EC476 Contracts and Organizations, Part III: Lecture 1 Leonardo - - PowerPoint PPT Presentation

EC476 Contracts and Organizations, Part III: Lecture 1

Leonardo Felli

32L.G.06

12 January 2015

Course Outline

Law and Economics

◮ Lecture 1: Contracts what are they? The Coase Theorem. ◮ Lecture 2: Principal Agent: Hidden Information and Hidden

Action.

◮ Lecture 3: Failures of the Coase Theorem: Asymmetric

Information and Transaction Costs.

◮ Lecture 4: The Role of Courts and the Legal System. ◮ Lecture 5: Power and Enforcement.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 2 / 52

Admin

◮ My coordinates: 32L.4.02, x7525, lfelli@econ.lse.ac.uk ◮ PA: Katharine Buckle, 32L.1.03, k.buckle@lse.ac.uk. ◮ Office Hours:

◮ Monday 11:30-12:30 a.m. ◮ or by appointment (e-mail lfelli@econ.lse.ac.uk).

◮ Course Material: available at:

http://econ.lse.ac.uk/staff/lfelli/teaching

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 3 / 52

References:

◮ Robert Gibbons, A Primer in Game Theory, London:

Harvester-Wheatsheaf, 1992.

◮ Bernard Salani´

e, The Economics of Contracts: A Primer, Cambridge: The MIT Press, 2nd Edition, 2005.

◮ Jean-Jacques Laffont and David Martimort, The Theory of

Inncentives: The Principal-Agent Model, Princeton and Oxford: Princeton University Press, 2002.

◮ Patrick Bolton and Mathias Dewatripont, Contract Theory,

Cambridge: M.I.T. Press, 2004.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 4 / 52

The Contract

The first natural question that needs to be answered is: What is a contract?

Definition

A contract is the ruling of an economic transaction: the description of the performance that the contracting parties agree to complete at a (possibly future) date.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 5 / 52

Example

◮ A contract for the purchase of a specific item, say a meal. It

specifies:

◮ the restaurant’s performance (number of courses, quality of

food, cooking details, etc. . . ),

◮ the customer’s performance (payment in full upon completion).

◮ Contracts involve not only the contracting parties, but also

• utsiders (enforcing authority: Court or Enforcer).

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 6 / 52

Implicit Contracts

◮ We distinguish between implicit and explicit contracts. ◮ A contract is implicit or self-enforcing whenever the

environment in which the contracting parties operate corresponds to the extensive form of a game whose (unique) Subgame Perfect Nash equilibrium exactly corresponds to the

• utcome the parties would like to implement.

◮ If you believe in SPE then there is no need for explicit

• communication. The two rational individuals will behave in

the way required.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 7 / 52

Explicit Contracts

◮ If the outcome the parties would like to implement is not the

subgame perfect Nash equilibrium of the environment in which they operate the parties might want to modify the environment.

◮ This is accomplished through an explicit contract. ◮ An explicit contract is a commitment device requiring:

◮ an explicit agreement between the parties, ◮ the intervention of a third party: the enforcer. Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 8 / 52

Contracts as Commitment

◮ The role of the enforcer is to force the parties to behave in a

way that differs from the one that would arise in the absence

• f any agreement.

◮ An explicit contract therefore specifies a new extensive form

corresponding to a new game for the parties.

◮ The usual way for the enforcer to guarantee that the parties

• perate in this new environment is by modifying the parties’

payoffs, when necessary.

◮ By agreeing to bring in an enforcer in the game the parties

commit to play a game that differs from the initial one they were in.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 9 / 52

A Model of Trade

◮ To see how the presence of an enforcer may work consider the

following example: (Kreps, 1984)

◮ A buyer B and a seller S wish to trade an indivisible item at

date 1.

◮ The buyer’s valuation: v, ◮ The seller’s delivery cost: c. ◮ Let

v > c In other words, trade is socially efficient.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 10 / 52

A Model of Trade (2)

◮ Let p be a reasonable price level (we abstract for the moment

from bargaining) such that: v > p > c.

◮ B’s and S’s situation may be described by the following

normal form: B\S deliver not deliver pay p v − p > 0, p − c > 0 −p, p not pay p v, −c 0, 0

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 11 / 52

No Trade Result

◮ The unique Nash equilibrium (dominant solvable) is:

(B does not pay, S does not deliver).

