Incomplete Contracts Theory

Incomplete Contracts Theory—formally anchored in the Hart–Moore Renegotiation Model—is the foundational paradigm in microeconomic contract theory, law and economics, and business and economics theory that analyzes strategic contracting, ex-post renegotiation, and relationship-specific investment when parties cannot write complete state-contingent contracts enforced by third-party courts. Formulated by economists Oliver Hart and John Moore in their landmark 1988 Econometrica paper "Incomplete Contracts and Renegotiation" and given its axiomatic microfoundation in their 1999 Review of Economic Studies article "Foundations of Incomplete Contracts", the theory provides the analytical backbone for the property rights theory of the firm and the Aghion–Bolton control-rights model of corporate finance. Addressing the gap between classical complete-contract mechanism design and commercial legal practice, Hart and Moore demonstrated that when trading partners observe the realized state of nature ω symmetrically ex post—including buyer valuation v(ω, β) and seller production cost c(ω, σ)—but external courts cannot verify ω, any initial contract specifying a trade price p₁ and a no-trade penalty price p₀ is subject to voluntary ex-post message-exchange renegotiation. Because contracting parties cannot credibly commit not to renegotiate mutually beneficial modifications once investments (β, σ) are sunk, the sensitivity of final transfer prices to court-verifiable evidence is compressed, inducing underinvestment in relationship-specific capital relative to the first-best benchmark.

The Classical Arrow–Debreu and Complete Mechanism Design Benchmark

In classical general equilibrium theory (Arrow and Debreu, 1954) and principal–agent contract theory (Holmström, 1979; Grossman and Hart, 1983), long-term contracts are assumed to be complete: every relevant future contingency, performance metric, or verifiable signal can be written into an initial agreement at Date 0 and enforced by an impartial court. Even when private information or hidden action creates adverse selection or moral hazard, complete-contract theory assumes that payments can be conditioned on every publicly observable variable without omission, ambiguity, or subsequent modification.

Commercial contracts, joint-venture charters, and corporate indentures depart from this benchmark. As Ronald Coase (1937) and Oliver Williamson (1975, 1985) emphasized in transaction cost economics, commercial contracts are sparse, omit foreseeable contingencies, rely on coarse delivery terms or fixed prices, and are frequently renegotiated as circumstances unfold.

Observable vs. Verifiable Information and Transaction Costs

Hart and Moore (1988, 1999) formalized why contracts are incomplete by distinguishing three structural frictions:

1. Unforeseen and Indescribable Contingencies: In complex engineering, research, or supply relationships, the physical nature of the good to be traded and the universe of possible future states ω ∈ Ω cannot be cataloged in advance at Date 0.
2. Writing and Computation Costs (Bounded Rationality): Drafting unambiguous contractual clauses for thousands of low-probability states imposes prohibitive legal and cognitive transaction costs.
3. Observability Without Third-Party Verifiability: An informational wedge exists between what the contracting parties themselves know (symmetric ex-post observability) and what can be proven with legal evidence before an outside judge or arbitrator (verifiability). A buyer and a specialized component supplier may both observe inside the factory whether a quality defect arose from the buyer's shifting engineering blueprints or the supplier's machining negligence, yet neither party can prove that state ω to a court.

Because courts can enforce only verifiable actions—such as whether a physical widget was delivered (q ∈ {0, 1}), what monetary payment t changed hands, and what written, signed messages were exchanged—initial contracts must be written on coarse verifiable events and are inherently incomplete.

Timeline, Relationship-Specific Investments, and State Realizations

Consider a bilateral trading relationship between a risk-neutral Buyer and a risk-neutral Seller over one unit of an indivisible intermediate good q ∈ {0, 1}. If trade occurs (q = 1), the Buyer realizes a gross valuation v and the Seller incurs a production cost c, yielding ex-post net gains from trade v − c. If no trade occurs (q = 0), both valuation and production cost are normalized to zero.

