Contract-Based Panel Market Design

• Contract-based panel market is a mechanism where panel capacity rights are traded ex ante, emphasizing expected generation value over spot output.
• It models buyer demand and seller leasing decisions that drive both short-term clearing and long-term investment outcomes.
• This design can lead to over-investment when solar premia are low, contrasting with spot and product-differentiated real-time market mechanisms.

A contract-based panel market is a market in which the traded object is specified by contract rather than by an ex post spot transfer of realized output. In the most explicit formulation under that name, the market “trades claims or rights to the production of certain panel capacity ex-ante, rather than the realized solar production ex-post” (Davoudi et al., 8 Sep 2025). In that setting, panel owners lease units of panel capacity, buyers receive the realized stochastic output generated by the leased capacity, and long-run panel investment is determined by the expected revenue produced by this contract structure rather than by a spot-only energy market (Davoudi et al., 8 Sep 2025).

1. Contract object and market semantics

In the distributed-solar formulation, the contract-based panel market is defined by a shift in the traded commodity. The seller does not sell realized electricity after uncertainty resolves; instead, the seller rents out units of panel capacity ex ante. The buyer then receives the realized generation associated with that rented capacity. Seller $i$ can rent out any amount in

$\mathcal Q_i^{\mathrm s}=[0,c],$

while buyer $i$ can lease any nonnegative amount in

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$

If buyer $i$ leases capacity $q_i^{\mathrm b}$, realized solar service is $q_i^{\mathrm b}G$, capped at load $L$ (Davoudi et al., 8 Sep 2025).

The buyer’s expected payoff is

$$\Pi_i^{\mathrm b}(q_i^{\mathrm b},\pi) = v_i\mathbb E\min\{q_i^{\mathrm b}G,L\} -\pi q_i^{\mathrm b} -\pi_{\mathrm u}\mathbb E(L-q_i^{\mathrm b}G)_+,$$

where $v_i$ is the buyer’s extra valuation for solar relative to utility supply, $\mathcal Q_i^{\mathrm s}=[0,c],$0 is per-unit panel generation, and $\mathcal Q_i^{\mathrm s}=[0,c],$1 is the utility backstop price (Davoudi et al., 8 Sep 2025). The seller payoff is linear in leased capacity,

$\mathcal Q_i^{\mathrm s}=[0,c],$2

This contract semantics differs sharply from two related real-time mechanisms analyzed in the same framework. In the single-product real-time market, realized solar and grid power are sold ex post as one undifferentiated product. In the product-differentiated real-time market, realized solar is sold ex post as a separate product. In the contract-based panel market, by contrast, buyers choose capacity based on expected service value from leased stochastic generation (Davoudi et al., 8 Sep 2025). A plausible implication is that the market internalizes a different notion of value: expected access to stochastic production, rather than only ex post scarcity value.

2. Short-term clearing and long-term equilibrium

The contract-based panel market is embedded in a two-level equilibrium model linking short-term market clearing to long-term investment. Potential investors form a nonatomic continuum $\mathcal Q_i^{\mathrm s}=[0,c],$3, each choosing $\mathcal Q_i^{\mathrm s}=[0,c],$4, with aggregate installed capacity

$\mathcal Q_i^{\mathrm s}=[0,c],$5

For mechanism $\mathcal Q_i^{\mathrm s}=[0,c],$6, investor $\mathcal Q_i^{\mathrm s}=[0,c],$7’s payoff is

$\mathcal Q_i^{\mathrm s}=[0,c],$8

where $\mathcal Q_i^{\mathrm s}=[0,c],$9 is the upfront capital-plus-installation cost per unit panel capacity (Davoudi et al., 8 Sep 2025).

Short-term clearing in the contract-based panel market is determined by buyer demand for panel-capacity rights. The key object is the truncated expectation

$i$0

which is differentiable and nonincreasing in $i$1 (Davoudi et al., 8 Sep 2025). Buyer $i$2’s optimal demand is

$i$3

and aggregate demand is

$i$4

Because seller payoff is linear and $i$5, each seller leases all capacity, so equilibrium in the short-term market is characterized by

$i$6

Seller lifetime revenue in the contract-based panel market is

$i$7

where $i$8 scales representative-period revenue to the panel lifetime (Davoudi et al., 8 Sep 2025). Long-run Nash equilibrium is then pinned down by the zero-profit condition

$i$9

For the contract-based panel market this becomes

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$0

This equilibrium representation is technically distinctive. The installed capacity is not obtained from expected realized-energy sales, but directly from a capacity-demand function evaluated at the zero-profit rental price. That feature distinguishes the contract-based panel market from both spot-like and product-differentiated real-time mechanisms (Davoudi et al., 8 Sep 2025).

