Teoria das organizações e contratos
|
|
- Brooke Todd
- 5 years ago
- Views:
Transcription
1 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 / 104
2 Outline 1 Introduction 2 A Model of Adverse Selection 3 Principals Competing for Agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
3 Outline 1 Introduction 2 A Model of Adverse Selection 3 Principals Competing for Agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
4 Informational structure Very often, parties to a contract do not have all the relevant information about each other Consider a person who hires a carpenter The task to be done may be well defined However, the worker s ability, cleanliness, and manners are not Adverse selection problem Before the signing of the contract, the agent has more information than the principal concerning certain aspects of his personal characteristics EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
5 Other examples A driver knows more than his insurance company about his driving habits: if he uses motorways or local roads, or the number of daily hours spent behind the wheel A firm has more information than the government about the costs of carrying out a certain project EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
6 Adverse selection in general Adverse selection refers not only when the agent s informational advantage concerns his own personal characteristics But also when there is asymmetric information regarding any variable relevant to the contractual relationship Consider the example of the homeowner who hires a carpenter He may not be aware of the job s difficulty Or the cost of the required materials A lawyer has more information than his client regarding the legal history concerning similar cases, which relates to the probability of winning the case A regulated firm may know more than the government about the market in which it operates EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
7 Informational asymmetries and efficiency The agent will only reveal his information to the principal if it is in his interest The agent may try to profit from information by keeping it private The principal s problem is to find a way to reduce her informational disadvantage The presence of asymmetric information can result in modifications with respect to the first-best agreement (when information is symmetric) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
8 Lemon s problem: Akerlof (1970) Consider the market for second-had cars The owner knows the quality of the car he is selling, but the buyer does not Some cars are placed on the market because their owners simply want a bigger or better one Others because they have been involved in a major accident or after having been used has driving-school vehicles EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
9 Lemon s problem: Akerlof (1970) Represent the quality of a second-hand car by a real number Quality k [0, 1] is uniformly distributed (for simplicity) Quality 0 is the worst and 1 the best We assume that both the seller and buyer are risk-neutral A seller is willing to sell a car of quality k for a price p s k A buyer values a car of quality k at p b k There are gains to trade if p b > p s Let s assume that p b = (3/2)p s EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
10 Lemon s problem: symmetric case Assume information is symmetric Any car s type would be sold A car of quality k would sell in the market at a price P (k) satisfying p s k P (k) p b k The value of P (k) depends on the trade protocol and the relative bargaining powers of the buyer and the seller If the buyer had all the bargaining power, the selling price of the car would be P (k) = p s k EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
11 Lemon s problem Assume now that the buyer does not know the quality of the car sold Denote by P the price at which a car is being offered The buyer needs to form expectations about the quality of the car sold at price P What is the available information? The buyer knows that the owner of a car with quality k is willing to sell at price P only if P p s k EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
12 Bayesian expectations Denote by µ the prior belief of the buyer on the cars quality µ is a probability measure on the set [0, 1] of a car s quality We assume (for simplicity) it is uniform µ([a, b]) = b a When observing the price P being offered, the buyer knows that the quality of the car belongs to K(P ) = {k [0, 1] : p s k P } = [0, P/p s ] We assume that buyer updates his beliefs using the Bayes rule µ( K(P )) : A [0, 1] µ(a K(p)) µ(k(p)) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
13 Bayesian expectations Since the agent is risk-neutral, he is willing to buy the car only if P p b [0,1] kµ(dk K(p)) = p b p s P P/ps 0 kdk = p b P 2p s Since p b = 3/2p s, no transactions will take place if P > 0 There will only be markets for lemons, i.e., cars with the lowest quality The informational problem is large enough to cause the disappearance of the market for second-hand cars EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
14 Outline 1 Introduction 2 A Model of Adverse Selection 3 Principals Competing for Agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
15 Production technology Consider a risk-neutral principal who contracts an agent to carry out some effort The relationship allows a certain result to be obtained Its monetary value is denoted by x X R represents the set of possible values for x The final result obtained depends on the effort that the agent dedicates to the task, denoted by e the realization of a random variable E R + represents the set of possible efforts The probability of outcome x i when effort e is exerted is denoted by p(x i e) or p i (e) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
16 Assumptions Effort e is assumed to be verifiable Denote by Π(e) the expected production Π(e) = n p i (e)x i = p(x e)e = E[x e] x X i=1 We assume that Π is twice differentiable with Π > 0 and Π < 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
17 Asymmetric information The agent could be either of two types {g, b} Types differ only with respect to disutility of effort U g (w, e) = u(w) v(e) and U b (w, e) = u(w) kv(e) where k > 1 Type-g agents are also called more efficient How much he requires to exert some effort level is lower Type-b agents are called less efficient EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
18 Assumption Assumption The functions u and v are twice differentiable with u > 0, u 0, v > 0 and v > 0 We have v : E R + R with v(0) = 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
19 Timing of the game 1 Nature chooses the type of the agent 2 The principal designs the contract 3 The agent accepts or rejects 4 The agent supplies effort (required by the accepted contract) 5 Nature chooses the random shock on the technology 6 Outcomes are realized and payoff are made EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
20 Symmetric information: type-g agent Assume there is no adverse selection: the principal observes the type of the agent With a type-g agent, the principal should solve subject to max e,w Π(e) w u(w) v(e) U There is no reason to allow for stochastic payments since the principal is risk-neutral and effort is observable (PC) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
