Strategic Bidding in Electricity Markets

Bi-level MPEC · Supply-function equilibrium

Game Theory · Price Formation · Market Power

A generator's bid in an electricity market is not its marginal cost. In a uniform-price auction, a strategic bidder who can move the market price — through scale or network position — has incentive to bid above marginal cost, capturing price-setting rents. The strategic-bidding problem is inherently game-theoretic: each producer's best bid depends on competitors' bids and the clearing mechanism. Formulations range from single-leader Stackelberg (bi-level MPEC) to Cournot and supply-function equilibrium (SFE) Nash games. Regulators use these models to detect market power.

The problem

Bidding as a game, not a report

In competitive electricity markets with many small producers, textbook theory says bid your marginal cost: doing otherwise only sacrifices awards you would have won profitably. But electricity markets are never perfectly competitive. Five or ten large generators in a given regional market can each move the clearing price by a few dollars per MWh. Strategic bidding exploits this — bid higher than marginal cost, accept less dispatch, but earn a higher price on what remains. For a 1000-MW baseload plant, a $2/MWh markup earns $17 million/year in extra revenue.

The OR problem: given competitors' bidding behavior and the market-clearing mechanism, compute the profit-maximizing bid curve. If the market clears as an LP (DC-OPF + merit order), the producer faces a bi-level program: upper level chooses its bid curve to maximize profit; lower level is the ISO's market-clearing LP with LMPs as duals. The upper-level payoff depends on the LMP at the producer's bus — a dual variable of the lower-level problem. This structure is a Mathematical Program with Equilibrium Constraints (MPEC), which can be reformulated as a MILP via KKT + big-M.

Historical note
Klemperer & Meyer (1989) derived the supply-function equilibrium (SFE) framework in Econometrica — the canonical multi-producer Nash equilibrium in bid curves. Green & Newbery (1992) applied it to the deregulated UK electricity pool in JPE and showed substantial market-power rents at pool concentration levels. Borenstein, Bushnell & Wolak (2002) quantified California crisis market power. Hobbs, Metzler & Pang (2000) and Gabriel et al. (2013) wrote the modern MPEC/EPEC references. Regulatory practice: FERC's Office of Enforcement and DG Energy routinely use these models in market-power investigations.

Mathematical formulation

Bi-level MPEC with KKT reformulation

Bi-level structure

Upper (leader): strategic producer $s$ chooses bid parameters $\alpha_s$ (markup) to maximize profit:

$$\max_{\alpha_s, p_s} \; (\lambda_s - c_s) \, p_s \qquad \text{(1)}$$

Lower (follower): ISO clears the market given all producers' bids:

$$\min_{p, \theta} \sum_{g} b_g(\alpha_g) \, p_g \quad \text{s.t. network + balance} \qquad \text{(2)}$$

LMP at bus of $s$: $\lambda_s$ = dual of nodal balance (2). Profit (1) depends on $\lambda_s$, which depends on $\alpha_s$ — a bi-level coupling.

KKT-based MPEC reformulation

Replace the lower-level LP (2) by its KKT conditions:

$$b_g - \lambda + \mu_g^{\max} - \mu_g^{\min} = 0, \; 0 \le \mu_g^{\max} \perp P_g^{\max} - p_g \ge 0, \ldots$$

Introduces complementarity ($a \perp b$) constraints. Linearize via big-M + binary disjunctive variables, yielding a MILP at the upper level.

Supply-function equilibrium (SFE)

Each of $N$ producers simultaneously chooses a bid curve $b_i(p)$; Nash equilibrium is a fixed point where no one wants to deviate. Analytical SFE solutions exist for symmetric duopolies (Klemperer-Meyer, Green-Newbery linear cost case); general cases solved numerically.

Complexity

Single-leader MPEC after big-M: tractable MILP for small (<50 node) networks. Multi-leader Nash (EPEC) is much harder — typically solved by diagonalization or best-response iteration without convergence guarantees. Full-scale strategic-bidding studies (CAISO, PJM) use hybrid Cournot + detailed network and run as bi-level LPs with successive linearization.

Real-world data

FERC Market Monitoring

US Federal Energy Regulatory Commission publishes annual state-of-the-market reports that detail price-cost markups, market concentration (HHI), and pivotal-supplier tests for all US RTOs.

EPRI Strategic Bidding Library

EPRI maintains research libraries on bidding-strategy tools used by IPPs and merchant generators.

Illustrative duopoly (this page)

2-producer single-period market clearing with linear demand and quadratic cost. Shows how markup changes with market share and price sensitivity. Single-leader Stackelberg + static SFE comparison.

Interactive solver

Duopoly strategic bidding with market-clearing game

Market parameters

600
600
900
30
35
Adjust and press Solve.

