Game Theory & Mean-Field Games

We develop a unified model in which AI adoption in financial markets generates systemic risk through three mutually reinforcing channels: performative prediction, algorithmic herding, and cognitive dependency. Within an extended rational expectations framework with endogenous adoption, we derive an

Risk allocation, the decomposition of a portfolio-wide risk measure into component contributions, is a fundamental problem in financial risk management due to the non-additive nature of risk measures, the layered organizational structures of financial institutions, and the range of possible allocati

Equity auctions display several distinctive characteristics in contrast to continuous trading. As the auction time approaches, the rate of events accelerates causing a substantial liquidity buildup around the indicative price. This, in turn, results in a reduced price impact and decreased volatility

Flashblocks divide a block’s priority gas auction into shorter sequential auctions that commit transaction order before the block is complete. We ask how this auction cadence affects bidding and competition among automated arbitrageurs, or searchers. In July 2025 Base replaced a single 2 s auction w

We study optimal auction design for Maximum Extractable Value (MEV) auction markets on Ethereum. Using a dataset of 2.2 million transactions across three major orderflow providers, we establish three empirical regularities: extracted values follow a log-normal distribution with extreme right-tail co

In this work, we investigate the market-making problem on a trading session in which a continuous phase on a limit order book is followed by a closing auction. Whereas standard optimal market-making models typically rely on terminal inventory penalties to manage end-of-day risk, ignoring the signifi

Revisiting the continuous-time Mean-Variance (MV) Portfolio Optimization problem, we model the market dynamics with a jump-diffusion process and apply Reinforcement Learning (RL) techniques to facilitate informed exploration within the control space. We recognize the time-inconsistency of the MV pro

Decentralized exchanges (DEXs) are alternative venues to centralized exchanges (CEXs) for trading cryptocurrencies and have become increasingly popular. An arbitrage opportunity arises when the exchange rate of two cryptocurrencies in a DEX differs from that in a CEX. Arbitrageurs can then trade on

We study the stochastic structure of cryptocurrency rates of returns as compared to stock returns by focusing on the associated cross-sectional distributions. We build two datasets. The first comprises forty-six major cryptocurrencies, and the second includes all the companies listed in the S&P 500.

We demonstrate market inefficiency in cryptoasset markets. Our approach examines investments that share a dominant risk factor but differ in their exposure to a secondary risk. We derive equilibrium restrictions that must hold regardless of how investors price either risk. Our empirical results stro

This study models the monopoly pricing of weather index insurance as a Bowley-type sequential game involving a profit-maximizing insurer (leader) and a farmer (follower). The farmer chooses an insurance payoff to minimize a convex distortion risk measure, while the insurer anticipates this best resp

Battery Energy Storage Systems (BESS) are a cornerstone of the energy transition, as their ability to shift electricity across time enables both grid stability and the integration of renewable generation. This paper investigates the profitability of different market bidding strategies for BESS in th

I study the dynamic, general equilibrium implications of climate-change-linked transition risk on macroeconomic outcomes and asset prices. Climate-change-linked expectations of fossil fuel restrictions can produce a ``run on fossil fuels’’ with accelerated production and decreasing spot prices, or a

Firms follow changing economic opportunities, but rivalry changes their response. We develop ESCAPE, a rational-share game of distribution-valued positioning with heterogeneous capability costs, establish a unique equilibrium, and derive an exact reallocation restriction separating opportunity and c

We study Arbitrum’s Express Lane Auction (ELA), an ahead-of-time second-price auction that grants the winner an exclusive latency advantage for one minute. Building on a single-round model with risk-averse bidders, we propose a hypothesis that the value of priority access is discounted relative to r

We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a path-wise loss function, enabling effici

This work introduces a framework for evaluating onchain order flow auctions (OFAs), emphasizing the metric of price improvement. Utilizing a set of open-source tools, our methodology systematically attributes price improvements to specific modifiable inputs of the system such as routing efficiency,