21 Symmetric information: type-g agent The optimal contract (e g, w g ) is characterized by The binding participation constraint The first-order condition u(w g ) v(e g ) = U Π (e g ) = v (e g ) u (w g ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
22 Symmetric information: type-b agent The optimal contract (e b, w b ) is characterized by The binding participation constraint The first-order condition u(w b ) kv(e b ) = U Π (e b ) = kv (e b ) u (w b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
23 The symmetric case Given a type i {g, b} we let Iso i (U) := {(w, e) : U i (w, e) = U} The curve Iso b (U) is beneath Iso g (U) because effort is more costly for type-b agents Let and FO b := {(w, e) : Π (e) = kv (e)/u (w)} FO g := {(w, e) : Π (e) = v (e)/u (w)} The curve FO b is beneath the curve FO g EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
24 The symmetric case EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
25 The symmetric case Proposition It is optimal for the principal to demand more effort from the agent to whom effort if less costly, i.e., e g > e b We cannot be sure about wages There are two effects of opposite sign For given a particular effort, type-b agent requires a greater wage in order to participate However, the principal demands less effort from B than from G EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
26 The symmetric case EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
27 Asymmetric information Assume now that the principal does not observe the agent s type He can offer a menu of contracts {(e 1, w 1 ), (e 2, w 2 ), (e 3, w 3 )} and let the agent choose A possible menu is {(e b, w b ), (e g, w g )} Proposition Type-B agent chooses (e b, w b ) Type-G agent also chooses (e b, w b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
28 Asymmetric information Type-G agents choose the contract (e b, w b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
29 Asymmetric information Symmetric information contracts are not optimal under asymmetric information EESP (FGV) Teoria das organizac o es e contratos 3o trimestre / 104
30 Principal s expected profits Assume that the principal has a prior about the distribution of types He believes that the fraction of agents being of type-g is q where 0 < q < 1 Alternatively, the principal believes that the probability of an agent being of type-g is q If type-g agent accepts contract (e g, w g ) and type-b agent accepts contract (e b, w b ) then the principal expected profit is q [Π(e g ) w g ] + (1 q) [Π(e b ) w b ] EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
31 Menus of contracts We assume that the principal offers a menu of contracts {(e b, w b ), (e g, w g )} The contract (e i, w i ) is directed to type-i agent It is as if the principal ask the agent what is his type and offers the corresponding contract Since the type is not observable, it is equivalent to let the agent choose among the two contracts EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
32 Truth-telling constraints The principal understands that each agent chooses the contract that suits him Therefore, the menu of contracts must be self-selective Type-B agent must prefer contract (e b, w b ) to (e g, w g ), i.e., u(w b ) kv(e b ) u(w g ) kv(e g ) (IC b ) Type-G agent must prefer contract (e g, w g ) to (e b, w b ), i.e., u(w g ) v(e g ) u(w b ) v(e b ) (IC g ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
33 More general contracts The principal could offer a menu with more than two contracts However, only two (or one) of them will be selected Therefore, without any loss of generality, we can restrict attention to menus with two contracts EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
34 The principal s problem max q (e g,w g ),(e b,w b ) [Π(eg ) w g ] + (1 q) [Π(e b ) w b ] subject to participation constraint of type-g participation constraint of type-b incentive compatibility of type-g incentive compatibility of type-b u(w g ) v(e g ) U (PC g ) u(w b ) kv(e b ) U (PC b ) u(w g ) v(e g ) u(w b ) v(e b ) (IC g ) u(w b ) kv(e b ) u(w g ) kv(e g ) (IC b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
35 Contracts with adverse selection Proposition The only participation constraint that the principal need to be concerned with is that corresponding to the least efficient agent Consider a menu of contracts ((e g, w g ), (e b, w b )) satisfying (PC b ) and (IC g ) Then (PC g ) is automatically satisfied If e b > 0 then (PC g ) is not binding EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
36 The principal s problem: reduced form subject to max q (e g,w g ),(e b,w b ) [Π(eg ) w g ] + (1 q) [Π(e b ) w b ] participation constraint of type-b incentive compatibility of type-g incentive compatibility of type-b u(w b ) kv(e b ) U (PC b ) u(w g ) v(e g ) u(w b ) v(e b ) (IC g ) u(w b ) kv(e b ) u(w g ) kv(e g ) (IC b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
37 Contracts with adverse selection Proposition If a menu of contracts satisfies the incentive-compatibility constraints then greater effort is demanded of the most efficient agent Consider a menu of contracts ((e g, w g ), (e b, w b )) satisfying (IC g ) and (IC b ) Then we must have e g e b Proof. Show that v(e g ) v(e b ) u(w g ) u(w b ) k[v(e g ) v(e b )] (IC) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
38 Optimal contracts with adverse selection Assume that ((e g, w g ), (e b, w b )) solves the principal s problem Denote by λ, µ and δ the Lagrange multipliers associated to (PC b ), (IC g ) and (IC b ) respectively µ δ = q u (w g ) λ µ + δ = 1 q u (w b ) µ δk = qπ (e g ) v (e g ) λk µ + δk = (1 q)π (e b ) v (e b ) (FO w g) (FO w b) (FO e g) (FO e b) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
39 Optimal contracts with adverse selection Proposition The participation constraint of the less efficient agent (type-b) binds, i.e., u(w b ) kv(e b ) = U This is because λ > 0 The principal extracts all the surplus of the type-b agent EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
40 Optimal contracts with adverse selection Proposition The self-selection constraint of the more efficient agent (type-g) binds, i.e., u(w g ) v(e g ) = u(w b ) v(e b ) This is because µ > 0 In particular we have u(w g ) v(e g ) = U + (k 1)v(e b ) The principal cannot extract all the surplus of the agent with the lowest cost The most efficient agent benefits from the adverse selection problem EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
41 Optimal contracts with adverse selection Proposition The principal does not demand the same effort from both agent s types, i.e., e g > e b Assume, by way of contradiction, that e g = e b Show that we necessarily have w g = w b Induce a contradiction EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
42 Optimal contracts with adverse selection Proposition The incentive condition for low-efficient agents does not bind This follows from (IC) and the fact that e g > e b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
43 Optimal contracts with adverse selection Proposition The first-best first order condition is satisfied for the type-g agents, i.e., 1 u (w g ) = Π (e g ) v (e g ) There is no distortion at the top : this is the same FO condition as in the symmetric case 1 u (w g ) = Π (e g ) v (e g ) The presence of adverse selection does not affect the efficient allocation of effort and wage for the agent with the best characteristics The contracts (e g, w g ) and (e g, w g ) differ because the expected utility is different EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
