As electricity market participants increasingly adopt learning-based agents for their bidding strategies, electricity markets are becoming algorithmic. Evidence from algorithmic markets in other domains shows that tacit collusion can arise purely through independent learning. Moreover, electricity markets are typically oligopolistic and feature repeated interaction among a small number of participants, making them structurally susceptible to non-competitive behavior. In the face of these observations, this paper investigates the hypothesis that tacit collusion may emerge in electricity markets where participants' actions are controlled by autonomous learning-based algorithms. We model strategic bidding as a repeated game with imperfect public monitoring, and model the participants' emergent behavior using multi-agent reinforcement learning. We propose a multi-dimensional set of criteria (going beyond profit comparisons against Nash equilibria) to assess whether the resulting behavior constitutes tacit collusion. Our experimental results showcase that such a danger is realistic for electricity markets: there are cases where agents do learn to sustain supra-competitive outcomes that are supportive of tacit collusion indicators, even though the agents were never instructed to collude.
Figures & tables
Generator
Bus
Pimax [MW]
Marginal cost [EUR/MWh]
Low
Medium
High
G1
N1
42
20
20
20
G2
N2
35
20
20
20
G5
N5
40
20
30
40
G6
N6
40
20
10
1
TABLE I: Strategic generators and marginal-cost cases.
Scenario
Demand
Cost diff.
Rationale
Grid – LowDemand – HighCostDiff
Low
High
Structured non-stationary regime with non-trivial deviation incentives.
Grid – LowDemand – MediumCostDiff
Low
Medium
Reference low-demand case with a more stationary learned profile.
Grid – MediumDemand – HighCostDiff
Medium
High
Higher-demand case that remains non-boundary and strategically informative.
TABLE II: Scenarios selected for behavioural validation.
Parameter
Value
Algorithm
Multi-agent TD3
Bid segments
12
Bidding parameter bounds
[0,4000]
Training length
100,000 market instances
Episodes / horizon
50×2,000
Evaluation window
Final 10,000 instances
TABLE III: Main MARL hyperparameters.
Fig. 1: Price markups across the nine demand and marginal-cost heterogeneity combinations: (a) NoGrid scenarios without active transmission constraints and (b) Grid scenarios with active transmission constraints.
Fig. 2: Agents’ bidding actions during the Punishment of Deviation test for the three selected scenarios. The shaded region denotes the forced-deviation window, and the black line identifies the deviating agent.
Fig. 3: Agents’ rewards during the Punishment of Deviation test for the three selected scenarios. The shaded region denotes the forced-deviation window, and the black line identifies the deviating agent.
Fig. 4: Evolution of episode-average bidding slopes under the baseline MARL configuration and the shortsight ablation for the three selected scenarios. Solid lines denote the baseline agents and dashed lines the ablated agents.
Fig. 5: Agents’ bidding actions during the Punishment of Deviation test under the shortsight ablation for the three selected scenarios. The shaded region denotes the forced-deviation window, and the black line identifies the deviating agent.
Fig. 6: Agent reward trajectories under Iterative Best Response (IBR), initialized from the learned MARL outcomes. Iteration 0 corresponds to the MARL endpoint, while the horizontal dashed lines indicate the corresponding MARL reward levels.
Scenario
Punish.
Shortsight
IBR
Interpretation
Grid – LowDemand – HighCostDiff
Supportive
Supportive
Supportive
Collusion-consistent
Grid – LowDemand – MediumCostDiff
Supportive
Supportive
Supportive
Collusion-consistent
Grid – MediumDemand – HighCostDiff
Not supp.
Not supp.
Not supp.
Structural market power
TABLE IV: Summary of behavioural evidence for Tacit Collusion.
Nov 12, 2025·Tobias R. Rebholz, Maxwell Uphoff, Christian H. R. Bernges +1Algorithmic Collusion
Department of Psychology, University of Tübingen · Fuqua School of Business, Duke University · Department of Economics, University of Minnesota Twin Cities