The game unfolds across five sequential dates:

• Date 0 (Initial Contract): The Buyer and Seller sign an initial court-enforceable contract before investments or state realizations occur.
• Date 1/2 (Relationship-Specific Investments): The Buyer chooses a relationship-specific investment β ∈ ℝ₊ at private cost h_b(β), and the Seller simultaneously chooses a relationship-specific investment σ ∈ ℝ₊ at private cost h_s(σ), where h_b(β) and h_s(σ) are increasing and convex. Neither β nor σ is observable to the court.
• Date 1 (State of Nature Realization): The state of nature ω ∈ Ω is drawn from a common-knowledge probability distribution and is observed symmetrically by both the Buyer and the Seller, determining the realized buyer valuation v(ω, β) and seller production cost c(ω, σ), with ∂v/∂β > 0 and ∂c/∂σ < 0. An external court cannot observe ω, v, or c.
• Date 1.5 (Ex-Post Renegotiation and Verifiable Message Game): Having observed ω (and therefore v and c), the Buyer and Seller can exchange verifiable written messages (offers, counteroffers, and signed contract revisions) and voluntarily renegotiate the Date 0 contract before delivery takes place.
• Date 2 (Trade Execution and Court Enforcement): The trade decision q ∈ {0, 1} and final monetary transfer t from Buyer to Seller are executed according to the prevailing contract (or its mutually signed renegotiated replacement), enforced by the court.

Ex-Post Efficiency vs. First-Best Investment Benchmark

In the first-best benchmark where both ω and investments (β, σ) are verifiable, trade occurs at Date 2 if and only if the realized valuation exceeds the realized production cost (q^FB = 1 iff v(ω, β) ≥ c(ω, σ)). Given efficient trade q^FB, the first-best relationship-specific investments (β^FB, σ^FB) maximize expected net social surplus E_ω[max{0, v(ω, β) − c(ω, σ)}] − h_b(β) − h_s(σ), satisfying the marginal return conditions:

Thus, first-best incentives require the Buyer to capture 100% of the marginal valuation gain ∂v/∂β across all trading states (v ≥ c), and simultaneously require the Seller to capture 100% of the marginal cost reduction −∂c/∂σ across all trading states (v ≥ c).

Why Simple At-Will Contracts (p₀, p₁) Are Renegotiated

Suppose the Date 0 contract specifies two numbers: a trade price p₁ paid by the Buyer if delivery occurs (q = 1), and a no-trade price (liquidated damages) p₀ paid if no delivery occurs (q = 0), with incremental trade price Δp ≡ p₁ − p₀. Because trading requires the physical cooperation of both the Seller (to deliver) and the Buyer (to accept delivery), either party can unilaterally force no-trade (q = 0) at Date 2 if no new agreement is reached, triggering the default transfer p₀.

Once state ω is realized at Date 1, three regions arise relative to Δp = p₁ − p₀:

1. No-Renegotiation Trade Region (v ≥ Δp ≥ c): Trading at p₁ gives the Buyer net surplus v − p₁ ≥ −p₀ and gives the Seller p₁ − c ≥ p₀. Both parties trade (q = 1) at t = p₁ without renegotiation.
2. Efficient Breach / No-Trade Region (v < c): Because v < c, no-trade (q = 0) is ex-post efficient, and no-trade occurs at transfer t = p₀.
3. Renegotiation Region (v ≥ c, but either Δp > v or Δp < c): Trade is ex-post efficient (v ≥ c), but one party refuses to trade under the original incremental price Δp. If Δp > v ≥ c, the Buyer refuses to buy at p₁, and the parties renegotiate the trade price downward so trade occurs (q = 1). Symmetrically, if v ≥ c > Δp, the Seller refuses to produce at Δp, and the parties renegotiate the price upward so efficient trade (q = 1) takes place.

Verifiable Message Games and Contractual Revision Rules

Hart and Moore (1988) also analyzed what can be achieved when the Date 0 contract specifies a general mechanism (q(μ), t(μ)) conditioned on verifiable written messages μ = (m_b, m_s) publicly exchanged between Date 1 and Date 2 (such as signed purchase orders or notarized price concessions retained by both sides). Even when the Date 0 contract includes a message game (q(μ), t(μ)), the parties cannot commit not to tear up the original contract and replace it with a newly signed contract (q′, t′) at the final moment before Date 2 if both prefer (q′, t′) to the outcome (q(μ), t(μ)).

