Econ 8801
Notes on the Thomas and Worrall paper Econ 880 Larry E. Jones Introduction The basic reference for these notes is: Thomas, J. and T. Worrall (990): Income Fluctuation and Asymmetric Information: An Example
More informationGeneral idea. Firms can use competition between agents for. We mainly focus on incentives. 1 incentive and. 2 selection purposes 3 / 101
3 Tournaments 3.1 Motivation General idea Firms can use competition between agents for 1 incentive and 2 selection purposes We mainly focus on incentives 3 / 101 Main characteristics Agents fulll similar
More information1. Linear Incentive Schemes
ECO 317 Economics of Uncertainty Fall Term 2009 Slides to accompany 20. Incentives for Effort - One-Dimensional Cases 1. Linear Incentive Schemes Agent s effort x, principal s outcome y. Agent paid w.
More informationExternalities and PG. MWG- Chapter 11
Externalities and PG MWG- Chapter 11 Simple Bilateral Externality When external e ects are present, CE are not PO. Assume: 1 Two consumers i = 1, 2 2 The actions of these consumers do not a ect prices
More informationMoral Hazard: Characterization of SB
Moral Hazard: Characterization of SB Ram Singh Department of Economics March 2, 2015 Ram Singh (Delhi School of Economics) Moral Hazard March 2, 2015 1 / 19 Characterization of Second Best Contracts I
More informationMoral Hazard and Persistence
Moral Hazard and Persistence Hugo Hopenhayn Department of Economics UCLA Arantxa Jarque Department of Economics U. of Alicante PRELIMINARY AND INCOMPLETE Abstract We study a multiperiod principal-agent
More informationBanks, depositors and liquidity shocks: long term vs short term interest rates in a model of adverse selection
Banks, depositors and liquidity shocks: long term vs short term interest rates in a model of adverse selection Geethanjali Selvaretnam Abstract This model takes into consideration the fact that depositors
More informationLecture Notes on Bargaining
Lecture Notes on Bargaining Levent Koçkesen 1 Axiomatic Bargaining and Nash Solution 1.1 Preliminaries The axiomatic theory of bargaining originated in a fundamental paper by Nash (1950, Econometrica).
More informationContracts in informed-principal problems with moral hazard
Contracts in informed-principal problems with moral hazard Nicholas C Bedard January 20, 2016 Abstract In many cases, an employer has private information about the potential productivity of a worker, who
More informationSome Notes on Adverse Selection
Some Notes on Adverse Selection John Morgan Haas School of Business and Department of Economics University of California, Berkeley Overview This set of lecture notes covers a general model of adverse selection
More informationUniversity of Warwick, Department of Economics Spring Final Exam. Answer TWO questions. All questions carry equal weight. Time allowed 2 hours.
University of Warwick, Department of Economics Spring 2012 EC941: Game Theory Prof. Francesco Squintani Final Exam Answer TWO questions. All questions carry equal weight. Time allowed 2 hours. 1. Consider
More informationEconS Microeconomic Theory II Homework #9 - Answer key
EconS 503 - Microeconomic Theory II Homework #9 - Answer key 1. WEAs with market power. Consider an exchange economy with two consumers, A and B, whose utility functions are u A (x A 1 ; x A 2 ) = x A
More informationWhat happens when there are many agents? Threre are two problems:
Moral Hazard in Teams What happens when there are many agents? Threre are two problems: i) If many agents produce a joint output x, how does one assign the output? There is a free rider problem here as
More information"A Theory of Financing Constraints and Firm Dynamics"
1/21 "A Theory of Financing Constraints and Firm Dynamics" G.L. Clementi and H.A. Hopenhayn (QJE, 2006) Cesar E. Tamayo Econ612- Economics - Rutgers April 30, 2012 2/21 Program I Summary I Physical environment
More informationMoral Hazard: Part 1. April 9, 2018
Moral Hazard: Part 1 April 9, 2018 Introduction In a standard moral hazard problem, the agent A is characterized by only one type. As with adverse selection, the principal P wants to engage in an economic
More informationMicroeconomics II Lecture 4: Incomplete Information Karl Wärneryd Stockholm School of Economics November 2016
Microeconomics II Lecture 4: Incomplete Information Karl Wärneryd Stockholm School of Economics November 2016 1 Modelling incomplete information So far, we have studied games in which information was complete,
More informationGaming and Strategic Ambiguity in Incentive Provision
Gaming and Strategic Ambiguity in Incentive Provision Florian Ederer y UCLA Richard Holden z Chicago and NBER June 0, 00 Margaret Meyer x Oxford and CEPR Abstract A central tenet of economics is that people
More informationEconS Advanced Microeconomics II Handout on Mechanism Design
EconS 503 - Advanced Microeconomics II Handout on Mechanism Design 1. Public Good Provision Imagine that you and your colleagues want to buy a co ee machine for your o ce. Suppose that some of you may
More informationInformed Principal in Private-Value Environments
Informed Principal in Private-Value Environments Tymofiy Mylovanov Thomas Tröger University of Bonn June 21, 2008 1/28 Motivation 2/28 Motivation In most applications of mechanism design, the proposer
More informationMechanism Design: Basic Concepts
Advanced Microeconomic Theory: Economics 521b Spring 2011 Juuso Välimäki Mechanism Design: Basic Concepts The setup is similar to that of a Bayesian game. The ingredients are: 1. Set of players, i {1,
More informationSolving Extensive Form Games
Chapter 8 Solving Extensive Form Games 8.1 The Extensive Form of a Game The extensive form of a game contains the following information: (1) the set of players (2) the order of moves (that is, who moves
More informationEcon 101A Problem Set 6 Solutions Due on Monday Dec. 9. No late Problem Sets accepted, sorry!