44 Optimal contracts with adverse selection Proposition The first order condition of the type-b agents is distorted Π (e b ) = kv (e b ) u (w b ) q(k 1) v (e b ) + (1 q) u (w g ) }{{} distortion The principal needs to make the contract (e b, w b ) less attractive to type-g agents By distorting, the principal looses efficiency with respect to type-b agents But she pays less informational rent to type-g agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
45 Optimal contracts with adverse selection: summary Participation constraints The participation constraint only binds for the agent with the highest cost (type-b) The most efficient agent (type-g) receives an informational rent of (k 1)v(e b ) The type-g agent receives utility greater than his reservation level due to his private information EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
46 Optimal contracts with adverse selection: summary Incentive compatibility constraints The IC condition binds for the high-efficiency agent The IC condition of the low-efficiency agent does not bind First best contracts The efficiency condition of the first best contract is satisfied for the good agent A distortion is introduced into the efficiency condition of the bad agent EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
47 Optimal contracts with adverse selection: distortion Why does the principal choose to distort the efficiency condition of the contract offered to the type-b agent? The intuition is to make the contract (e b, w b ) less attractive to type-g agents By distorting, the principal loses efficiency with respect to type-b agents However, she pays less informational rent to type-g agents The trade-off between these two effects is favourable to the distortion EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
48 Optimal contracts with adverse selection: distortion EESP (FGV) Teoria das organizac o es e contratos 3o trimestre / 104
49 Optimal contracts with adverse selection: distortion Why the trade-off is favourable to the distortion? Start from agent B s efficiency effort level (e b, w b ) satisfying Π (e b ) = kv (e b ) u (w b ) Make a marginal change (de b, dw b ) but keeping the (PC b ) binding u (w b )dw b = kv (e b )de b We have to evaluate the impact on the principal s profit The first order term is zero Π(e b + de b ) Π(e b ) dw b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
50 Optimal contracts with adverse selection: distortion A marginal change in the agent B s contract... induces a second order negative effect on the welfare the principal extracts from agent B while it causes a first order negative effect on agent G s information rent which implies a first order positive effect on the principal s profit EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
51 Optimal contracts with adverse selection: Size of the distortion The distortion in the efficiency of agent B is C = q(k 1) (1 q) u (e b ) u (w b ) When q 0, the probability of type-g agents vanishes and the distortion is not anymore beneficial When q 1, the distortion is maximal to reduce the informational rent to the type-g agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
52 Asymmetric vs symmetric: agent G The efficiency condition is the same in both situations The participation constraint binds in the symmetric information case But it does not under asymmetric information u(w g ) v(e g ) = U + A > U = u(w g ) v(e g ) where A = (k 1)v(e b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
53 Asymmetric vs symmetric: agent G EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
54 Asymmetric vs symmetric: agent B EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
55 Asymmetric vs symmetric Due to the distortion, for the type-b agent, we have e b < e b and w b < w b We also have e g > e b and w g > w b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
56 Role of risk-aversion The problem of adverse selection is present independently of the agent s risk-aversion Even if both types of agents are risk-neutral, the problem has the same basic characteristics The reason is that there is no insurance incentive problem Rather, the principal is unsure to whom she is offering a contract EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
57 Selecting only the good ones We have analyzed the principal s problem when she wants to contract the agent independently of his type There is an alternative option The principal could simply offer the contract (e g, w g ) Only the type-g agents will accept the contract: with probability 1 q, the transaction will not take place Since there is only one contract in the menu, there is no informational rent for the type-g agents The principal will prefer to offer the optimal menu {(e g, w g ), (e b, w b )} only if q[π(e g ) w g ] + (1 q)[π(e b ) w b ] q[π(e g ) w g ] EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
58 Outline 1 Introduction 2 A Model of Adverse Selection 3 Principals Competing for Agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
59 Agents differences We continue to consider the case with two types of agents: G and B Now, there are not different with respect to their effort disutility Rather, agent G is more productive than agent B We assume that agent G is more careful than B He commits fewer errors and his average result is better EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
60 Production technology The productive process is not deterministic The final result depends on a random variable We assume that effort is not a choice variable: it is unique and observable The principal cannot separate the two agent types by demanding greater effort from one of them EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
61 Production technology: success or failure When the agent exerts effort, the result could be either a success (S) or a failure (F) The probability of success if p i for type i {g, b} with p g > p b The result in case of success is x s, in case of failure it is x f x s > x f The result is verifiable: the principal can pay the agent according to the result Denote by w s the payment in case of success and w f in case of failure EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
62 Competing principals There are several competitive principals trying to contract with the agents Principals are identical and risk-neutral If the probability of success is p, and the wages offered to agents are (w s, w f ) Then a principal s expected profit is E[x w p] := p(x s w s ) + (1 p)(x f w f ) We also use the notation Π b (w) = E[x w p b ] and Π g (w) = E[x w p g ] EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
63 Risk-averse agents Agents are risk averse with Bernoulli function u We assume that u > 0 and u < 0 Fix a wage contract (w s, w f ) The expected utility of type G agents is U g (w) = E[u(w) p g ] := p g u(w s ) + (1 p g )u(w f ) The expected utility of type B agents is U b (w) = E[u(w) p b ] := p b u(w s ) + (1 p b )u(w f ) Since only one effort is possible and effort implies the same disutility for each agent type, we can transfer effort into the reservation utility EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
