Nicolas Eschenbaum

Competing firms increasingly delegate market decisions to algorithms supplied by the same third-party providers. We study whether a shared algorithm leads competitors to internalise one another’s profits, using data from the Australian National Electricity Market, where batteries’ bids are observed at 5-minute frequency and can be linked to an autobidding provider. Bids constructed by the same provider co-move, and do so more strongly after a disclosure reform made the scarcity state easier to observe: the same information that steers batteries towards efficient arbitrage also synchronises the bids of competitors who share a provider. To separate co-movement from joint profit maximisation, we perform a conduct test by estimating each battery’s dynamic value of stored energy and reclearing the market under counterfactual bids. We find that batteries forgo profitable dispatch in the evening peak when it would lower the profit of same-provider batteries owned by rival firms. The estimated conduct parameter is close to one. But this effect arises only where a provider’s share of near-margin battery capacity exceeds roughly 30%. The identified conduct costs consumers an annualised $5.5 million given the battery fleet from 2025, and concentration analysis based on ownership would treat these batteries as independent competitors and miss the impact of shared autobidding software.

Concerns about algorithmic collusion rest on theory and a growing body of empirical work, and regulators and courts increasingly face algorithmic coordination in practice. This paper aims to connect the pricing and bidding systems firms actually use to theories of harm and to established concepts of competition law. Drawing on practical experience with such systems, we examine the technical architecture of several archetypes, including revenue management, repricing software, and algorithmic bidding, and ask which theories of harm their design supports and how these fit concepts such as concerted practices and information exchange. Our starting point is that algorithmic collusion is not a single problem and that understanding it requires studying these systems at a technical level.

Detecting algorithmic collusion is challenging because regulators often have limited access to firms’ algorithms, training data, and market information. We study an intermediate-information regime in which an auditor can query firms’ frozen pricing policies and construct the induced strategy graph. Using a complete characterization of Nash equilibria in a repeated pricing game, we identify graph-theoretic features of strategy graphs that are associated with collusive reward-and-punishment schemes, including maximum betweenness, attractor in-degree, and average path length. We then test these metrics on policies learned by decentralized Q-learning and the Q-learning algorithm of Calvano et al. (2020). We find that especially the maximum betweenness and attractor in-degree are strongly correlated with the standard profit-based Collusion Index. Importantly, the proposed metrics rely only on the unlabeled topology of strategy graphs and require neither price histories, demand estimates, nor competitive and monopoly benchmarks. Our results suggest that the structure of frozen pricing policies contains robust signals of collusion among reinforcement learning algorithms and provides a promising basis for auditing algorithmic pricing systems under limited information.

The transition towards decentralised energy systems creates a need for local electricity platforms on which prosumers trade energy at endogenously determined prices. We develop a differentiable multi-agent control framework for such platforms, drawing on neural stochastic control and the pathwise optimisation principle used in Deep Hedging, whose appeal stems from its simplicity, computational efficiency, industrial use, and scalability to large-scale optimisation problems. The proposed approach embeds physical storage dynamics, feasible prosumer actions, and the market-clearing rule in a single computational graph, allowing decentralised agents to train trading policies by backpropagating through aggregate supply, aggregate demand, and cleared prices. A stop-gradient construction at the clearing layer separates two economically distinct learning modes: price-aware learning, in which agents internalise their marginal price impact, and price-taking learning, in which prices are treated as exogenous. This yields a market-mechanism-aware alternative to reward-only multi-agent reinforcement learning methods such as Multi-Agent Proximal Policy Optimisation, which treat the market as a black-box environment component. We evaluate the framework on peer-to-peer electricity markets with heterogeneous prosumers, photovoltaic generation, battery storage, and multiple non-discriminatory pricing rules, using both large-scale synthetic simulations and Swiss smart-meter demand data. The experiments show that Multi-Agent Neural Network Control learns effective decentralised policies, reduces community cost relative to rule-based control, and outperforms Multi-Agent Proximal Policy Optimisation in the studied settings in both cost and training efficiency. The learned policies exhibit emergent, economically sensible behaviour: they recover standard storage arbitrage and, under price-aware learning, reveal capacity withholding under quantity-sensitive clearing, which benefits flexible agents at the expense of aggregate community cost. Embedding market clearing in the training graph therefore provides both an efficient learning signal and a diagnostic tool for strategic behaviour in local electricity-market design.

This article examines the extent to which designated “gatekeepers” implement the provisions of the EU’s Digital Markets Act outside its territorial scope ("Brussels Effect"). Drawing on transparency reports, contractual documents, and informal communications, we reveal significant disparities in compliance strategies. Apple, Google, and Booking predominantly restrict their implementation to the EU or EEA, whereas Microsoft, Meta, and ByteDance extend certain measures to non-EU jurisdictions, notably Switzerland. Crucially, obligations subject to non-compliance proceedings by the European Commission are rarely extended beyond the EU, suggesting a strategic approach to territorial extensions of the DMA’s implementation. The article also uncovers a pattern of complex and sometimes contradictory communication by gatekeepers, raising questions about the transparency of the DMA’s implementation. These inconsistencies, coupled with selective extensions of specific data-related DMA provisions, point to a fragmented “Brussels Effect” of the law. The findings also imply that gatekeepers weigh the economic and strategic costs of compliance when deciding on territorial scope, and that the DMA’s global impact may depend on further coordination between regulators as well as more stringent enforcement.

This paper develops a unified analytical framework for dynamic monopoly pricing that allows for multiple durable, rental, or mixed varieties. We show that trading-up opportunities are the driving force behind Coasian-type price dynamics: prices adjust over time to reallocate buyer types to higher-valued consumption options. Price adjustments persist until these opportunities are exhausted or the game ends. When trading-up opportunities are absent, equilibrium prices are static, resulting in Coasian failure. We illustrate the mechanism with examples and extend the analysis to transitional games in which one variety is only indirectly accessible.

This paper develops a formal framework to assess policies of learning algorithms in economic games. We investigate whether reinforcement-learning agents with collusive pricing policies can successfully extrapolate collusive behavior from training to the market. We find that in testing environments collusion consistently breaks down. Instead, we observe static Nash play. We then show that restricting algorithms’ strategy space can make algorithmic collusion robust, because it limits overfitting to rival strategies. Our findings suggest that policy-makers should focus on firm behavior aimed at coordinating algorithm design in order to make collusive policies robust.