Econ 0A Problem Set 6 Solutions Due on Monday Dec. 9. No late Problem Sets accepted, sry! This Problem set tests the knowledge that you accumulated mainly in lectures 2 to 26. The problem set is focused
More informationLayo Costs and E ciency with Asymmetric Information
Layo Costs and E ciency with Asymmetric Information Alain Delacroix (UQAM) and Etienne Wasmer (Sciences-Po) September 4, 2009 Abstract Wage determination under asymmetric information generates ine ciencies
More informationDynamic Principal Agent Models: A Continuous Time Approach Lecture III
Dynamic Principal Agent Models: A Continuous Time Approach Lecture III Dynamic Financial Contracting II - Convergence to Continuous Time (Biais et al. 2007) Florian Ho mann Sebastian Pfeil Stockholm April
More information(a) Output only takes on two values, so the wage will also take on two values: z(0) = 0 0 z(0) 0. max s(d)z { d. n { z 1 0 (n + d) 2.
Steve Pischke/Jin Li Labor Economics II Problem Set Answers. An Agency Problem (a) Output only takes on two values, so the wage will also take on two values: z( ) z 0 z The worker s problem: z(0) 0 0 z(0)
More informationLecture 7. Simple Dynamic Games
Lecture 7. Simple Dynamic Games 1. Two-Stage Games of Complete and Perfect Information Two-Stages dynamic game with two players: player 1 chooses action a 1 from the set of his feasible actions A 1 player
More informationThe Principal-Agent Problem
Andrew McLennan September 18, 2014 I. Introduction Economics 6030 Microeconomics B Second Semester Lecture 8 The Principal-Agent Problem A. In the principal-agent problem there is no asymmetric information
More informationContracts under Asymmetric Information
Contracts under Asymmetric Information 1 I Aristotle, economy (oiko and nemo) and the idea of exchange values, subsequently adapted by Ricardo and Marx. Classical economists. An economy consists of a set
More informationA New Class of Non Existence Examples for the Moral Hazard Problem
A New Class of Non Existence Examples for the Moral Hazard Problem Sofia Moroni and Jeroen Swinkels April, 23 Abstract We provide a class of counter-examples to existence in a simple moral hazard problem
More informationMicroeconomics. 3. Information Economics
Microeconomics 3. Information Economics Alex Gershkov http://www.econ2.uni-bonn.de/gershkov/gershkov.htm 9. Januar 2008 1 / 19 1.c The model (Rothschild and Stiglitz 77) strictly risk-averse individual
More informationx ax 1 2 bx2 a bx =0 x = a b. Hence, a consumer s willingness-to-pay as a function of liters on sale, 1 2 a 2 2b, if l> a. (1)
Answers to Exam Economics 201b First Half 1. (a) Observe, first, that no consumer ever wishes to consume more than 3/2 liters (i.e., 1.5 liters). To see this, observe that, even if the beverage were free,
More informationEconS Advanced Microeconomics II Handout on Subgame Perfect Equilibrium (SPNE)
EconS 3 - Advanced Microeconomics II Handout on Subgame Perfect Equilibrium (SPNE). Based on MWG 9.B.3 Consider the three-player nite game of perfect information depicted in gure. L R Player 3 l r a b
More informationMoral Hazard in Teams
Moral Hazard in Teams Ram Singh Department of Economics September 23, 2009 Ram Singh (Delhi School of Economics) Moral Hazard September 23, 2009 1 / 30 Outline 1 Moral Hazard in Teams: Model 2 Unobservable
More informationWORKING PAPER SERIES
DEPARTMENT OF ECONOMICS UNIVERSITY OF MILAN - BICOCCA WORKING PAPER SERIES EQUILIBRIUM PRINCIPAL-AGENT CONTRACTS Competition and R&D Incentives Federico Etro, Michela Cella No. 180 March 2010 Dipartimento
More informationExtensive Form Games with Perfect Information
Extensive Form Games with Perfect Information Pei-yu Lo 1 Introduction Recap: BoS. Look for all Nash equilibria. show how to nd pure strategy Nash equilibria. Show how to nd mixed strategy Nash equilibria.
