Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and strategic participation. This paper formulates prediction markets as Bayesian inverse problems in which the unknown event outcome \(Y\in\{0,1\}\) is inferred from an observed history of market-implied probabilities and traded volumes. We introduce a mechanism-agnostic observation model in log-odds space in which price increments conditional on volume arise from a latent mixture of trader types. The resulting likelihood class encompasses informed and uninformed trading, heavy-tailed microstructure noise, and adversarial or manipulative flow, while requiring only price and volume as observables. Within this framework we define posterior uncertainty quantification for \(Y\), provide identifiability and well-posedness criteria in terms of Kullback--Leibler separation between outcome-conditional increment laws, and derive posterior concentration statements and finite-sample error bounds under general regularity assumptions. We further study stability of posterior odds to perturbations of the observed price--volume path and define realized and expected information gain via the posterior-vs-prior KL divergence and mutual information. The inverse-problem formulation yields explicit diagnostics for regimes in which market histories are informative and stable versus regimes in which inference is ill-posed due to type-composition confounding or outcome--nuisance symmetries. Extensive experiments on synthetic data validate our theoretical predictions regarding posterior concentration rates and identifiability thresholds.

In online bilateral trade, a platform posts prices to incoming pairs of buyers and sellers that have private valuations for a certain good. If the price is lower than the buyers' valuation and higher than the sellers' valuation, then a trade takes place. Previous work focused on the platform perspective, with the goal of setting prices maximizing the *gain from trade* (the sum of sellers' and buyers' utilities). Gain from trade is, however, potentially unfair to traders, as they may receive highly uneven shares of the total utility. In this work we enforce fairness by rewarding the platform with the _fair gain from trade_, defined as the minimum between sellers' and buyers' utilities.After showing that any no-regret learning algorithm designed to maximize the sum of the utilities may fail badly with fair gain from trade, we present our main contribution: a complete characterization of the regret regimes for fair gain from trade when, after each interaction, the platform only learns whether each trader accepted the current price. Specifically, we prove the following regret bounds: $\Theta(\ln T)$ in the deterministic setting, $\Omega(T)$ in the stochastic setting, and $\tilde{\Theta}(T^{2/3})$ in the stochastic setting when sellers' and buyers' valuations are independent of each other. We conclude by providing tight regret bounds when, after each interaction, the platform is allowed to observe the true traders' valuations.

As foundation models are increasingly deployed as interacting agents in multi-agent systems, their collective behavior raises new challenges for trustworthiness, transparency, and accountability. Traditional coordination mechanisms, such as centralized oversight or adversarial adjudication, struggle to scale and often obscure how decisions emerge. We introduce a market-making framework for multi-agent large language model (LLM) coordination that organizes agent interactions as structured economic exchanges. In this setup, each agent acts as a market participant, updating and trading probabilistic beliefs, to converge toward shared, truthful outcomes. By aligning local incentives with collective epistemic goals, the framework promotes self-organizing, verifiable reasoning without requiring external enforcement. Empirically, we evaluate this approach across factual reasoning, ethical judgment, and commonsense inference tasks. Market-based coordination yields accuracy gains of up to 10% over single-shot baselines while preserving interpretability and transparency of intermediate reasoning steps. Beyond these improvements, our findings demonstrate that economic coordination principles can operationalize accountability and robustness in multi-agent LLM systems, offering a scalable pathway toward self-correcting, socially responsible AI capable of maintaining trust and oversight in real world deployment scenarios.

We analyze sources of error in prediction market forecasts in order to bound the difference between a security's price and the ground truth it estimates.

Fears of a growing bubble around the artificial intelligence frenzy resurfaced on Thursday as leading US stock markets fell, less than 24 hours after strong results from chipmaker Nvidia sparked a rally. Wall Street initially rose after Nvidia, the world's largest public company, reassured investors of strong demand for its advanced data center chips. But the relief dissipated, and technology stocks at the heart of the AI boom came under pressure. The benchmark S&P 500 closed down 1.6%, and the Dow Jones industrial average closed down 0.8% in New York. The tech-focused Nasdaq Composite closed down 2.2%.

Prior work has investigated variations of prediction markets that preserve participants' (differential) privacy, which formed the basis of useful mechanisms for purchasing data for machine learning objectives. Such markets required potentially unlimited financial subsidy, however, making them impractical.

Prior work has investigated variations of prediction markets that preserve participants' (differential) privacy, which formed the basis of useful mechanisms for purchasing data for machine learning objectives. Such markets required potentially unlimited financial subsidy, however, making them impractical.

Shares of major technology companies have fallen over fears about the valuations of firms linked to the artificial intelligence (AI) industry. Investors have grown increasing wary about what they are calling an AI bubble this year that has seen tech stock valuations hit record highs. Major indexes in Asia were the hardest hit on Wednesday, following a sell-off in the US. Japan's Nikkei 225 closed 2.5%, dragged lower by tech investment giant, SoftBank, which plunged more than 10%. AI valuation concerns took hold in the US as well after it was revealed the trader who inspired The Big Short has bet $1.1bn (£840m) on a fall in prices for AI-related stocks Nvidia and Palantir.

We present ABIDES-MARL, a framework that combines a new multi-agent reinforcement learning (MARL) methodology with a new realistic limit-order-book (LOB) simulation system to study equilibrium behavior in complex financial market games. The system extends ABIDES-Gym by decoupling state collection from kernel interruption, enabling synchronized learning and decision-making for multiple adaptive agents while maintaining compatibility with standard RL libraries. It preserves key market features such as price-time priority and discrete tick sizes. Methodologically, we use MARL to approximate equilibrium-like behavior in multi-period trading games with a finite number of heterogeneous agents-an informed trader, a liquidity trader, noise traders, and competing market makers-all with individual price impacts. This setting bridges optimal execution and market microstructure by embedding the liquidity trader's optimization problem within a strategic trading environment. We validate the approach by solving an extended Kyle model within the simulation system, recovering the gradual price discovery phenomenon. We then extend the analysis to a liquidity trader's problem where market liquidity arises endogenously and show that, at equilibrium, execution strategies shape market-maker behavior and price dynamics. ABIDES-MARL provides a reproducible foundation for analyzing equilibrium and strategic adaptation in realistic markets and contributes toward building economically interpretable agentic AI systems for finance.

We investigate the mechanisms by which medium-frequency trading agents are adversely selected by opportunistic high-frequency traders. We use reinforcement learning (RL) within a Hawkes Limit Order Book (LOB) model in order to replicate the behaviours of high-frequency market makers. In contrast to the classical models with exogenous price impact assumptions, the Hawkes model accounts for endogenous price impact and other key properties of the market (Jain et al. 2024a). Given the real-world impracticalities of the market maker updating strategies for every event in the LOB, we formulate the high-frequency market making agent via an impulse control reinforcement learning framework (Jain et al. 2025). The RL used in the simulation utilises Proximal Policy Optimisation (PPO) and self-imitation learning. To replicate the adverse selection phenomenon, we test the RL agent trading against a medium frequency trader (MFT) executing a meta-order and demonstrate that, with training against the MFT meta-order execution agent, the RL market making agent learns to capitalise on the price drift induced by the meta-order. Recent empirical studies have shown that medium-frequency traders are increasingly subject to adverse selection by high-frequency trading agents. As high-frequency trading continues to proliferate across financial markets, the slippage costs incurred by medium-frequency traders are likely to increase over time. However, we do not observe that increased profits for the market making RL agent necessarily cause significantly increased slippages for the MFT agent.