3. Comparative welfare properties and over-investment

The same framework yields three benchmark mechanisms.

Mechanism	Traded object	Long-run property
Single-product real-time market	Realized electricity ex post	Under-investment
Product-differentiated real-time market	Realized solar ex post as a separate product	Socially optimal investment
Contract-based panel market	Claims or rights to panel capacity ex ante	Over-investment when extra valuations are small

The formal ordering is

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$1

and, for sufficiently small positive solar premia under the stated regularity condition,

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$2

with the sharper statement

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$3

for some $\mathcal Q_i^{\mathrm b}=\mathbb R_+.$4 (Davoudi et al., 8 Sep 2025).

The product-differentiated real-time market is efficient because its long-run condition coincides with the social planner’s condition. The contract-based panel market is generally distorted because decentralized entry is driven by ex-ante demand for panel-capacity rights rather than by the ex-post scarcity value of realized solar generation (Davoudi et al., 8 Sep 2025). The paper’s explanation is that the contract market monetizes expected access to stochastic solar output in a way that can support a rental price, and therefore an investment level, above the socially optimal level when user solar premia are positive but small.

The no-premium case is a knife-edge benchmark. If $\mathcal Q_i^{\mathrm b}=\mathbb R_+.$5, then

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$6

Thus the distortion is not intrinsic to the ex-ante contract form alone; it emerges when heterogeneous positive premia for solar interact with ex-ante capacity-right trading (Davoudi et al., 8 Sep 2025).

The numerical experiments reinforce the analytical ranking. For $\mathcal Q_i^{\mathrm b}=\mathbb R_+.$7, the reported capacities are

$\mathcal Q_i^{\mathrm b}=\mathbb R_+.$8

For $\mathcal Q_i^{\mathrm b}=\mathbb R_+.$9, all four coincide at $i$0 (Davoudi et al., 8 Sep 2025). The contract-based panel market therefore appears in this model as a market form that can support more deployment than the planner benchmark.

4. Related contract-market mechanisms

The contract-based panel market sits within a wider literature in which contracts define market participation, quantity, payment, or quality before spot realization.

In forward electricity contracting, the equilibrium price can be represented as the dual variable of a centralized welfare maximization problem. The core equilibrium condition is

$i$1

and if $i$2 is the dual variable of the market-clearing constraint $i$3, then

$i$4

This gives a rigorous shadow-price interpretation of a centralized cleared contract market (Cavaliere et al., 2019).

In brokered reservation markets, the intermediary offers a menu of contract items

$i$5

where $i$6 is reservation amount and $i$7 is payment. In the TV white space model, the database-bearing-risk regime yields reservation closer to first-best than the WSD-bearing-risk regime, and the paper shows that the optimal contract under DB-bearing-risk leads to a higher profit for the database and a higher total network profit (Luo et al., 2015). This suggests that, in panel markets with an intermediary, the placement of quantity risk is itself a design variable rather than a purely contractual afterthought.

In continuous-type service markets, contract design appears as a menu

$i$8

with incentive compatibility, individual rationality, and an average-quality constraint

$i$9

The IoT-enabled data-market model derives separating, pooled, and fully nondiscriminative outcomes, including the result that if $q_i^{\mathrm b}$0 is increasing, the optimal contract is fully pooled (Chen et al., 2023). A plausible implication is that a panel market can rationally collapse many nominally distinct customer types into a small number of standardized panel packages.

In dynamic energy-control settings, contract design enters through a reward functional

$q_i^{\mathrm b}$1

and the planner’s problem reduces to choosing a price-like process $q_i^{\mathrm b}$2 and a participation payment $q_i^{\mathrm b}$3. In the ancillary-service formulation, the intended control is implemented by

$q_i^{\mathrm b}$4

so the contract functions as a dynamic market mechanism rather than as a static transfer schedule (Wasa et al., 2017).

5. Platform and infrastructure realizations

Several adjacent papers treat the contract market not primarily as an equilibrium object, but as a platform architecture.