64 Competition between principals Principals are competing to attract agents We are then interested in the set of equilibrium contracts in the game played by principals Equilibrium contracts are Nash equilibria We will focus on symmetric Nash equilibria EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
65 Symmetric equilibria A principal can choose to offer a menu of contracts {(w g s, w g f ), (w b s, w b f)} Given a type t {g, b}, the contract (w t s, w t f) is intended to type-t agents This means that, either information is symmetric and this contract is restricted to type t Or, information is asymmetric and this contract is self-selecting EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
66 Symmetric equilibria Consider two principals, the first one is offering the menu {(w g s, w g f ), (w b s, w b f)} The second one is offering the menu {(ŵ g s, ŵ g f ), (ŵ b s, ŵ b f)} Both principals must make the same expected profit Otherwise, one will switch to the other s principal menu This motivates our interest to symmetric equilibria where all principals offer the same menu If two principals offer the same menu, half of agents choose one principal and the other half choose the other principal EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
67 Symmetric information Assume that principals can perfectly distinguish agent types Then we can analyze two separate markets: one for type-g contracts and another for type-b contracts We look for the characteristics of an equilibrium contract for type-t agents Proposition (ws t, wf t ) At equilibrium, the expected profits of the principals must be zero EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
68 Proof Let (ws t, wf t ) be an equilibrium contract Assume that the expected profit for each agent hired is positive, i.e., Π := E[x w t p t ] = p t [x s ws t ] + (1 p t )[x f wf t ] > 0 Remember that all principal have the same expected profit Agents will split among principals, each principal expecting to get a fraction µ (0, 1) of the agents, say µ = 1 2 Or equivalently, each principal s probability to hire a type-t agent is µ EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
69 Proof Consider a principal deviating and offering the contract (w t s + επ, w t f + επ) where 0 < ε < 1 This contract is strictly preferred by type-t agent Therefore the principal will hire all agents, and not only the fraction µ The expected profit for each agent hired is (1 ε)π The principal makes less profits from each agent but hires a larger fraction of agent If ε is close enough to 0, we get (1 ε)π > µπ This contradicts the requirement that (ws t, wf t ) is a Nash equilibrium EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
70 Efficiency Proposition Any equilibrium contract (ws t, wf t ) must be Pareto optimal No other contract exists that would be preferred by both principal and agent If such a contract did exist, some principal would have sufficient incentives to deviate and offer the new contract The new contract gives positive expected profits And the agent has sufficient incentives to accept it since it gives him greater expected utility EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
71 Efficiency Fix an equilibrium contract (ws t, wf t ) Denote by U the type-t agent s expected utility U := p t u(ws t ) + (1 p t )u(ws t ) Since the equilibrium contract is Pareto optimal It must solve the following constrained maximization problem subject to max (w pt [x s w s ] + (1 p t )[x f w f ] s,w f) p t u(w s ) + (1 p t )u(w f ) U EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
72 Symmetric information: characterizing equilibrium contracts If follows from the Kuhn-Tucker conditions that w t s = w t f This was predictable: the optimal risk-sharing requires the risk-neutral principal to fully insure the agent Principals make zero profits w t s = w t f = E[x p t ] EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
73 Symmetric information EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
74 Indifference curves Denote by Iso t (U) the type-t agent indifference curve with expected utility U Iso t (U) := {(w s, w f ) : E[u(w) p t ] = U} We can construct an implicit function where (w s, w f ) Iso t (U) w f = h t (w s ) ( 1 h t (x) = u 1 [ U p t 1 p t u(x) ] ) The slope of the indifference curve at the contract w = (w s, w f ) is defined by [h t ] dw f (w s ) and denoted by dw s U t =cst EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
75 Single crossing For any given contract w = (w s, w f ), the indifference curves of G is steeper than that of B dw f = pg u (w s ) dw s (1 p g )u (w f ) < pb u (w s ) (1 p b )u (w f ) = dw f dw s U g =cst Indifference curves cross at most once U b =cst EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
76 Asymmetric information The menu {C g, C b } = {(ws g, wf g ), (ws b, wf b )} is not information revealing in the sense that each type-t agent prefers his corresponding contract C t Indeed, all type-b agents have incentives to pass themselves off as type-g Since all principals anticipate this behaviour, the menu {C g, C b } will not be offered Indeed, the actual expected profits with type-b agents would be negative p b [x s ws g ]+(1 p b )[x f wf g ] < p b [x s ws b ]+(1 p b )[x f wf b ] = 0 and the expected profits with type-g agents remains zero EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
77 Asymmetric information Assume that the principal cannot observe the type of agent When a principal offers a contract intended for agents She must make sure that, given the rest of contracts offered, type-g agents are effectively interested in signing the contract, and type-b agents are not The same reasoning is applied to a principal who wants to offer a contract intended for both agent types (a contract that pools all agents) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
78 Equilibrium with asymmetric information We look for an equilibrium where all principals offer a menu {C g, C b } = {(ws g, wf g ), (ws b, wf)} b This menu of contracts should be such that U g (C g ) U g (C b ) and U b (C b ) U b (C g ) In that case, the principal expected profits for each agent hired is qπ g (C g ) + (1 q)π b (C b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
79 Equilibrium with asymmetric information Proposition At equilibrium, contracts give zero expected profits to principals, i.e., qπ g (C g ) + (1 q)π b (C b ) = 0 Proof. If not, one of the principals would be prepared to increase wages (reducing her expected profits per agent), but take on all the agents in the market Be careful with the self-selecting conditions EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
80 Necessary conditions Fix an equilibrium menu of contracts {C g, C b } Proposition There does not exists a contract C = (w s, w f ) such that it is preferred to C g by good agents it is not preferred to C b by bad agents gives strictly positive expected profits to the principal offering it, given that only type-g agents will agree to sign it, i.e., Π G (C) = p g [x s w s ] + (1 p g )[x f w f ] > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