◮ This is clearly an inefficient outcome: no trade. ◮ The situation does not change if any of the following two

extensive forms are played.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 12 / 52

No Trade Result (2)

The unique SPE of the following game is: {B does not pay, S does not deliver at both nodes}

❜ ❅ ❅ ❅ ❅ ❅ ❅ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ q

• ☞

☞ ☞ ☞ ☞ ☞ ☞ ☞ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ q q q q q

B S S (v − p, p − c) (−p, p) (v, −c) (0, 0) pay p not pay p deliver not deliver not deliver deliver

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 13 / 52

No Trade Result (3)

The unique SPE of the following game is: {S does not deliver, B does not pay at both nodes}

❜ ❅ ❅ ❅ ❅ ❅ ❅ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ q

• ☞

☞ ☞ ☞ ☞ ☞ ☞ ☞ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ q q q q q

S B B (p − c, v − p) (−c, v) (p, −p) (0, 0) deliver not deliver pay p not pay p not pay p pay p

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 14 / 52

Trade by Contract

◮ Solution: to this inefficiency is an explicit contract enforced by

a third party (enforcer).

◮ It specifies:

◮ the payment p that B is supposed to make contingent on S

delivering the item,

◮ the punishment FB > p (implicit in the legal system) imposed

by the enforcer on B in the event that S delivers and B does not pay,

◮ the punishment FS > c (implicit in the legal system) imposed

by the enforcer on S in the event that B pays but S does not deliver.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 15 / 52

Trade by Contract (2)

◮ In this case the normal form describing the contracting parties

problem once the contract is in place is: B\S deliver not deliver pay p v − p, p − c FS − p, p − FS not pay p v − FB, FB − c 0, 0

◮ The unique Nash equilibrium is now:

(B pays p, S delivers).

◮ This contract is budget balanced off-the-equilibrium-path

(renegotiation proof).

◮ The latter property does not always hold.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 16 / 52

Imperfect Enforcement

◮ Consider now an environment in which when a party goes to

the enforcer (goes to court) detection is costly (κ) and is successful only with probability π.

◮ The payoffs associated with (not pay p, deliver) (British rule)

are: v − π (FB + κ), π FB − (1 − π)κ − c

◮ The payoffs associated with (pay p, not deliver) (British rule)

are: π FS − (1 − π)κ − p, p − π (FS + κ)

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 17 / 52

Imperfect Enforcement (2)

◮ Let π FB > p, π FS > c. Notice that as deterrence goes: π

and the size of the punishment, FB and FS, are substitutes (Becker 1968).

◮ The game assumes the British rule: the enforcer’s costs κ are

paid by the loosing party B\S deliver not deliver pay p v − p, p − c π FS − (1 − π)κ − p, p − π (FS + κ) not pay p v − π (FB + κ), π FB − (1 − π)κ − c 0, 0

◮ If court’s costs κ are too high the game has multiple Nash

equilibria: (pay p, deliver) and (not pay p, not deliver).

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 18 / 52

Enforcement Mechanism

◮ This example clearly shows the need for an enforcement

mechanism.

◮ This mechanism may be due to:

◮ the parties being involved in a repeated relationship

relationship/implicit contracting, (multiplicity might be a problem).

◮ the presence of a legal system that enforces the parties

agreement (explicit contracting).

◮ Notice that according to this interpretation the enforcer is

essentially a commitment device available to the parties that can be used when the parties agree to call it in.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 19 / 52

Enforcement as a Player

◮ An alternative interpretation is that the enforcer itself is one

• f the players of the game.

◮ It should therefore be endowed with a payoff function and an

action space and should be explicitly considered in the analysis

• f the contractual situation (we will come back to this).

◮ It should be mentioned that using this line of argument one

could obtain a rather extreme interpretation of a contract (a law) (Mailath, Morris and Postlewaite 2000).

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 20 / 52

Contracts as Cheap Talk

◮ The view is that enforcement/punishment is the only relevant

activity.

◮ A contract (a law) can at best be interpreted as cheap talk

that allows the parties to coordinate on a particular equilibrium of the game.

◮ No new equilibrium is introduced by the parties agreeing on a

contract or by the parliament passing a law.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 21 / 52

Implicit Enforcement

◮ From now on we will assume that the two (or more) parties

involved in the contractual relationship operate in a market economy with a well functioning legal system.