One approach to reducing greenhouse gas (GHG) emissions is to incentivize carbon capturing and carbon reducing projects while simultaneously penalising excess GHG output. In this work, we present a novel market framework and characterise the optimal behaviour of GHG offset credit (OC) market partici

The M6 Competition assessed the performance of competitors using a ranked probability score and an information ratio (IR). While these metrics do well at picking the winners in the competition, crucial questions remain for investors with longer-term incentives. To address these questions, we compare

We derive a specific functional form for factor alpha decay – hyperbolic decay alpha(t) = K/(1+lambda*t) – from a game-theoretic equilibrium model, and test it against linear and exponential alternatives. Using eight Fama-French factors (1963–2024), we find: (1) Hyperbolic decay fits mechanical fact

Counterfactual estimators are critical for learning and refining policies using logged data, a process known as Off-Policy Evaluation (OPE). OPE allows researchers to assess new policies without costly experiments, speeding up the evaluation process. Online experimental methods, such as A/B tests, a

Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how these requests are to be matched. The two most common object

Operational decisions relying on predictive distributions of electricity prices can result in significantly higher profits compared to those based solely on point forecasts. However, the majority of models developed in both academic and industrial settings provide only point predictions. To address

In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction and delayed effects are often desired features in a model, but

What is the demand elasticity of statistical arbitrageurs that invest according to the advice of modern cross-sectional asset pricing models? Thirteen models from the literature exhibit strikingly inelastic demand, in contrast to classical models that rely on statistical arbitrageurs to create elast

I examine the value of information from sell-side analysts by analyzing a large corpus of their written reports. Using embeddings from state-of-the-art large language models, I show that qualitative information in analyst reports explains above 10% of contemporaneous stock returns out-of-sample, a v

In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence

Neural network-based approaches have emerged as efficient alternatives to traditional optimization-based procedures for the calibration of stochastic volatility models. However, existing work has focused primarily on predictive accuracy, with comparatively little attention devoted to understanding t

USDC and USDT are the dominant stablecoins pegged to $1 with a total market capitalization of over $300B and rising. Stablecoins make dollar value globally accessible with secure transfer and settlement. Yet in practice, these stablecoins experience periods of stress and de-pegging from their $1

This paper establishes a new and comprehensive theoretical analysis for the application of reinforcement learning (RL) in high-frequency market making. We bridge the modern RL theory and the continuous-time statistical models in high-frequency financial economics. Different with most existing litera

We investigate the behavior of liquidity providers (LPs) by modeling a decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with heterogeneous characteristics choose optimal liquidity positions subject to uncertainty regarding the size of exogenous incoming transactions and the price

This paper develops a continuous framework for analyzing financial contagion that incorporates both geographic proximity and interbank network linkages. The framework characterizes stress propagation through a master equation whose solution admits a Feynman-Kac representation as expected cumulative

Existence and uniqueness of solutions to the multi-dimensional mean-field Libor market model (introduced by [7]) is shown. This is used as the basis for a numerical asset-liability management (ALM) model capable of calculating future discretionary benefits in accordance with Solvency~II regulation.

Aggregated curves are common structures in economics and finance, and the most prominent examples are supply and demand curves. In this study, we exploit the fact that all aggregated curves have an intrinsic hierarchical structure, and thus hierarchical reconciliation methods can be used to improve

Agent-based models (ABMs) are valuable for modelling complex, potentially out-of-equilibria scenarios. However, ABMs have long suffered from the Lucas critique, stating that agent behaviour should adapt to environmental changes. Furthermore, the environment itself often adapts to these behavioural c

Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive optimal portfolios is energy-intensive for digital computers. W

Over the past few decades, machine learning models have been extremely successful. As a result of axiomatic attribution methods, feature contributions have been explained more clearly and rigorously. There are, however, few studies that have examined domain knowledge in conjunction with the axioms.

