When agents trade in a Duality-based Cost Function prediction market, they collectively implement the learning algorithm Follow-The-Regularized-Leader [Abernethy et al., 2013]. We ask whether other learning algorithms could be used to inspire the design of prediction markets. By decomposing and modifying the Duality-based Cost Function Market Maker's (DCFMM) pricing mechanism, we propose a new prediction market, called the Smooth Quadratic Prediction Market, the incentivizes agents to collectively implement general steepest gradient descent. Relative to the DCFMM, the Smooth Quadratic Prediction Market has a better worst-case monetary loss for AD securities while preserving axiom guarantees such as the existence of instantaneous price, information incorporation, expressiveness, no arbitrage, and a form of incentive compatibility. To motivate the application of the Smooth Quadratic Prediction Market, we independently examine agents' trading behavior under two realistic constraints: bounded budgets and buy-only securities. Finally, we provide an introductory analysis of an approach to facilitate adaptive liquidity using the Smooth Quadratic Prediction Market. Our results suggest future designs where the price update rule is separate from the fee structure, yet guarantees are preserved.

Americans Are Trading Billions of Dollars on Polymarket's Banned Offshore Platform It's the first estimate of how many Americans are sneaking onto Polymarket's banned crypto-based platform. Approximately 30 percent of the trading volume on Polymarket comes from the United States, according to a new study--an eye-popping number, considering that none of those people are legally allowed to use the crypto -based platform. The study, conducted by Rutgers University statistician Harry Crane, estimated that people in the US funneled between $10.6 to $26.7 billion through Polymarket. To track the platform's activity, Crane looked at what appeared to be US-based trades on offshore prediction market platforms from May 2025 to the end of April 2026. He found that many of the highest-volume markets on Polymarket were US-centric, including those covering US elections and sporting events.

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.