Why Renegotiation Compresses Price Sensitivity

Hart and Moore (1988) proved a characterization of all subgame-perfect equilibria of the ex-post message and renegotiation game: whenever v(ω, β) ≥ c(ω, σ), ex-post renegotiation ensures that efficient trade always occurs (q = 1), and whenever v(ω, β) < c(ω, σ), no trade occurs (q = 0). However, because the parties can replace the outcome of any message game μ before Date 2, the equilibrium transfer price t when trade occurs (q = 1) takes the piecewise-clamped form:

When v ≥ c, the Buyer's net payoff U_b = v − t(v, c) and the Seller's net payoff U_s = t(v, c) − c across the three ordering regimes are:

1. High-Price Regime (Δp > v ≥ c): Along any boundary where the renegotiated price tracks v, the Seller captures ∂v/∂β while the Buyer's marginal return to β vanishes (∂U_b/∂β = 0).
2. Interior Contract Regime (v ≥ Δp ≥ c): Trade occurs at the fixed price t = p₁; here ∂U_b/∂β = ∂v/∂β and ∂U_s/∂σ = −∂c/∂σ (full marginal incentives for both parties).
3. Low-Price Regime (v ≥ c > Δp): Along any boundary where the renegotiated price tracks c, the Buyer reimburses the Seller's realized cost, eliminating the Seller's marginal incentive to reduce cost (∂U_s/∂σ = 0).

General Underinvestment and Specific First-Best Exceptions

Because random shocks ω cause the realized interval [c(ω, σ), v(ω, β)] to fluctuate across states of nature, no constant incremental price Δp = p₁ − p₀ can lie inside [c(ω, σ), v(ω, β)] in every state ω simultaneously unless the distributions of valuations and costs do not overlap.

Hart–Moore (1988) Underinvestment Theorem: When valuations v(ω, β) and costs c(ω, σ) have overlapping support across states ω and both parties make self-investments (∂v/∂β > 0, ∂c/∂σ < 0), any renegotiation-proof incomplete contract induces underinvestment by at least one (and generically both) parties: β* ≤ β^FB and σ* ≤ σ^FB.

Hart and Moore (1988) also identified three special cases in which an incomplete contract (p₀, p₁) achieves the first-best investment outcome (β^FB, σ^FB):

1. Only One Party Invests: If only the Buyer invests (σ is fixed), setting Δp ≤ min_ω c(ω) ensures the Seller always renegotiates up to p₀ + c(ω), allowing the Buyer to capture the net surplus v − c and invest at β^FB.
2. Uniform Separation of Supports (v_min ≥ c_max): If trade is efficient in every state ω (v(ω, β) ≥ c(ω, σ) with probability 1), a specific-performance contract setting Δp ∈ [c_max, v_min] ensures that v ≥ Δp ≥ c holds in every state without renegotiation.
3. Verifiable Action Asymmetry: If a court-verifiable action (such as who initiates delivery refusal) separates states, message-contingent contracts can expand incentives.

The Maskin–Tirole (1999) Critique: Subgame-Perfect Implementation

In "Unforeseen Contingencies and Incomplete Contracts" (1999, Review of Economic Studies), Eric Maskin and Jean Tirole questioned whether observable-but-non-verifiable information and indescribable contingencies justify restricting contracts to simple ownership allocations or (p₀, p₁) price pairs. Drawing on the Maskin Nash implementation theorem and Moore–Repullo (1988) subgame-perfect implementation, Maskin and Tirole showed that if contracting parties have symmetric ex-post knowledge of their payoff functions and can commit not to renegotiate ex post, a sequential revelation mechanism over payoffs forces both parties to report the true state ω in subgame-perfect equilibrium, implementing the first-best investment (β^FB, σ^FB). Similarly, Georg Nöldeke and Klaus M. Schmidt (1995) showed that if the court can verify sequential delivery refusal, a simple option contract can achieve the first-best when investments are purely selfish (∂v/∂σ = 0 and ∂c/∂β = 0).

