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Incomplete Contracts. Renegotiation, Communications and Theory December 10, 2007. Introduction – “Show me the money!”. Long term contracts tend to be “incomplete” Difficult (and costly) to specify every contingency that might arise in a trading relationship - PowerPoint PPT Presentation

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  • Incomplete ContractsRenegotiation, Communications and TheoryDecember 10, 2007

  • *Introduction Show me the money!Long term contracts tend to be incompleteDifficult (and costly) to specify every contingency that might arise in a trading relationshipCommunication (content and method) can be used during the contract process to affect outcomeMost contractual disputes revolve around contractual incompletenessExamples: real estate contracts, M&A transactions (MAC clauses)

    Hart and Moore (1988) build a model of incomplete contracts and renegotiation that focuses on communication and contract revisions between two parties

    *

  • *Introduction Show me the money!*

  • *Model Setup & AssumptionsTwo parties who write an incomplete contract in Date 0Parties have the option to renegotiate or revise the contractExpectations of revisions has an effect on the original contractParties are interested in creating an optimal revision game that is sensitive to each parties benefits and costs

    After signing contract in Date 0 (but before Date 1), the buyer and seller make investments , Known to each other, but not publicly verifiableSigning contract at Date 0 commits parties to these investments

    After Date 0 (but before Date 2), v (buyers valuation) and c (sellers costs) are realized

    *

  • *Model Setup & Assumptions (contd)Realizations of v and c are determined by and and the state of the world at Date 1, Each partys investments only affect his or her own payoffBoth buyer and seller must enact the trade at Date 2The Contract Process:

    *Date 0Contract SignedDate 1v, c learned by partiesDate 2Trade?Payments, Disputes?Investments (, )Revision / Renegotiation

  • *The TransactionAt Date 2, trade happens (q = 1) or not (q = 0)Price to the seller is p1 or p0 Messages (m) exchanged by buyer and seller between Dates 1 and 2Contract can specify price functions p0 (m) or p1(m) Trade occurs when the following are satisfied:

    The above equations show that both buyer and seller prefer that the trade happens (q = 1)*

  • *Messages and the Revision ProcessParties exchange messages between Dates 1 and 2 the revision processParties can tear up the Date 0 contract and write a new one

    Messages can be sent reliably and cannot be forged

    Hart and Moore look at two message technologiesCase A Impossible to publicly record messages (ie parties can deny the receipt of certain messages)Case B Messages can be publicly recorded and cannot be deniedThe form of the optimal contract is very sensitive to each case

    *

  • The revision process can be thought of a game, consisting of two subgamesthe message game between Date 1 and 2 and the dispute game after Date 2Proposition 1 (equilibrium trading rule)( ) are the prices specified at the Date 0 contract The Trading Rule that will prevail at Date 2 are:If v < c, q = 0, buyer pays seller If v c, q = 1, buyer pays sellerIf v c > , q = 1, buyer pays seller + cIf > v c, q = 1, buyer pays seller + vHow does this look?

    *Case A: Messages Cannot be Verified*

  • *Equilibrium Trading Rule GraphedProposition 1:*

  • *Trading Rule Intuition Part I*12ResultGame Insight / Messaging1v < c, q = 02v p1 p0 c, q = 1

    1Valuation (v) is less than costs (c), so trade will not happen (ie q=1), so price will be p0Messages sent dont matter (and either party can choose not to reveal them) so price ends up at equilibrium p02Valuation is more than the difference between p1 and p0 so buyer and seller agree to trade (q=1) and price is p1 Messages also dont matter, buyer can choose to send no messages or reveal none from the seller so equilibrium is p1

  • *Trading Rule Intuition Part 2*43ResultGame Insight / Messaging3v c > p1 p0, q = 14p1 p0 > v c, q = 1