◮ Whatever contract the parties agree to, it will be enforced by

the court.

◮ The penalties for breaching the contract will be assumed to be

sufficiently severe that no contracting party will ever consider the possibility of not honoring the contract.

◮ We will abstract from explicitly specifying these penalties.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 22 / 52

Coase Theorem

◮ Once we have established what a contract is and how it works

the next natural question is:

◮ What could parties achieve in an economic environment in

which they can costlessly negotiate a contractual agreement?

◮ The answer to this question is the celebrated Coase Theorem.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 23 / 52

Coase Theorem (2)

Theorem (Coase Theorem: Coase (1960))

In an economy where ownership rights are well defined and transacting is costless gains from trade will be exploited (a contract will be agreed upon) and efficiency achieved whatever the distribution of entitlements.

◮ That is rational agents write contracts that are individually

rational and Pareto efficient.

◮ A contract is individually rational if each contracting party is

not worse off by deciding to sign the contract rather then choosing not to sign it.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 24 / 52

Freedom of Contract

◮ This is the reflection of an other basic principle of a well

functioning legal system known as: freedom of contract.

◮ This is equivalent to assume that the action space of the

contracting parties always contains the option not to sign the contract.

◮ A contract is Pareto efficient if there does not exist an other

feasible contract that makes at least one of the contracting party strictly better off without making any other contracting party worse off.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 25 / 52

A Model of Production Externality

◮ Consider the following simple model of a production

externality.

◮ Consider two parties, labelled A and B. ◮ Party A generates revenue RA(eA) (strictly concave) by

choosing the input eA at a linear cost c eA (c > 0).

◮ A’s payoff function is then:

ΠA(eA) = RA(eA) − c eA

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 26 / 52

A Model of Production Externality (2)

◮ Party B generates revenue RB(eB) (strictly concave) by

choosing the input eB at the linear cost c eB (c > 0).

◮ Party B also suffers from an externality γ eA (γ > 0) imposed

by A on B.

◮ B’s payoff function is then:

ΠB(eB) − γ eA = RB(eB) − c eB − γ eA

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 27 / 52

Social Efficient Outcome

◮ Consider first the social efficient amounts of input e∗ A and e∗ B. ◮ These solve the Central Planner’s problem:

max

eA,eB ΠA(eA) + ΠB(eB) − γ eA ◮ In other words (e∗ A, e∗ B) are such that:

R′

A(e∗ A) = c + γ

R′

B(e∗ B) = c

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 28 / 52

No Agreement Outcome

◮ Assume now that parties choose the amounts of input eA and

eB simultaneously and independently.

◮ Party A’s problem:

max

eA

ΠA(eA)

◮ Party B’s problem:

max

eB

ΠB(eB) − γ eA

◮ In equilibrium the inputs chosen (ˆ

eA, ˆ eB) are: R′

A(ˆ

eA) = c, R′

B(ˆ

eB) = c

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 29 / 52

Gains form Trade

◮ Comparing (ˆ

eA, ˆ eB) and (e∗

A, e∗ B) we obtain using concavity of

RA(·): e∗

B = ˆ

eB, e∗

A < ˆ

eA

◮ In other words:

[ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] − [ΠA(ˆ

eA) + ΠB(ˆ eB) − γ ˆ eA] = = [ΠA(e∗

A) − ΠA(ˆ

eA)] + γ (ˆ eA − e∗

A) > 0 ◮ The joint surplus is reduced by the inefficiency generated by

the externality.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 30 / 52

Gains form Trade (2)

◮ Assume now that the two contracting parties get together and

agree on a contract before the amounts of input are chosen: exploit the gains from trade.

◮ A reduction of input eA from ˆ

eA to e∗

A generates:

◮ a decrease in the net revenues from A’s technology:

ΠA(e∗

A) < ΠA(ˆ

eA)

◮ reduction in the negative externality

γ e∗

A < γ ˆ

eA

and the former effect is more than compensated by the latter

• ne

γ (ˆ eA − e∗

A) > [ΠA(ˆ

eA) − ΠA(e∗

A)]

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 31 / 52

Negotiation and Ownership Rights

◮ This may create room for negotiation. ◮ For simplicity normalize to 1 the total size of the surplus that

is available to share between the two contracting parties (parties negotiate on which percentage of the surplus accrues to each one).