81 Necessary conditions Fix an equilibrium menu of contracts {C g, C b } Proposition There does not exists a contract C = (w s, w f ) such that it is preferred to C b by bad agents it is not preferred to C g by good agents gives strictly positive expected profits to the principal offering it, given that only type-b agents will agree to sign it, i.e., Π b (C) = p b [x s w s ] + (1 p b )[x f w f ] > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
82 Necessary conditions Fix an equilibrium menu of contracts {C g, C b } Proposition There does not exists a contract C = (w s, w f ) such that it is preferred to C b by bad agents it is preferred to C g by good agents gives strictly positive expected profits to the principal offering it, given that both types of agent will agree to sign it, i.e., qπ G (C) + (1 q)π b (C) > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
83 Necessary conditions Proposition At an equilibrium {C g, C b } principals make zero profits with each agent s types, i.e., Π g (C g ) = 0 and Π b (C b ) = 0 Split the proof in two cases Case 1: Π g (C g ) > 0 and Π b (C b ) < 0 Case 2: Π g (C g ) < 0 and Π b (C b ) > 0 Use the property that indifference curves have different slopes when they cross EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
84 Pooling and separating equilibria Definition An equilibrium menu of contracts {C g, C b } is said to be pooling if C g = C b separating if C g C b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
85 Non-existence of pooling equilibria Proposition Pooling equilibria do not exist If an equilibrium does exist, it must be such that each type of agent is offered a different contract EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
86 Non-existence of pooling equilibria: proof Assume C i is a pooling equilibrium then we must have 0 = Π i (C i ) := p i [x s w i s] + (1 p i )[x f w i f] where p i = qp g + (1 q)p b is the probability that the result will be successful when the principal does not know which type accepts the contract We first analyze the case where Π g (C i ) > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
87 Non-existence of pooling equilibria EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
88 Non-existence of pooling equilibria: proof We can follow a similar argument when Π b (C i ) > 0 We still have to analyze the case Π g (C i ) = Π b (C i ) = 0 This is only possible when C i = x = (x s, x f ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
89 Non-existence of pooling equilibria: proof EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
90 Finding the separating equilibrium Assume there exists a separating equilibrium {C g, C b } Proposition We must have C b = C b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
91 Finding the separating equilibrium EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
92 Finding the separating equilibrium Consider a principal offering a contract C in the shaded area, on the 45 o line below C b The type-b agent will be better off and the principal makes strictly profits with this type of agents The type-g agent may want to sign this contract too The principal will also make positive profits with type-g agents EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
93 Finding the separating equilibrium Proposition The contract C g belongs to the zero profit line Π g ( ) = 0 and satisfies U b (C g ) = U b (C b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
94 Finding the separating equilibrium EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
95 Finding the separating equilibrium We must have U b (C b ) U b (C g ) This conditions locates C g on the zero profit line Π g ( ) = 0 and below the intersection with the indifference curve U b ( ) = U b (C b ) It cannot be strictly lower, otherwise a principal can deviate and make strictly positive profits Observe that we have U g (C g ) U g (C b ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
96 Separating equilibrium: necessary conditions Assume there exists a separating equilibrium {C b, C g } Then we must have C b = C b The contract C g is characterized by the condition that U b (C b ) = U b (C g ), i.e., u(w b ) = p b u(ws g ) + (1 p b )u(wf g ) the condition of zero profits p g x s + (1 p g )x f = p g w g s + (1 p g )w g f EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
97 Separating equilibrium: sufficient conditions It is not possible to find C b that is strictly preferred by type-b agents, not preferred by type-g agents and with strictly positive profits Π b (C b ) > 0 It is not possible to find C g that is strictly preferred by type-g agents, not preferred by type-b agents and with strictly positive profits Π g (C g ) > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
98 Separating equilibrium: sufficient conditions Depending on the value of parameters, a principal can deviate offering a unique contract C that both types of agents strictly prefer and that gives strictly expected profits, i.e., Π i (C ) > 0 There exists q 0 (0, 1) such that for each q > q 0, the above situation occurs, implying that there is no equilibrium When q is large enough, the incentive to attract all the agents increases, even though there is a risk that the agent will turn out to be bad (this is a low-probability event) In that case, separating the agent types is too difficult EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
99 Separating equilibrium: no equilibrium when q > q 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
100 What happens when q q 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
101 What happens when q q 0 Macho-Stadler and Pérez-Castrillo claim that the candidate {C b, C g } is a separating equilibrium How can we prove that a principal cannot deviate by offering a menu {C g, C b } where contracts are self-selecting, strictly preferred by each corresponding type and with positive expected profits? EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
102 Possible deviations? EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
103 Possible deviations? EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
104 Summary Adverse selection may provoke the absence of any equilibrium If an equilibrium does exist, it will be a separating equilibrium Contracts with contingent pay-offs permit the more efficient agents to be separated from the less efficient ones The existence of contracts that include contingent pay-offs need not be attributed to the existence of a moral hazard problem, this type of contract may also be the consequence of adverse selection In the equilibrium, the least efficient agent is offered the same contract as under symmetric information The more efficient agent loses expected utility, while the expected pay-off is the same The more efficient agent needs to sacrifice efficiency so that type-b agents do not prefer the type-g contract to their own contract EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 104
EC476 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 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 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 informationDepartment of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno ANSWERS TO PRACTICE PROBLEMS 18
Department of Economics, University of California, Davis Ecn 00C Micro Theory Professor Giacomo Bonanno ANSWERS TO PRACTICE PROBEMS 8. If price is Number of cars offered for sale Average quality of cars
More informationMoral Hazard: Hidden Action