More informationAdding an Apple to an Orange: A General Equilibrium Approach to Aggregation of Beliefs
Adding an Apple to an Orange: A General Equilibrium Approach to Aggregation of Beliefs Yi Jin y, Jianbo Zhang z, Wei Zhou x Department of Economics, The University of Kansas August 2006 Abstract This paper
More informationLearning and Risk Aversion
Learning and Risk Aversion Carlos Oyarzun Texas A&M University Rajiv Sarin Texas A&M University January 2007 Abstract Learning describes how behavior changes in response to experience. We consider how
More informationCombinatorial Agency of Threshold Functions
Combinatorial Agency of Threshold Functions Shaili Jain 1 and David C. Parkes 2 1 Yale University, New Haven, CT shaili.jain@yale.edu 2 Harvard University, Cambridge, MA parkes@eecs.harvard.edu Abstract.
More informationModule 16: Signaling
Module 16: Signaling Information Economics (Ec 515) George Georgiadis Players with private information can take some action to signal their type. Taking this action would distinguish them from other types.
More informationModule 8: Multi-Agent Models of Moral Hazard
Module 8: Multi-Agent Models of Moral Hazard Information Economics (Ec 515) George Georgiadis Types of models: 1. No relation among agents. an many agents make contracting easier? 2. Agents shocks are
More informationMoral Hazard: Part 2. April 16, 2018
Moral Hazard: Part 2 April 16, 2018 The basic model: A is risk neutral We now turn to the problem of moral hazard (asymmetric information), where A is risk neutral. When A is risk neutral, u (t) is linear.
More informationLecture 5: Labour Economics and Wage-Setting Theory
Lecture 5: Labour Economics and Wage-Setting Theory Spring 2017 Lars Calmfors Literature: Chapter 7 Cahuc-Carcillo-Zylberberg: 435-445 1 Topics Weakly efficient bargaining Strongly efficient bargaining
More informationRenegotiation proof mechanism design with imperfect type veri cation
Renegotiation proof mechanism design with imperfect type veri cation Francisco Silva y December 7, 2017 Abstract I consider the interaction between an agent and a principal who is unable to commit not
More informationGame Theory. Monika Köppl-Turyna. Winter 2017/2018. Institute for Analytical Economics Vienna University of Economics and Business
Monika Köppl-Turyna Institute for Analytical Economics Vienna University of Economics and Business Winter 2017/2018 Static Games of Incomplete Information Introduction So far we assumed that payoff functions
More informationFall Final Examination Solutions Thursday 10 January 2012
EC 20.2 & 20. Fall 202 Deniz Selman Bo¼gaziçi University Final Examination Solutions Thursday 0 January 202. (9 pts) It is the heart of winter the isl of Ludos has been devastated by a violent snowstorm
More informationLecture Notes in Information Economics
Lecture Notes in Information Economics Juuso Valimaki February, 2014 Abstract These lecture notes are written for a rst-year Ph.D. course in Microeconomic Theory. They are based on teaching material from
More information1 Uncertainty. These notes correspond to chapter 2 of Jehle and Reny.