◮ To establish a well defined negotiation ownership rights need

to be specified.

◮ Entitlements/ownership rights define the outside option of

each party to the contract.

◮ In other words they define the payoff each party is entitled to

without need for the other party to agree.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 32 / 52

Bargaining

◮ Denote wA and wB the entitlements of party A, respectively B

where: wA + wB < 1.

◮ In general, the Coase Theorem is stated without a specific

reference to a bargaining protocol: extensive form of the costless negotiation between the two parties.

◮ In what follows we will show the result for three examples of a

specific bargaining game with outside options.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 33 / 52

Bargaining (2)

Denote:

◮ δ the parties’ common discount factor, ◮ x the share of the pie to party A, ◮ (1 − x) the share of the pie to party B.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 34 / 52

Take-it-or-leave-it offer by Party A

Extensive form:

◮ A makes an offer x ∈ [0, 1] to B; ◮ B observes the offer x and decides whether to accept or reject

it.

◮ If the offer is accepted the game ends and the players payoffs

are: PA = x [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = (1 − x)[ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ If the offer is rejected the game ends and the players’ payoffs

are: PA = wA [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = wB [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A]

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 35 / 52

Take-it-or-leave-it offer by Party A (2)

◮ Subgame Perfect Equilibria Outcome:

Shares: x = 1 − wB (1 − x) = wB

◮ SPE Strategies:

◮ A offers share 1 − x = wB; ◮ B accepts any share 1 − x′ ≥ wB. Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 36 / 52

Take-it-or-leave-it offer by Party A (3)

Proof: backward induction:

◮ In the last stage of the game B gets wB if he rejects A’s offer,

hence B accepts any offer x′ such that (1 − x′) ≥ wB;

◮ In the first stage of the game A makes the offer that gives A

the highest payoff. A’s payoff is x hence the unique equilibrium offer is x = 1 − wB.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 37 / 52

Take-it-or-leave-it offer by Party A (3)

◮ The Payoffs associated with this equilibrium agreement are

then: PA = (1 − wB) [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = wB [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ Clearly, efficiency applies:

PA + PB = [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ In other words input choices are efficient (e∗ A, e∗ B). ◮ The ownership rights/entitlements of player B determine the

shares of the two parties.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 38 / 52

Take-it-or-leave-it offer by Party B

Extensive form:

◮ B makes an offer x ∈ [0, 1] to A; ◮ A observes the offer x and decides whether to accept or reject

it.

◮ As before, if the offer is accepted the game ends and the

players payoffs are: PA = x [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = (1 − x)[ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ If the offer is rejected the game ends and the players’ payoffs

are: PA = wA [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = wB [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A]

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 39 / 52

Take-it-or-leave-it offer by Party B (2)

◮ Subgame Perfect Equilibria Outcome:

Shares: x = wA (1 − x) = 1 − wA

◮ SPE Strategies:

◮ B offers share x = wA; ◮ A accepts any share x′ ≥ wA. Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 40 / 52

Take-it-or-leave-it offer by Party B (3)

Proof: backward induction:

◮ In the last stage of the game A gets wA if he rejects B’s offer,

hence A accepts any offer x′ such that x′ ≥ wA;

◮ In the first stage of the game B makes the offer that gives B

the highest payoff. B’s payoff is 1 − x hence the unique equilibrium offer is x = wA.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 41 / 52

◮ The Payoffs associated with this equilibrium agreement are

then: PA = wA [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = (1 − wA) [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ Once again, efficiency applies:

PA + PB = [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ Input choices are efficient: (e∗ A, e∗ B). ◮ The ownership rights/entitlements of player A, this time,

determine the shares of the two parties.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 42 / 52

Two Periods Alternating Offers

Period 1: Stage I: A makes an offer xA to B, Stage II: B observes the offer and has three alternatives:

◮ he can accept the offer, then x = xA and the

game terminates;

◮ he can reject the offer and take his outside

• ption wB and the game terminates;

◮ he can reject the offer and not take his outside

• ption, then the game moves to Stage I of the

following period.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 43 / 52

Two Periods Alternating Offers (2)

Period 2: Stage I: B makes an offer xB to A, Stage II: A observes the offer and has two alternative choices:

◮ he can accept the offer, then x = xB and the

game terminates;