A “contract aware marketplace” built on WS-Agreement uses a class-level versus instance-level split, with domain contracts defining market-facing structure and service contracts capturing provider-specific implementation. Its workflow is explicitly:

1. the consumer gets a domain template;
2. the consumer fills it to create a domain offer;
3. class-level and instance-level microflows collect provider templates;
4. templates are filtered and aggregated;
5. selected templates become service offers;
6. negotiation yields service agreements;
7. a domain agreement is persisted after use (Vigne et al., 2023). This architecture separates common contract structure, provider-specific adaptation, and buyer preference logic.

In permissioned-blockchain designs, a CSP community forms a contract domain implementing contract primitives, policies, and a contract-ledger. The model replaces token-for-operations pricing with fixed-fee contract services, and the basic primitives are asset transfer, escrow, ingress, and egress (Hardjono et al., 2020). This suggests a panel-market infrastructure in which multiple regulated providers share a domain-specific contract rail rather than a general-purpose gas market.

A closely related B2B platform uses permissioned blockchain, repeated-game incentives, and cryptographic regulation. Buyers submit feedback, a public perception protocol aggregates ratings, and a monitoring protocol checks buyer honesty while preserving buyer anonymity (Narang, 2020). The mechanism is not a panel market by name, but it has the structure of a managed supplier panel in which future allocation depends on contract-governed ratings.

For bilateral data exchange, BlockMarkchain implements smart-contract escrow with bilateral deposits, off-chain encrypted delivery, and on-chain dispute resolution. Its final protocol achieves $q_i^{\mathrm b}$5 blockchain communication in dispute by using signed chunk packages (Ehteram et al., 2020). A plausible implication is that a contract-based panel market with sensitive panel data could externalize bulk data transfer while keeping contractual verification and sanctions on-chain.

6. Trade-offs, limits, and adjacent extensions

The literature does not treat stronger contractual risk reduction as unambiguously preferable. In long-duration energy storage, contracts that eliminate revenue volatility achieve the lowest costs but may weaken operational incentives, while contracts that preserve market exposure maintain incentives at higher costs (Suski et al., 18 May 2026). In renewable CfD design, the basic CfD, 2way CfD, and financial CfD differ in exactly this way: production-based own-price hedging reduces investor volatility strongly but weakens dispatch and system-friendliness incentives, whereas benchmarked or capacity-based designs preserve more market structure at the cost of residual risk (Johanndeiter et al., 19 Dec 2025).

A related limitation concerns market structure. In constrained trading networks with bilateral contracts, competitive equilibrium exists for two-sided markets under polymatroidal constraints and separable utility, but may fail in genuinely multi-sided markets even under simple polymatroid constraints (Kizilkale et al., 2020). This suggests that a contract-based panel market is structurally safer when participants are partitioned into buyer-side and seller-side roles than when the same participants both buy and sell in tightly coupled ways.

Another limit concerns coordination under network or system constraints. In coordinated trading of contingent contracts, the system operator only checks feasibility and curtails infeasible trades; there is no centralized price-setting mechanism. Under the paper’s assumptions, the sequential process converges arbitrarily close to the stochastic welfare optimum (Qin et al., 2017). A plausible implication is that some contract-based panel markets need not be centralized auctions; they can instead be rolling admission systems with operator screening.

Finally, richer bundle structures can be incorporated. In ParlayMarket, conjunction contracts

$q_i^{\mathrm b}$6

are priced from a shared pairwise exponential-family state

$q_i^{\mathrm b}$7

and the AMM dynamics converge to a unique fixed point corresponding to the best approximation to the true joint distribution within the model class (Rana et al., 23 Mar 2026). The paper shows that aggregate market-maker loss remains controlled and grows at most quadratically in the number of base markets, while parlay trades improve identifiability of dependence structure. This suggests a route from simple capacity-right panel contracts to fully joint, bundle-based contract panels with coherent pooled liquidity.

A contract-based panel market is therefore best understood not as a single mechanism, but as a family of market designs in which contract form determines what is traded, how uncertainty is allocated, and which incentives survive decentralization. In the distributed-solar model, ex-ante capacity-right trading yields a distinctive equilibrium map and can generate over-investment relative to the planner benchmark (Davoudi et al., 8 Sep 2025). In adjacent literatures, the same structural idea reappears as reservation menus, forward-clearing constraints, quality-price schedules, dynamic incentive contracts, and platform-governed contract rails (Luo et al., 2015, Cavaliere et al., 2019, Chen et al., 2023, Wasa et al., 2017, Vigne et al., 2023, Hardjono et al., 2020).