    3Seller can always obtain p0 but buyer wants the sale and pays p0 + c for trade to go throughSeller can ignore messages and get p0, so buyer needs q=1, so he offers + c on the last day of renegotiation to ensure q = 14Seller offers p0 + v and the buyer take the offer because that is still less than or equal to his valuationOn the last day of renegotiation, seller can send a message of p0 + v and the buyer accepts because its still within rule 4

  • Unverified messages constrain the ability of the buyer and seller to renegotiate the Date 0 contractThe outcomes are determined by the graph in the previous slides

    The trading mechanism can affect the buyer and sellers decisions in equilibrium

    Hart and Moore comment that the results are also sensitive to what the courts can retrospectively determine (which depends on the trading mechanism)

    *Case A: Conclusions*

  • Case B: Verifiable MessagesIf a message is sent from outside prescribed set, a player who sends a message from outside this set (or does not send a message at all) can be penalizedLead to revised contract prices,(p0ij, p1ij) Messages, mappings are choice variables at date 0

  • Final Trading Prices with Verifiable MessagesIf v c whatever messages are sent, trade occursIf v < c trade will not occur and the price will be p0ijAs before,

  • Value Function of the GameIf v c Expected Payoff to the seller:If v < c Expected Payoff to the SellerWhere = probability seller assigns to p1ij, = probability buyer assigns to p1ij

  • Aside: General Intuition of the Minmax TheoremZero sum gameEach player responds by minimizing the maximum expected payoff of the other playerMinmax same as maxmin same as NE

  • Expected Trade and Non-trade Prices with Verifiable Messages (1): The price that the buyer must pay for the good cannot fall if the sellers cost rises or if the buyers valuation rises

    (2): If v and c rise by , p1* rises by no more than

    (3):Neither the buyer nor the seller can be worse off trading than not

  • First Best Conditions (unverifiable)

    If any one of these holds, first best can be achieved:

    (1): Set p1-p0 = k, trade occurs, neither the buyer nor the seller influence the terms of the trade

    (2): Value for the buyer is independent of buyers investment decision, only sellerinvestment matters give seller all surplus, and hell invest optimally

    (3): Cost for the seller is independent of sellers investment decision, only buyerinvestment matters give buyer all surplus, and hell invest optimally

    (4) No uncertainty split surplus to make both parties better off trading

  • Second Best Conditions First best cannot be achievedThe distribution of the buyers valuation is a convex combination of two probability vectors, one which FOSD the otherGreater investment in puts more relative weight on the preferred lotteryCreate externality v now increasing in Decrease , decrease v, which negatively affects the seller because either no trade or lower price trade

  • Second Best (contd.)(3) Ensures a unique interior solution for , (4) If vc, always achieve first best

  • Case B Conclusions: UnderinvestmentThere exist (strict) conditions under which first best can be achieved (even with non-verifiable messages)There exist conditions under which first best cannot be achieved (even with verifiable messages)Second best can be achieved with verifiable messages Even with verifiable messages, underinvestment

    *Exactly the same intuition as Sharat should have talked about *Proven by Nash, in Luce and Raiffa

    *First best outcome: buyer and seller have the correct private incentives to invest

    (2) This can be done by setting the difference between p1 and p0 to be larger than the buyers highest valuation, so buyer never want to trade and the selling price is p0 + v, which gives the seller all of the surplus

    (3) This can be done by setting the difference between p1 and p0 to be smaller than the sellers lowest cost, so the revised trading price is p0 + c, which gives the buyer all of the surplus

    (4) No uncertainty. Buyer/seller either expect trade, invest efficiently or they dont expect to trade, make minimum investment. Dividing the surplus so tha both parties are better off than if their were no relationship. *Ton of conditions to where first-best outcome cannot be achieved.

    Even with verifiable messages, second best with verifiable is equivalent to second best veriable

    Under these conditions, under-investment

    FOSD: one lottery is superior to the other

    *This should be c upper bar. Under special assumptions about the stochastic technology, even with verifiable messages there will be under investment

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