These notes correspond to chapter of Jehle and Reny. Uncertainty Until now we have considered our consumer s making decisions in a world with perfect certainty. However, we can extend the consumer theory
More informationRobust Mechanism Design and Robust Implementation
Robust Mechanism Design and Robust Implementation joint work with Stephen Morris August 2009 Barcelona Introduction mechanism design and implementation literatures are theoretical successes mechanisms
More informationECON2285: Mathematical Economics
ECON2285: Mathematical Economics Yulei Luo Economics, HKU September 17, 2018 Luo, Y. (Economics, HKU) ME September 17, 2018 1 / 46 Static Optimization and Extreme Values In this topic, we will study goal
More informationMechanism Su cient Statistic. in the Risk-Neutral Agency Problem
Mechanism Su cient Statistic in the Risk-Neutral Agency Problem Dominique Demougin and Claude Fluet Otto-von-Guericke University, Magdeburg and Université du Québec à Montréal Final version, February 1998
More informationAsymmetric Information and Bank Runs
Asymmetric Information and Bank uns Chao Gu Cornell University Draft, March, 2006 Abstract This paper extends Peck and Shell s (2003) bank run model to the environment in which the sunspot coordination
More information5. Relational Contracts and Career Concerns
5. Relational Contracts and Career Concerns Klaus M. Schmidt LMU Munich Contract Theory, Summer 2010 Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer 2010
More informationVeto Constraint in Mechanism Design: Ine ciency with Correlated Types
Veto Constraint in Mechanism Design: Ine ciency with Correlated Types Olivier Compte and Philippe Jehiel y Revised, November 2006 Abstract We consider bargaining problems in which parties have access to
More informationThird down with a yard to go : the Dixit-Skeath conundrum on equilibria in competitive games.
June 28, 1999 Third down with a yard to go : the Dixit-Skeath conundrum on equilibria in competitive games. Abstract In strictly competitive games, equilibrium mixed strategies are invariant to changes
More informationD i (w; p) := H i (w; S(w; p)): (1)
EC0 Microeconomic Principles II Outline Answers. (a) Demand for input i can be written D i (w; p) := H i (w; S(w; p)): () where H i is the conditional demand for input i and S is the supply function. From
More informationA Principal-Agent Model of Sequential Testing
A Principal-Agent Model of Sequential Testing Dino Gerardi y Lucas Maestri z July 2011 Abstract This paper analyzes the optimal provision of incentives in a dynamic information acquisition process. In
More informationBounded Rationality Lecture 4
Bounded Rationality Lecture 4 Mark Dean Princeton University - Behavioral Economics The Story So Far... Introduced the concept of bounded rationality Described some behaviors that might want to explain
More informationLabor Economics, Lectures 5 and 6: Career Concerns and Multitasking
Labor Economics, 14.661. Lectures 5 and 6: Career Concerns and Multitasking Daron Acemoglu MIT November 9 and 13, 2018 Daron Acemoglu (MIT) Moral Hazard November 9 and 13, 2018 1 / 63 Introduction Introduction
More informationLabor Economics, Lecture 11: Partial Equilibrium Sequential Search
Labor Economics, 14.661. Lecture 11: Partial Equilibrium Sequential Search Daron Acemoglu MIT December 6, 2011. Daron Acemoglu (MIT) Sequential Search December 6, 2011. 1 / 43 Introduction Introduction
More informationStatic Information Design
Static nformation Design Dirk Bergemann and Stephen Morris European Summer Symposium in Economic Theory, Gerzensee, July 2016 Mechanism Design and nformation Design Mechanism Design: Fix an economic environment
More informationSimplifying this, we obtain the following set of PE allocations: (x E ; x W ) 2
Answers Answer for Q (a) ( pts:.5 pts. for the de nition and.5 pts. for its characterization) The de nition of PE is standard. There may be many ways to characterize the set of PE allocations. But whichever
More informationOn Overdissipation of Rents in Contests with Endogenous Intrinsic Motivation. Volker Schlepütz
On Overdissipation of Rents in Contests with Endogenous Intrinsic Motivation Volker Schlepütz Diskussionsbeitrag Nr. 421 Februar 2008 Diskussionsbeiträge der Fakultät für Wirtschaftswissenschaft der FernUniversität
More informationA Folk Theorem For Stochastic Games With Finite Horizon
A Folk Theorem For Stochastic Games With Finite Horizon Chantal Marlats January 2010 Chantal Marlats () A Folk Theorem For Stochastic Games With Finite Horizon January 2010 1 / 14 Introduction: A story
More informationECO421: Communication
ECO421: Communication Marcin P ski February 9, 2018 Plan Introduction Asymmetric information means some players know more than the others. In real life, information can be transmitted A simple model of
More informationTime is discrete and indexed by t =0; 1;:::;T,whereT<1. An individual is interested in maximizing an objective function given by. tu(x t ;a t ); (0.
