Sunshine Trading Theory in Energy Markets

• Sunshine Trading Theory is a framework linking market design, price formation, and long-run solar investment incentives, with applications in both renewable energy and trading microstructure.
• It models equilibrium solar capacity as an endogenous outcome driven by individual installation decisions and short-term competitive market mechanisms.
• The theory demonstrates that different market designs can lead to under- or over-investment, highlighting the impact of transparency on achieving socially optimal outcomes.

Searching arXiv for the cited papers and closely related uses of the term "Sunshine Trading Theory". First, I’ll look up the exact arXiv entries by ID. Searching for arXiv paper (Davoudi et al., 8 Sep 2025). Sunshine Trading Theory, in recent arXiv usage, denotes a framework that links market design, price formation, and long-run investment incentives in distributed solar panels, while a separate market-microstructure literature uses “sunshine trading” to describe publicly disclosed trading intentions that reduce adverse selection. In the solar-investment formulation, the theory studies how aggregate installed capacity $Q$ enters short-term competitive equilibria and, through expected revenues, feeds back into the long-run Nash equilibrium of investors. In the microstructure formulation, the same transparency motif appears in the prediction that preannounced order flow is treated as uninformed liquidity demand and therefore faces lower execution costs (Davoudi et al., 8 Sep 2025, Barone et al., 14 Jun 2026).

1. Non-atomic investment game

The solar-investment formulation is built as a non-atomic game of solar investors. The players are an atomless continuum of identical potential investors indexed by $i\in[0,1]$. Investor $i$ chooses $x_i\in\{0,1\}$, where $x_i=1$ means installing one normalized unit of panel capacity $\bar c$, and $x_i=0$ means not installing. Aggregate installed capacity is

$Q=\bar c\int_0^1 x_i\,di.$

The up-front amortized cost per unit capacity is $\pi_0>0$, and the expected short-term revenue from market $m$ over the panel’s lifespan is $i\in[0,1]$0. The long-run payoff of investor $i\in[0,1]$1 is

$i\in[0,1]$2

Because each infinitesimal investor cannot affect $i\in[0,1]$3 alone, the Nash equilibrium $i\in[0,1]$4 satisfies the zero-profit condition

$i\in[0,1]$5

This formulation makes the long-run capacity choice an equilibrium object rather than an exogenous parameter. It ties individual installation decisions directly to the revenue schedule generated by the short-term market design, so the theory is explicitly about endogenous capacity formation rather than only dispatch or pricing (Davoudi et al., 8 Sep 2025).

2. Short-term competitive equilibria under alternative market designs

The short-term environment is parameterized by $i\in[0,1]$6, the per-unit panel solar output, $i\in[0,1]$7, the fixed inelastic load, and $i\in[0,1]$8, each buyer’s extra per-unit willingness-to-pay for solar. The theory studies three market mechanisms: a product-differentiated real-time market, a single-product real-time market, and a contract-based panel market.

Market	Core equilibrium object	Revenue expression
Product-differentiated real-time ($i\in[0,1]$9)	If $i$0, $i$1	$i$2
Single-product real-time ($i$3)	If $i$4, market price is always $i$5	$i$6
Contract-based panel ($i$7)	Capacity is leased ex-ante at price $i$8 per unit	$i$9

In the product-differentiated real-time market, each seller has up to $x_i\in\{0,1\}$0 units of solar and each buyer values solar at $x_i\in\{0,1\}$1 up to $x_i\in\{0,1\}$2, with remaining demand met at utility price $x_i\in\{0,1\}$3. The competitive equilibrium $x_i\in\{0,1\}$4 satisfies individual optimality and market clearing. When $x_i\in\{0,1\}$5,

$x_i\in\{0,1\}$6

and otherwise $x_i\in\{0,1\}$7, $x_i\in\{0,1\}$8.

In the single-product real-time market, the structure is identical except that buyers cannot distinguish solar from grid energy, so the price does not incorporate the extra willingness-to-pay $x_i\in\{0,1\}$9 when $x_i=1$0.

In the contract-based panel market, sellers rent out panel capacity ex ante at price $x_i=1$1 per unit of capacity. Buyer $x_i=1$2’s payoff is

$x_i=1$3

and competitive equilibrium requires $x_i=1$4 with each $x_i=1$5 maximizing $x_i=1$6. The first-order condition yields

$x_i=1$7

The three mechanisms therefore differ not in the existence of equilibrium per se, but in how they encode the value of solar scarcity and uncertainty into prices and revenues (Davoudi et al., 8 Sep 2025).

3. Revenue schedules and long-run equilibrium capacities

The theory writes the expected revenue function generically as

$x_i=1$8

where $x_i=1$9 is the equilibrium price in market $\bar c$0. In particular,

$\bar c$1

$\bar c$2

and

$\bar c$3

with $\bar c$4 determined by $\bar c$5.

Substituting these revenue schedules into the zero-profit condition yields the long-run Nash equilibrium capacities. The single-product equilibrium $\bar c$6 solves

$\bar c$7

The product-differentiated equilibrium $\bar c$8 solves

$\bar c$9

The contract-based equilibrium $x_i=0$0 is given implicitly by

$x_i=0$1

This structure makes the coupling between short-term and long-term equilibrium explicit: aggregate capacity determines short-term prices and allocations, those outcomes determine expected revenues, and those revenues determine which aggregate capacity can satisfy the investors’ zero-profit condition. The theory is therefore a closed equilibrium system rather than a sequence of disconnected optimization problems (Davoudi et al., 8 Sep 2025).