In hedge funds, convex compensation schemes are adopted to stimulate a high-profit performance for portfolio managers. In economics, non-monotone risk aversion is proposed to argue that individuals may not be risk-averse when the wealth level is low. Combining these two ingredients, we study the opt

Flaws of a continuous limit order book mechanism raise the question of whether a continuous trading session and a periodic auction session would bring better efficiency. This paper wants to go further in designing a periodic auction when both a continuous market and a periodic auction market are ava

This research presents a predictive model to identify potential targets of activist investment funds–entities that acquire significant corporate stakes to influence strategic and operational decisions, ultimately enhancing shareholder value. Predicting such targets is crucial for companies aiming to

This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log returns, giving rise to time inconsistency and motivating t

This article investigates the influence of luck and strategic considerations on performance of teams participating in the M6 investment challenge. We find that there is insufficient evidence to suggest that the extreme Sharpe ratios observed are beyond what one would expect by chance, given the numb

Using high-quality data, we report several statistical regularities of equity auctions in the Paris stock exchange. First, the average order book density is linear around the auction price at the time of auction clearing and has a large peak at the auction price. While the peak is due to slow trader

Credit Scoring is one of the problems banks and financial institutions have to solve on a daily basis. If the state-of-the-art research in Machine and Deep Learning for finance has reached interesting results about Credit Scoring models, usage of such models in a heavily regulated context such as th

Climate change is a major threat to the future of humanity, and its impacts are being intensified by excess man-made greenhouse gas emissions. One method governments can employ to control these emissions is to provide firms with emission limits and penalize any excess emissions above the limit. Exce

Decentralized perpetuals protocols have collectively reached billions of dollars of daily trading volume, yet are still not serious competitors on the basis of trading volume with centralized venues such as Binance. One of the main reasons for this is the high cost of capital for market makers and s

The use of reinforcement learning algorithms in financial trading is becoming increasingly prevalent. However, the autonomous nature of these algorithms can lead to unexpected outcomes that deviate from traditional game-theoretical predictions and may even destabilize markets. In this study, we exam

We investigate the portfolio frontier and risk premia in equilibrium when institutional investors aim to minimize the tracking error variance under an ESG score mandate. If a negative ESG premium is priced in the market, this mandate can reduce portfolio inefficiency when the return over-performance

We consider the interaction between centralized trading and decentralized Proof of Stake (PoS) blockchain ecosystems. Motivated by the increasing dominance of centralized exchanges and the institutionalization of crypto markets, we study how trading activities on centralized exchanges affect staking

The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power – in particular in the context of group experience rating. The inclusion of collective health claims leads to a computationally challenging many-body pro

In this study, we developed a computational framework for simulating large-scale agent-based financial markets. Our platform supports trading multiple simultaneous assets and leverages distributed computing to scale the number and complexity of simulated agents. Heterogeneous agents make decisions i

This paper addresses the challenges of pricing exotic options and structured products, which traditional models often fail to handle due to their inability to capture real-world market phenomena like fat-tailed distributions and volatility clustering. We introduce a Diffusion-Conditional Probability

We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, and the corresponding equivalent martingale measure

Corporate insiders trade for diverse reasons, often possessing Material Non-Public Information (MNPI). Determining whether specific trades leverage MNPI is a significant challenge due to inherent complexity. This study focuses on two critical objectives: accurately detecting Unlawful Insider Trading

This study introduces an inverse behavioral optimization framework that integrates QALY-based health outcomes, ROI-driven incentives, and adaptive behavioral learning to quantify how policy design shapes national healthcare performance. Building on the FOSSIL (Flexible Optimization via Sample-Sensit

We present a general computational framework for solving continuous-time financial market equilibria under minimal modeling assumptions while incorporating realistic financial frictions, such as trading costs, and supporting multiple interacting agents. Inspired by generative adversarial networks (G

I examine whether the imposition of fiduciary duty on municipal advisors affects bond yields and advising fees. Using a difference-in-differences analysis, I show that bond yields reduce by $\sim$9% after the imposition of the SEC Municipal Advisor Rule due to lower underwriting spreads. Larger mun

We present a comprehensive analysis of the implications of artificial latency in the Proposer-Builder Separation framework on the Ethereum network. Focusing on the MEV-Boost auction system, we analyze how strategic latency manipulation affects Maximum Extractable Value yields and network integrity.