Chapter 0 Discrete Time Dynamic Programming 0.1 The Finite Horizon Case Time is discrete and indexed by t =0; 1;:::;T,whereT
More informationContracting with Heterogeneous Externalities
Contracting with Heterogeneous Externalities Shai Bernstein y Eyal Winter z August 8, 2009 Abstract We model situations in which a principal provides incentives to a group of agents to participate in a
More informationG5212: Game Theory. Mark Dean. Spring 2017
G5212: Game Theory Mark Dean Spring 2017 Adverse Selection We have now completed our basic analysis of the adverse selection model This model has been applied and extended in literally thousands of ways
More informationNTU IO (I) : Auction Theory and Mechanism Design II Groves Mechanism and AGV Mechansim. u i (x, t i, θ i ) = V i (x, θ i ) + t i,
Meng-Yu Liang NTU O : Auction Theory and Mechanism Design Groves Mechanism and AGV Mechansim + 1 players. Types are drawn from independent distribution P i on [θ i, θ i ] with strictly positive and differentiable
More informationExclusive contracts and market dominance
Exclusive contracts and market dominance Giacomo Calzolari and Vincenzo Denicolò Online Appendix. Proofs for the baseline model This Section provides the proofs of Propositions and 2. Proof of Proposition.
More informationCapital Structure and Investment Dynamics with Fire Sales
Capital Structure and Investment Dynamics with Fire Sales Douglas Gale Piero Gottardi NYU April 23, 2013 Douglas Gale, Piero Gottardi (NYU) Capital Structure April 23, 2013 1 / 55 Introduction Corporate
More informationAdvanced Microeconomics
Advanced Microeconomics ECON5200 - Fall 2012 Introduction What you have done: - consumers maximize their utility subject to budget constraints and firms maximize their profits given technology and market
More informationMechanism Design: Bayesian Incentive Compatibility
May 30, 2013 Setup X : finite set of public alternatives X = {x 1,..., x K } Θ i : the set of possible types for player i, F i is the marginal distribution of θ i. We assume types are independently distributed.
More informationImplementation with Interdependent Valuations Preliminary and Incomplete
Implementation with Interdependent Valuations Preliminary and Incomplete Richard P. McLean Rutgers University Andrew Postlewaite University of Pennsylvania April 1, 004 1. Introduction There is a large
More informationOptimal Incentive Contract with Costly and Flexible Monitoring
Optimal Incentive Contract with Costly and Flexible Monitoring Anqi Li 1 Ming Yang 2 1 Department of Economics, Washington University in St. Louis 2 Fuqua School of Business, Duke University May 2016 Motivation
More informationGame theory lecture 4. September 24, 2012
September 24, 2012 Finding Nash equilibrium Best-response or best-reply functions. We introduced Nash-equilibrium as a profile of actions (an action for each player) such that no player has an incentive
More informationOnline Appendix for Sourcing from Suppliers with Financial Constraints and Performance Risk
Online Appendix for Sourcing from Suppliers with Financial Constraints and Performance Ris Christopher S. Tang S. Alex Yang Jing Wu Appendix A: Proofs Proof of Lemma 1. In a centralized chain, the system
More informationWage Floors and Optimal Job Design
Wage Floors and Optimal Job Design Jenny Kragl y and Anja Schöttner z January 0, 0 Abstract We analyze the e ects of lower bounds on wages, e.g., minimum wages or liability limits, on job design within
More informationDynamic Mechanism Design:
Dynamic Mechanism Design: Revenue Equivalence, Pro t Maximization, and Information Disclosure Alessandro Pavan, Ilya Segal, Juuso Toikka May 2008 Motivation Mechanism Design: auctions, taxation, etc...
More informationOverview. Producer Theory. Consumer Theory. Exchange
Overview Consumer Producer Exchange Edgeworth Box All Possible Exchange Points Contract Curve Overview Consumer Producer Exchange (Multiplicity) Walrasian Equilibrium Walrasian Equilibrium Requirements:
More informationMarriage as a Rat Race: Noisy Pre-Marital Investments with Assortative Matching
Marriage as a Rat Race: Noisy Pre-Marital Investments with Assortative Matching V. Bhaskar y Department of Economics University College London WC1E 6BT, UK Ed Hopkins z School of Economics University of
More information1. The General Linear-Quadratic Framework
ECO 317 Economics of Uncertainty Fall Term 2009 Slides to accompany 21. Incentives for Effort - Multi-Dimensional Cases 1. The General Linear-Quadratic Framework Notation: x = (x j ), n-vector of agent
More informationAll Entrepreneurial Productivity Increases are Not Created Equal
All Entrepreneurial Productivity Increases are Not Created Equal by Arup Bose,* Debashis Pal,** and David E. M. Sappington*** Abstract We examine the impact of productivity increases in a simple model
More informationCPS 173 Mechanism design. Vincent Conitzer
CPS 173 Mechanism design Vincent Conitzer conitzer@cs.duke.edu edu Mechanism design: setting The center has a set of outcomes O that she can choose from Allocations of tasks/resources, joint plans, Each
More information