Hart and Moore's (1999) Theorem on Indescribable Contingencies and Renegotiation

In "Foundations of Incomplete Contracts" (1999, Review of Economic Studies), published in the same symposium issue, Oliver Hart and John Moore answered this critique and established the axiomatic foundation of incomplete contracts under three realistic conditions:

1. Indescribable Widgets and Payoff Richness: At Date 0, the customized widget to be traded cannot be described in the contract, while N artificial "decoy" widgets exist whose costs and values can be permuted across states of nature.
2. Inability to Commit Against Renegotiation: The Buyer and Seller can always collude ex post to bypass a third-party penalty collector and substitute a newly signed contract whenever an outcome is ex-post Pareto inefficient.
3. Cooperative (Cross-Effect) Investments: The Seller's investment σ improves the Buyer's valuation v(ω, σ) (such as a supplier investing in quality engineering that raises the downstream durability of the Buyer's final product, ∂v/∂σ > 0) rather than merely lowering the Seller's own cost c.

Hart and Moore (1999) proved the Irrelevance of Clever Mechanisms Theorem: as the degree of payoff richness N grows large and ex-post renegotiation cannot be prevented, no message-game mechanism can outperform the complete absence of a contract (the null contract / spot market governance). Because any attempt by the Seller to exercise a high-price option on a decoy widget triggers ex-post renegotiation back to the true efficient widget, the Seller's payoff collapses back to the standard Nash bargaining share under asset ownership, restoring the conclusions of the Grossman–Hart–Moore property rights model and Che and Hausch's (1999) theorem on cooperative investments.

Contracts as Reference Points (Hart and Moore, 2008)

In 2008, Hart and Moore introduced a complementary paradigm in "Contracts as Reference Points" (Quarterly Journal of Economics). Whereas the 1988–1999 literature assumed that ex-post renegotiation is frictionless, Hart and Moore (2008) proposed that an initial incomplete contract serves as a psychological and legal reference point for entitlement. When a flexible contract leaves a range of ex-post prices [p_L, p_H] open, each party feels entitled to the best permitted outcome (p_L for the Buyer, p_H for the Seller); the party who receives less than their perceived entitlement shades on non-verifiable performance quality (shading), creating deadweight execution losses.

What is the difference between observable information and verifiable information in contract theory?

A variable (such as buyer valuation v, seller production cost c, or component quality) is observable if both contracting parties know its true value once the state of nature ω is realized. However, that variable is non-verifiable if neither party can prove its value to a judge or arbitrator using legally admissible evidence. Because courts enforce payments only conditional on verifiable variables (such as delivery q ∈ {0, 1} or signed notices), symmetric observability is insufficient to write a complete state-contingent contract.

Why can't contracting parties simply include a clause forbidding future renegotiation?

In common law and civil law jurisdictions, courts refuse to enforce "no-modification" or "anti-renegotiation" clauses when both contracting parties mutually sign a new agreement superseding their earlier contract (e.g., Restatement (Second) of Contracts § 283). Even if the parties involve a third party who collects a penalty upon contract modification, the Buyer, the Seller, and the third party have a joint incentive to renegotiate around any ex-post inefficient waste and split the saved surplus.

When do option contracts fail to solve the holdup problem under incomplete contracts?

While Nöldeke and Schmidt (1995) showed that an option contract can solve the holdup problem when investments are selfish (the Buyer's investment affects only the Buyer's valuation v, and the Seller's investment affects only the Seller's cost c), Che and Hausch (1999) and Hart and Moore (1999) proved that option contracts fail when investments are cooperative (where the Seller's engineering effort raises the Buyer's valuation v(ω, σ)). When renegotiation cannot be prevented, any option strike price that tries to reward the Seller for raising v is undone by ex-post renegotiation over which widget is delivered.

1. Hart, O., & Moore, J. (1988). "Incomplete Contracts and Renegotiation." Econometrica, 56(4), 755–785. https://doi.org/10.2307/1912698
2. Hart, O., & Moore, J. (1999). "Foundations of Incomplete Contracts." Review of Economic Studies, 66(1), 115–138. https://doi.org/10.1111/1467-937X.00080
3. Maskin, E., & Tirole, J. (1999). "Unforeseen Contingencies and Incomplete Contracts." Review of Economic Studies, 66(1), 83–114. https://doi.org/10.1111/1467-937X.00079
4. Che, Y.-K., & Hausch, D. B. (1999). "Cooperative Investments and the Value of Contracting." American Economic Review, 89(1), 125–147. https://doi.org/10.1257/aer.89.1.125
5. Hart, O., & Moore, J. (2008). "Contracts as Reference Points." Quarterly Journal of Economics, 123(1), 1–48. https://doi.org/10.1162/qjec.2008.123.1.1