Moral Hazard: Hidden Action Part of these Notes were taken (almost literally) from Rasmusen, 2007 UIB Course 2013-14 (UIB) MH-Hidden Actions Course 2013-14 1 / 29 A Principal-agent Model. The Production
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 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 informationIntroduction to Game Theory
Introduction to Game Theory Part 3. Dynamic games of incomplete information Chapter 3. Job Market Signaling Ciclo Profissional 2 o Semestre / 2011 Graduação em Ciências Econômicas V. Filipe Martins-da-Rocha
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 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 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 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 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 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 informationAdverse Selection, Signaling, and Screening in Markets
BGPE Intensive Course: Contracts and Asymmetric Information Adverse Selection, Signaling, and Screening in Markets Anke Kessler Anke Kessler p. 1/27 Stylized Facts: Market Failure used cars, even if they
More informationIntroduction: Asymmetric Information and the Coase Theorem
BGPE Intensive Course: Contracts and Asymmetric Information Introduction: Asymmetric Information and the Coase Theorem Anke Kessler Anke Kessler p. 1/?? Introduction standard neoclassical economic theory
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 informationBargaining, Contracts, and Theories of the Firm. Dr. Margaret Meyer Nuffield College
Bargaining, Contracts, and Theories of the Firm Dr. Margaret Meyer Nuffield College 2015 Course Overview 1. Bargaining 2. Hidden information and self-selection Optimal contracting with hidden information
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 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 informationIntroduction to Game Theory
Introduction to Game Theory Part 2. Dynamic games of complete information Chapter 2. Two-stage games of complete but imperfect information Ciclo Profissional 2 o Semestre / 2011 Graduação em Ciências Econômicas
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 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 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 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 informationModels of Wage Dynamics
Models of Wage Dynamics Toshihiko Mukoyama Department of Economics Concordia University and CIREQ mukoyama@alcor.concordia.ca December 13, 2005 1 Introduction This paper introduces four different models
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 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 informationG5212: Game Theory. Mark Dean. Spring 2017
G5212: Game Theory Mark Dean Spring 2017 Adverse Selection We are now going to go back to the Adverse Selection framework Mechanism Design with 1 agent Though that agent may be of many types Note that
More informationGame 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 informationIntroduction to Game Theory
Introduction to Game Theory Part 3. Static games of incomplete information Chapter 2. Applications Ciclo Profissional 2 o Semestre / 2011 Graduação em Ciências Econômicas V. Filipe Martins-da-Rocha (FGV)
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 informationAdverse selection, signaling & screening
, signaling & screening Applications of game theory 2 Department of Economics, University of Oslo ECON5200 Fall 2009 Seller Buyer Situation 1: Symmetric info One market 1 2 prob high quality 1 2 prob high
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 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 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 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 information5. Externalities and Public Goods. Externalities. Public Goods types. Public Goods
5. Externalities and Public Goods 5. Externalities and Public Goods Externalities Welfare properties of Walrasian Equilibria rely on the hidden assumption of private goods: the consumption of the good
More information5. Externalities and Public Goods
5. Externalities and Public Goods Welfare properties of Walrasian Equilibria rely on the hidden assumption of private goods: the consumption of the good by one person has no effect on other people s utility,
More informationCompetition relative to Incentive Functions in Common Agency
Competition relative to Incentive Functions in Common Agency Seungjin Han May 20, 2011 Abstract In common agency problems, competing principals often incentivize a privately-informed agent s action choice
More informationA : a b c d a : B C A E B : d b c a b : C A B D E C : d c a c : E D B C D : a d b d : A D E B C E : a b d. A : a b c d a : B C A D E
Microeconomics II( ECO 50) Questions on the comprehensive exam will be chosen from the list below( with possible minor variations) CALCULATORS ARE ALLOWED Matching. Consider the Gale-Shapley marriage problem
More informationEC319 Economic Theory and Its Applications, Part II: Lecture 7
EC319 Economic Theory and Its Applications, Part II: Lecture 7 Leonardo Felli NAB.2.14 27 February 2014 Signalling Games Consider the following Bayesian game: Set of players: N = {N, S, }, Nature N strategy
More informationGovernment 2005: Formal Political Theory I
Government 2005: Formal Political Theory I Lecture 11 Instructor: Tommaso Nannicini Teaching Fellow: Jeremy Bowles Harvard University November 9, 2017 Overview * Today s lecture Dynamic games of incomplete
More informationIndescribable Contingencies versus Unawareness and Incomplete Contracting
Indescribable Contingencies versus Unawareness and Incomplete Contracting Wenjun Ma Burkhard C. Schipper Job Market Paper November 4, 204 Abstract Maskin and Tirole (999) postulated that even though agents
More informationSealed-bid first-price auctions with an unknown number of bidders
Sealed-bid first-price auctions with an unknown number of bidders Erik Ekström Department of Mathematics, Uppsala University Carl Lindberg The Second Swedish National Pension Fund e-mail: ekstrom@math.uu.se,
More informationPerfect Bayesian Equilibrium. Definition. The single-crossing property. This is a draft; me with comments, typos, clarifications, etc.
Economics 0c: week This is a draft; email me with comments, typos, clarifications, etc. Perfect Bayesian Equilibrium We are by now familiar with the concept of Bayesian Nash equilibrium: agents are best
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 informationDeceptive Advertising with Rational Buyers
Deceptive Advertising with Rational Buyers September 6, 016 ONLINE APPENDIX In this Appendix we present in full additional results and extensions which are only mentioned in the paper. In the exposition
More informationPlatform Competition under Asymmetric Information preliminary
Platform Competition under Asymmetric Information preliminary Hanna Ha laburda Harvard University Yaron Yehezkel Tel Aviv University January 31, 2011 Abstract In the context of platform competition in
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 informationContract Theory - Intro. Roman Inderst
1 Contract Theory - Intro Roman Inderst 2017 2 Overview Focus is contract theory. We explore a principal - agent setting, with core applications to firm - consumer, firm - worker and lender - borrower.
