market regulators

Abstract: We study a class of strategic hypothesis testing problems in which a principal aims to allocate resources among competing agents who possess data or data-generating mechanisms that may be relevant to the principal's goals. Each agent can pay a participation cost to opt into a statistical contract, in which case they generate data from a private distribution and receive an allocation based on a predetermined (and publicly known) mechanism. Each agent is either "null" or "non-null" and the principal's goal is to design the contract to limit the allocation to the former while maximizing transactions with the latter. Using e-values, we define a "continuous-closure," a set of allocations which prevents null agents from profiting in expectation and provides post-hoc risk control for general loss functions under arbitrary dependence. When the loss is the fraction of resources allocated to null agents, the region admits polynomial-time linear optimization. We also give explicit, interpretable closed-form approximations, and we analyze participation from a non-null agent's perspective, giving conditions under which entry into the contract is profitable. Finally, we extend the framework to support online arrival of the agents, in which case the principal has to make irrevocable on-the-fly decisions, and provide a method which gives time-uniform error-control in this setting.

Abstract: In this paper, we extend earlier findings of supra-competitive outcomes in optimal-execution games by identifying a learned punitive mechanism that deters deviations and provides behavioural evidence of collusion. We investigate this mechanism in a two-player, finite-horizon Almgren-Chriss liquidation game. Independent proximal policy optimisation agents with access to within-episode price and action histories achieve costs below the Nash benchmark. We identify a profitable deviation by training against the mean learned liquidation schedule, then impose its first trade on one of the original agents. The opponent responds by accelerating liquidation. This response more than offsets the deviator's gain in every run and both player roles, while leaving the punisher's average payoff materially unchanged relative to not punishing under the same deviation. The punisher imposes greater losses on the deviator while preserving its own average payoff, despite the availability of more profitable, less punitive liquidation plans. Matching deviations and subsequent additional selling rise and later decline during training, while final policies retain an effective punitive response. We formalise two checks: whether punishment outweighs the gain from deviating, and whether the change in trading behaviour is large enough to account for the loss imposed. Both checks hold for the tested deviation. Together, these findings provide behavioural and economic evidence supporting a collusive interpretation of the learned supra-competitive outcomes.

Abstract: Recent work shows that LLM-based pricing agents can produce supracompetitive outcomes in repeated oligopoly environments without being explicitly instructed to collude. We reproduce the qualitative prompt-sensitivity effect of Fish et al. using DeepSeek-V3.1: the P1 prompt produces significantly higher prices and profits than P2, although our outcomes are less monopoly-like than the original GPT-4 results. We then evaluate three regulatory interventions: a prompt-only warning, a Harrington-inspired expected-damages payoff regulator, and an active random entrant. The prompt-only regulator reduces but does not eliminate above-Nash pricing. The Harrington regulator brings P1 outcomes close to the duopoly Nash benchmark and removes the statistically significant P1--P2 gap. The active entrant produces the strongest effect, pushing both prompts below the appropriate random-entrant Nash benchmark. Overall, our experiments provide preliminary evidence that interventions that alter incentives or market participation can reduce supracompetitive pricing more effectively than prompt warnings alone.