◮ he can reject the offer and take his outside

• ption wA and the game terminates.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 44 / 52

Two Periods Alternating Offers Payoffs

◮ If parties agree on x in period 1:

PA = x [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = (1 − x)[ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ If parties agree on x in period 2:

PA = δ x [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = δ (1 − x)[ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ If they do not agree and either party takes his outside option

in period t = 1, 2: PA = δt−1 wA [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = δt−1 wB [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A]

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 45 / 52

Two Periods Alternating Offers, Equilibrium

◮ Subgame Perfect Equilibrium Outcome:

Agreement is reached in the first period with payoffs: (1 − max{wB, δ(1 − wA)}, max{wB, δ(1 − wA)})

◮ SPE Strategies:

◮ A offers share 1 − xA = max{wB, δ(1 − wA)} in period 1; ◮ B accepts any share 1 − x′ ≥ max{wB, δ(1 − wA)} in period 1; ◮ B rejects any share 1 − x′ < max{wB, δ(1 − wA)} in period 1; ◮ B offers share xB = wA in the period 2; ◮ A accepts any share x′ ≥ wA in the period 2. Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 46 / 52

Two Periods Alternating Offers, Equilibrium (2)

Proof: backward induction:

◮ In the last stage of the second period of the game B makes a

take-it-or-leave-it offer to A, hence as seen above A gets wA while B gets 1 − wA.

◮ Notice that B’s value in the first period of his expected payoff

in the second period is δ (1 − wA).

◮ Recall that in the first period B has also the option to take

wB.

◮ This implies that in the first period B accepts any offer such

that 1 − x′ ≥ max{wB, δ(1 − wA)}.

◮ Therefore A will make the offer that maximizes her payoff and

is accepted: xA = 1 − max{wB, δ(1 − wA)}.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 47 / 52

◮ The Payoffs associated with this equilibrium agreement are

then: PA = [1 − max{wB, δ(1 − wA)}][ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A],

PB = max{wB, δ(1 − wA)} [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ Once again, efficiency applies:

PA + PB = [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] ◮ Input choices are efficient: (e∗ A, e∗ B). ◮ The ownership rights/entitlements of player A, this time,

determine the shares of the two parties.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 48 / 52

Efficiency and Ownership Rights

◮ Notice that an efficient agreement is reached in all these cases

independently of the size of the entitlements (wA, wB).

◮ Clearly in all cases the result above implies that we would get

the efficient outcome: (e∗

A, e∗ B). ◮ However, the share that accrues to each party depends on the

entitlements wA and wB.

◮ The equilibrium contract specifies a transfer (that depends on

wA and wB) between the two parties and A’s choice of input e∗

A.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 49 / 52

Ownership Rights

◮ In particular if each party is entitled to the choice of his input,

then: wA = ΠA(ˆ eA) ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A

wB = ΠB(ˆ eB) − γ ˆ eA ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A ◮ In the case of A’s TIOLI equilibrium payoffs are:

PA = [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] − [ΠB(ˆ

eB) − γ ˆ eA], PB = [ΠB(ˆ eB) − γ ˆ eA]

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 50 / 52

Ownership Rights (2)

◮ In the case of B’s TIOLI equilibrium payoffs are:

PA = ΠA(ˆ eA), PB = [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] − ΠA(ˆ

eA)

◮ In the case of two periods alternating offers bargaining

equilibrium payoffs are: PA = [ΠA(e∗

A) + ΠB(e∗ B) − γ e∗ A] − PB,

PB = max{[ΠB(ˆ eB)−γ ˆ eA], δ[ΠA(e∗

A)+ΠB(e∗ B)−γ e∗ A−ΠA(ˆ

eA)]}

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 51 / 52

The Coasian Contract

◮ It is important to recall that the parties need to agree to the

contract before choosing the investments (eA, eB).

◮ The Coasian contract specifies: their choice of investments

(e∗

A, e∗ B) and the transfers that the parties have to make to

each other.

◮ As seen above, in the case of non-performance the enforcer

will duly punish the non-performing party (damages) so as to guarantees the terms of the contract.

◮ Notice that if the parties just meet and negotiate after their

choice of (eA, eB), no gains of trade will be present hence no Coasian agreement can be reached.

Leonardo Felli (LSE) EC476 Contracts and Organizations, Part III 12 January 2015 52 / 52