More informationEquilibrium Refinements
Equilibrium Refinements Mihai Manea MIT Sequential Equilibrium In many games information is imperfect and the only subgame is the original game... subgame perfect equilibrium = Nash equilibrium Play starting
More informationOn the Unique D1 Equilibrium in the Stackelberg Model with Asymmetric Information Janssen, M.C.W.; Maasland, E.
Tilburg University On the Unique D1 Equilibrium in the Stackelberg Model with Asymmetric Information Janssen, M.C.W.; Maasland, E. Publication date: 1997 Link to publication General rights Copyright and
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 informationEx Post Cheap Talk : Value of Information and Value of Signals
Ex Post Cheap Talk : Value of Information and Value of Signals Liping Tang Carnegie Mellon University, Pittsburgh PA 15213, USA Abstract. Crawford and Sobel s Cheap Talk model [1] describes an information
More informationLecture Slides - Part 4
Lecture Slides - Part 4 Bengt Holmstrom MIT February 2, 2016. Bengt Holmstrom (MIT) Lecture Slides - Part 4 February 2, 2016. 1 / 65 Mechanism Design n agents i = 1,..., n agent i has type θ i Θ i which
More informationSolution to Tutorial 9
Solution to Tutorial 9 2011/2012 Semester I MA4264 Game Theory Tutor: Xiang Sun October 27, 2011 Exercise 1. A buyer and a seller have valuations v b and v s. It is common knowledge that there are gains
More informationAdvanced Microeconomics
Advanced Microeconomics Leonardo Felli EC441: Room D.106, Z.332, D.109 Lecture 8 bis: 24 November 2004 Monopoly Consider now the pricing behavior of a profit maximizing monopolist: a firm that is the only
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 informationDuopoly and Project Uncertainty
Duopoly and Project Uncertainty An analysis of the Bertrand and Cournot duopolies under uncertainty for the buyer Draft Master Thesis Rik Bos Student 345327 June 2016 Erasmus School of Economics Master
More informationPerfect Competition in Markets with Adverse Selection
Perfect Competition in Markets with Adverse Selection Eduardo Azevedo and Daniel Gottlieb (Wharton) Presented at Frontiers of Economic Theory & Computer Science at the Becker Friedman Institute August
More informationIncreasingly, economists are asked not just to study or explain or interpret markets, but to design them.
What is market design? Increasingly, economists are asked not just to study or explain or interpret markets, but to design them. This requires different tools and ideas than neoclassical economics, which
More informationEconS 501 Final Exam - December 10th, 2018
EconS 501 Final Exam - December 10th, 018 Show all your work clearly and make sure you justify all your answers. NAME 1. Consider the market for smart pencil in which only one firm (Superapiz) enjoys a
More informationThe Revenue Equivalence Theorem 1
John Nachbar Washington University May 2, 2017 The Revenue Equivalence Theorem 1 1 Introduction. The Revenue Equivalence Theorem gives conditions under which some very different auctions generate the same
More informationTheory of Auctions. Carlos Hurtado. Jun 23th, Department of Economics University of Illinois at Urbana-Champaign
Theory of Auctions Carlos Hurtado Department of Economics University of Illinois at Urbana-Champaign hrtdmrt2@illinois.edu Jun 23th, 2015 C. Hurtado (UIUC - Economics) Game Theory On the Agenda 1 Formalizing
More informationAdvanced Economic Theory Lecture 9. Bilateral Asymmetric Information. Double Auction (Chatterjee and Samuelson, 1983).
Leonardo Felli 6 December, 2002 Advanced Economic Theory Lecture 9 Bilateral Asymmetric Information Double Auction (Chatterjee and Samuelson, 1983). Two players, a buyer and a seller: N = {b, s}. The seller
More informationMechanism Design. Christoph Schottmüller / 27
Mechanism Design Christoph Schottmüller 2015-02-25 1 / 27 Outline 1 Bayesian implementation and revelation principle 2 Expected externality mechanism 3 Review questions and exercises 2 / 27 Bayesian implementation
More informationSupplementary Material to Monopoly Insurance and Endogenous Information
Supplementary Material to Monopoly Insurance and Endogenous Information Johan N. M. Lagerlöf Christoph Schottmüller May 27, 2016 Not intended for publication Contents 1 Introduction 2 1.1 Notation.............................................