4. Welfare characterization and comparative outcomes

The central welfare result is that the social planner allocates scarce solar in each realization to the highest-$x_i=0$2 buyers, and the resulting welfare-maximizing capacity $x_i=0$3 solves exactly the same equation as the product-differentiated real-time equilibrium. Hence,

$x_i=0$4

The single-product market does not internalize buyers’ extra value $x_i=0$5. Its revenue curve $x_i=0$6 lies strictly below the social planner’s for any nonzero $x_i=0$7, so its zero-profit solution $x_i=0$8 is strictly below $x_i=0$9. The contract-based market can overshoot: when buyer premiums $Q=\bar c\int_0^1 x_i\,di.$0 are small, buyers lock in capacity ex ante, and the clearing price both embeds expected renewable scarcity and hedges uncertainty, which can raise $Q=\bar c\int_0^1 x_i\,di.$1 above $Q=\bar c\int_0^1 x_i\,di.$2. The paper summarizes the ordering as

$Q=\bar c\int_0^1 x_i\,di.$3

If $Q=\bar c\int_0^1 x_i\,di.$4, all three designs collapse to the same equilibrium $Q=\bar c\int_0^1 x_i\,di.$5.

These results identify a precise misconception to avoid: exposure to solar-related scarcity alone does not guarantee efficient investment. The model assigns social optimality only to the product-differentiated real-time market; the single-product market consistently results in under-investment, and the contract-based market leads to over-investment when the extra valuations of users for solar energy are small (Davoudi et al., 8 Sep 2025).

5. Relation to sunshine trading in market microstructure

A separate arXiv paper uses sunshine trading in the Admati–Pfleiderer sense: publicly disclosing trading intentions can reduce adverse selection and attract liquidity provision, lowering execution costs. Hyperliquid provides a natural setting because protocol-native TWAP orders disclose their terms from inception and remain visible while active. Using address-level data, the paper reconstructs $Q=\bar c\int_0^1 x_i\,di.$6 million hidden metaorders and compares them with $Q=\bar c\int_0^1 x_i\,di.$7 visible TWAP executions. Hidden metaorders follow front-loaded, U-shaped schedules consistent with transient-impact optimal execution, whereas TWAPs trade nearly uniformly (Barone et al., 14 Jun 2026).

Execution costs are measured with the volatility-normalized temporary impact

$Q=\bar c\int_0^1 x_i\,di.$8

and the paper also studies transient and permanent impact trajectories. The empirical findings are that visible TWAPs face lower execution costs than comparable hidden metaorders, lie below statistical metaorders in temporary impact for most $Q=\bar c\int_0^1 x_i\,di.$9, and, in order-level regression, pay about $\pi_0>0$0 bp less slippage at median $\pi_0>0$1. Native TWAPs also leave $\pi_0>0$2–$\pi_0>0$3 bp less permanent displacement across $\pi_0>0$4–$\pi_0>0$5, consistent with lower informational content. At the same time, hidden metaorders that overlap already-visible same-side TWAP flow incur higher permanent costs: permanent impact rises by about $\pi_0>0$6 bp per unit of same-side dominance, while opposite-side dominance lowers cost by about $\pi_0>0$7 bp per unit. During active TWAP windows, displayed depth rises, the book tilts toward the absorbing side, $\pi_0>0$8k USD sweep cost falls, and quoted spread widens; the displayed-liquidity response is larger for larger announced orders (Barone et al., 14 Jun 2026).

The microstructure results are not a restatement of the solar-investment model, but they preserve the same organizing idea: transparency changes equilibrium responses. In one context, the relevant response variable is liquidity provision and adverse selection in a limit order book; in the other, it is long-run capacity investment under alternative market designs.

6. Interpretive scope, limits, and common points of confusion

The solar-investment formulation ties, in a single analytic framework, how investors’ individual installation decisions aggregate into $\pi_0>0$9, how aggregate $m$0 determines short-term prices and quantities, how those market outcomes shape expected revenues, and how those revenues feed back into the long-run equilibrium $m$1. The common substantive theme with market-microstructure sunshine trading is therefore not the asset class but the effect of observability and market design on equilibrium incentives (Davoudi et al., 8 Sep 2025).

Several limits are explicit. In the Hyperliquid evidence, the comparison between TWAP and statistical metaorders is an equilibrium comparison rather than a randomized treatment, because the two regimes are populated by largely disjoint sets of taker addresses, with $m$2 pure-regime. “Hidden” orders are learnable ex post via wallet-level inference, so the contrast is public versus latent observability rather than perfect anonymity. The on-chain environment also includes differences such as MEV and mempool timing, which caution against direct mapping to off-chain equity or futures markets (Barone et al., 14 Jun 2026).

A second point of confusion concerns welfare. The solar model does not imply that every institutional arrangement that prices renewable scarcity is socially efficient. On the contrary, only the product-differentiated real-time market supports socially optimal investment; pooling solar with grid energy suppresses the green premium and produces under-investment, while trading capacity rights ex ante can produce over-investment when extra valuations for solar are small. Likewise, the microstructure evidence does not imply that disclosure benefits every participant uniformly: public TWAP orders face lower costs, but non-announcers on the same side face higher permanent costs. A plausible implication is that sunshine trading should be understood as a redistribution of informational and liquidity conditions across trading regimes, not as a uniformly beneficial transparency rule (Davoudi et al., 8 Sep 2025, Barone et al., 14 Jun 2026).