Bid curves & clearing

Strategic bid curves (solid) vs marginal cost (dashed) · market-clearing price shown as horizontal gold line

Solution interpretation

The markup — how much each producer bids above its marginal cost — is the key output. In a monopoly, markup is set by the demand elasticity alone (Lerner index). In a duopoly, each producer's markup is lower: the competitor's supply response limits how much price the strategic bidder can move. As the market gets more competitive (more producers, or more elastic demand), markups shrink toward marginal-cost bidding (the Cournot-to-perfect-competition transition).

The pivotal supplier concept is operationally important. A producer is pivotal at load $D$ if $D$ exceeds the combined capacity of all other producers: the ISO is forced to dispatch them, and their bid sets the price regardless. Pivotal suppliers have unbounded price-setting power absent bid caps; this is why ISOs enforce offer caps (CAISO $1000/MWh, ERCOT $5000/MWh) and scarcity pricing rules (ORDC).

In markets with transmission constraints, local market power is distinct from system-wide market power: a producer in a congested load pocket can set the local LMP even if system-wide there are ample supplies. This is why FERC's Alternative Mitigation Method screens bid deviations at the local rather than system level.

Extensions & variants

Multi-leader EPEC

Every producer strategically bids; equilibrium is a Nash-MCP. Typically solved by diagonalization (Gauss-Seidel on single-leader MPECs) without global guarantees.

Refs: Ehrenmann (2004); Yao, Adler & Oren (2008).

Stochastic strategic bidding

Producers bid before knowing load or competitor bids exactly. Two-stage stochastic MPEC over scenarios. Used to study risk-averse bidding.

Refs: Kazempour & Conejo (2012); Ruiz & Conejo (2009).

Wind producer bidding

Strategic bidding with uncertain renewable output. Producers balance expected price impact against imbalance penalties for forecast errors.

Refs: Morales, Conejo & Perez-Ruiz (2010); Zugno et al. (2013).

Reserve-market bidding

Joint energy-reserve strategic bidding. Scarcity-pricing rules (ORDC) change the game substantially during tight conditions.

Refs: Baringo & Conejo (2012); Siddiqui, Tanaka & Chen (2019).

Storage strategic bidding

Strategic battery operators bid into arbitrage markets. Intertemporal coupling (SOC dynamics) makes the problem harder than generator bidding.

Refs: Schill & Kemfert (2011); Pozo, Contreras & Sauma (2014).

Market-power mitigation

ISO-side problem: detecting and mitigating strategic bidding. Three-pivotal-supplier tests, conduct-impact tests, automatic mitigation rules.

Refs: FERC state-of-the-market reports; Helman & Hobbs (2010).

Key references

[1]
Klemperer, P. D., & Meyer, M. A. (1989).
“Supply function equilibria in oligopoly under uncertainty.”
Econometrica, 57(6), 1243–1277. doi:10.2307/1913707
[2]
Green, R. J., & Newbery, D. M. (1992).
“Competition in the British electricity spot market.”
Journal of Political Economy, 100(5), 929–953. doi:10.1086/261846
[3]
Hobbs, B. F., Metzler, C. B., & Pang, J.-S. (2000).
“Strategic gaming analysis for electric power systems: An MPEC approach.”
IEEE Transactions on Power Systems, 15(2), 638–645. doi:10.1109/59.867153
[4]
Borenstein, S., Bushnell, J. B., & Wolak, F. A. (2002).
“Measuring market inefficiencies in California's restructured wholesale electricity market.”
American Economic Review, 92(5), 1376–1405. doi:10.1257/000282802762024557
[5]
Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2013).
Complementarity Modeling in Energy Markets.
Springer. doi:10.1007/978-1-4419-6123-5
[6]
Kazempour, S. J., & Conejo, A. J. (2012).
“Strategic generation investment under uncertainty via Benders decomposition.”
IEEE Transactions on Power Systems, 27(1), 424–432. doi:10.1109/TPWRS.2011.2159251
[7]
Ruiz, C., & Conejo, A. J. (2009).
“Pool strategy of a producer with endogenous formation of locational marginal prices.”
IEEE Transactions on Power Systems, 24(4), 1855–1866. doi:10.1109/TPWRS.2009.2030378
[8]
Morales, J. M., Conejo, A. J., & Pérez-Ruiz, J. (2010).
“Short-term trading for a wind power producer.”
IEEE Transactions on Power Systems, 25(1), 554–564. doi:10.1109/TPWRS.2009.2036810
[9]
Baringo, L., & Conejo, A. J. (2012).
“Strategic offering for a wind power producer.”
IEEE Transactions on Power Systems, 28(4), 4645–4654. doi:10.1109/TPWRS.2013.2273276
[10]
Helman, U., & Hobbs, B. F. (2010).
“Large-scale market power modeling: Analysis of the US Eastern Interconnection and regulatory applications.”
IEEE Transactions on Power Systems, 25(3), 1434–1448. doi:10.1109/TPWRS.2009.2039942
In-browser solver uses closed-form best-response for a duopoly with linear demand. Production strategic-bidding tools use MILP MPEC reformulations with big-M linearization.