More informationEndogenous Matching: Adverse Selection & Moral Hazard On-Demand
Endogenous Matching: Adverse Selection & Moral Hazard On-Demand IPAM July 2015 Economic Motivation Technology (computers, internet, smartphones... ) has made revolution in provision/delivery of goods to
More informationAnswer Key: Problem Set 1
Answer Key: Problem Set 1 Econ 409 018 Fall Question 1 a The profit function (revenue minus total cost) is π(q) = P (q)q cq The first order condition with respect to (henceforth wrt) q is P (q )q + P (q
More informationOptimal contract under adverse selection in a moral hazard model with a risk averse agent
Optimal contract under adverse selection in a moral hazard model with a risk averse agent Lionel Thomas CRESE Université de Franche-Comté, IUT Besanon Vesoul, 30 avenue de l Observatoire, BP1559, 25009
More informationTwo-sided investments and matching with multi-dimensional cost types and attributes
Two-sided investments and matching with multi-dimensional cost types and attributes Deniz Dizdar 1 1 Department of Economics, University of Montréal September 15, 2014 1/33 Investments and matching 2/33
More informationMechanism Design II. Terence Johnson. University of Notre Dame. Terence Johnson (ND) Mechanism Design II 1 / 30
Mechanism Design II Terence Johnson University of Notre Dame Terence Johnson (ND) Mechanism Design II 1 / 30 Mechanism Design Recall: game theory takes the players/actions/payoffs as given, and makes predictions
More informationLecture 10: Mechanism Design
Computational Game Theory Spring Semester, 2009/10 Lecture 10: Mechanism Design Lecturer: Yishay Mansour Scribe: Vera Vsevolozhsky, Nadav Wexler 10.1 Mechanisms with money 10.1.1 Introduction As we have
More informationOn the Pareto Efficiency of a Socially Optimal Mechanism for Monopoly Regulation
MPRA Munich Personal RePEc Archive On the Pareto Efficiency of a Socially Optimal Mechanism for Monopoly Regulation Ismail Saglam Ipek University 4 May 2016 Online at https://mpra.ub.uni-muenchen.de/71090/
More informationOptimal Insurance of Search Risk
Optimal Insurance of Search Risk Mikhail Golosov Yale University and NBER Pricila Maziero University of Pennsylvania Guido Menzio University of Pennsylvania and NBER November 2011 Introduction Search and
More informationMarkets with Asymetric Information
Microeconomics 2 Presentation: Francis Bloch, Slides: Bernard Caillaud Master APE - Paris School of Economics March 6, 2017 (Lecture 9) I. Asymmetric information I.1. Introduction The economy is fundamentally
More informationContagious Adverse Selection
Stephen Morris and Hyun Song Shin Princeton Economics Department Seminar November 2008 Credit Crunch "market condence" Credit Crunch "market condence" undermined by unexpected losses (in housing and some
More informationOn the Informed Principal Model with Common Values
On the Informed Principal Model with Common Values Anastasios Dosis ESSEC Business School and THEMA École Polytechnique/CREST, 3/10/2018 Anastasios Dosis (ESSEC and THEMA) Informed Principal with Common
More informationSolution to Tutorial 9
Solution to Tutorial 9 2012/2013 Semester I MA4264 Game Theory Tutor: Xiang Sun November 2, 2012 Exercise 1. We consider a game between two software developers, who sell operating systems (OS) for personal
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 informationTheory Field Examination Game Theory (209A) Jan Question 1 (duopoly games with imperfect information)
Theory Field Examination Game Theory (209A) Jan 200 Good luck!!! Question (duopoly games with imperfect information) Consider a duopoly game in which the inverse demand function is linear where it is positive
More informationOnline Addendum for Dynamic Procurement, Quantity Discounts, and Supply Chain Efficiency
Online Addendum for Dynamic Procurement, Quantity Discounts, and Supply Chain Efficiency Feryal Erhun Pınar Keskinocak Sridhar Tayur Department of Management Science and Engineering, Stanford University,
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 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 informationArea I: Contract Theory Question (Econ 206)
Theory Field Exam Winter 2011 Instructions You must complete two of the three areas (the areas being (I) contract theory, (II) game theory, and (III) psychology & economics). Be sure to indicate clearly
More informationIndustrial Organization Lecture 7: Product Differentiation
Industrial Organization Lecture 7: Product Differentiation Nicolas Schutz Nicolas Schutz Product Differentiation 1 / 57 Introduction We now finally drop the assumption that firms offer homogeneous products.
More informationFirms and returns to scale -1- John Riley
Firms and returns to scale -1- John Riley Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Natural monopoly 1 C. Constant returns to scale 21 D. The CRS economy 26 E. pplication
More informationLecture Note II-3 Static Games of Incomplete Information. Games of incomplete information. Cournot Competition under Asymmetric Information (cont )
Lecture Note II- Static Games of Incomplete Information Static Bayesian Game Bayesian Nash Equilibrium Applications: Auctions The Revelation Principle Games of incomplete information Also called Bayesian
More informationSF2972 Game Theory Exam with Solutions March 15, 2013
SF2972 Game Theory Exam with s March 5, 203 Part A Classical Game Theory Jörgen Weibull and Mark Voorneveld. (a) What are N, S and u in the definition of a finite normal-form (or, equivalently, strategic-form)
More informationDesign Patent Damages under Sequential Innovation
Design Patent Damages under Sequential Innovation Yongmin Chen and David Sappington University of Colorado and University of Florida February 2016 1 / 32 1. Introduction Patent policy: patent protection
More informationThe Impact of Advertising on Media Bias. Web Appendix
1 The Impact of Advertising on Media Bias Esther Gal-Or, Tansev Geylani, Tuba Pinar Yildirim Web Appendix DERIVATIONS OF EQUATIONS 16-17 AND PROOF OF LEMMA 1 (i) Single-Homing: Second stage prices are
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 informationBayesian Games and Mechanism Design Definition of Bayes Equilibrium
Bayesian Games and Mechanism Design Definition of Bayes Equilibrium Harsanyi [1967] What happens when players do not know one another s payoffs? Games of incomplete information versus games of imperfect
More informationMechanism Design. Terence Johnson. December 7, University of Notre Dame. Terence Johnson (ND) Mechanism Design December 7, / 44
Mechanism Design Terence Johnson University of Notre Dame December 7, 2017 Terence Johnson (ND) Mechanism Design December 7, 2017 1 / 44 Market Design vs Mechanism Design In Market Design, we have a very
More informationOrganization, Careers and Incentives
Organization, Careers and Incentives Chapter 4 Robert Gary-Bobo March 2018 1 / 31 Introduction Introduction A firm is a pyramid of opportunities (Alfred P. Sloan). Promotions can be used to create incentives.
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 informationFirms and returns to scale -1- Firms and returns to scale
Firms and returns to scale -1- Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Constant returns to scale 19 C. The CRS economy 25 D. pplication to trade 47 E. Decreasing
More informationMoney, Barter, and Hyperinflation. Kao, Yi-Cheng Department of Business Administration, Chung Yuan Christian University
Money, Barter, and Hyperinflation Kao, Yi-Cheng Department of Business Administration, Chung Yuan Christian University 1 Outline Motivation The Model Discussion Extension Conclusion 2 Motivation 3 Economist
More informationGeneral Equilibrium and Welfare
and Welfare Lectures 2 and 3, ECON 4240 Spring 2017 University of Oslo 24.01.2017 and 31.01.2017 1/37 Outline General equilibrium: look at many markets at the same time. Here all prices determined in the
More information