In private wealth management, a manager delegating to artificial intelligence (AI) acts as the client’s agent and the system’s principal. We introduce a model-independent formulation that combines nested principal–agent delegation with constrained joint maximisation as the task assigned to the AI s

We consider a Kyle-type model where insider trading takes place among a potentially large population of liquidity traders and is subject to legal penalties. Insiders exploit the liquidity provided by the trading masses to “camouflage” their actions and balance expected wealth with the necessary stea

Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider the subgame perfect strategies. The later are characterized

Liquidity providers are currently incentivised to provide liquidity through the LP Incentives Programme on dYdX. Based on the various parameters - makerVolume, depths and spreads, they are rewarded accordingly based on their activities. Given the maturity of the BTC and ETH markets, alongside other

We study how AI agents form expectations and trade in experimental asset markets. Using a simulated open-call auction populated by autonomous Large Language Model (LLM) agents, we document three main findings. First, AI agents exhibit classic behavioral patterns: a pronounced disposition effect and

In the current market practice, many cyber insurance products offer a coverage bundle for losses arising from various types of incidents, such as data breaches and ransomware attacks, and the coverage for each incident type comes with a separate limit and deductible. Although this gives prospective

As of 2022, greenhouse gases (GHG) emissions reporting and auditing are not yet compulsory for all companies and methodologies of measurement and estimation are not unified. We propose a machine learning-based model to estimate scope 1 and scope 2 GHG emissions of companies not reporting them yet. O

This paper investigates both short and long-run interaction between BIST-100 index and CDS prices over January 2008 to May 2015 using ARDL technique. The paper documents several findings. First, ARDL analysis shows that 1 TL increase in CDS shrinks BIST-100 index by 22.5 TL in short-run and 85.5 TL

We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader-follower stochastic game, where the venue is the leader and a representa

This paper proposes a model that enables permissionless and decentralized networks for complex computations. We explore the integration and optimize load balancing in an open, decentralized computational network. Our model leverages economic incentives and reputation-based mechanisms to dynamically

Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whereon these NOs operate. A significant gap remains between theory and practice: worst-case parameter bounds from universa

This paper extends the optimal-trading framework developed in arXiv:2409.03586v1 to compute optimal strategies with real-world constraints. The aim of the current paper, as with the previous, is to study trading in the context of multi-player non-cooperative games. While the former paper relies on m

We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand, observes the trading speed of each of his clients and provides liqu

We find an approximate Nash equilibrium in a game between decentralized exchanges (DEXs) that compete for order flow by setting dynamic trading fees. We characterize the equilibrium via a coupled system of partial differential equations and derive tractable approximate closed-form expressions for th

We study the optimal liquidation problem in both lit and dark pools for investors facing execution uncertainty in a continuous-time setting with market impact. First, we design an optimal make–take fee policy for a large investor liquidating her position across both pools, interacting with small in

This paper presents a dynamic game framework to analyze the role of large banks in interbank markets. By extending existing models, we incorporate a large bank as a dynamic decision-maker interacting with multiple small banks. Using the mean-field game methodology and convex analysis, best-response

This thesis develops equilibrium asset pricing models in incomplete markets with a large number of heterogeneous agents using mean field game theory. The market equilibrium is characterized by a novel form of mean field backward stochastic differential equations (BSDEs). First, we propose a theoreti

This paper studies the continuous-time q-learning in mean-field jump-diffusion models when the population distribution is not directly observable. We propose the integrated q-function in decoupled form (decoupled Iq-function) from the representative agent’s perspective and establish its martingale c

Cyber risk has become a critical financial threat in today’s interconnected digital economy. This paper introduces a cyber-risk management framework for networked digital systems that combines the strategic behavior of players with contagion dynamics within a security game. We address the problem of

Financial models do not merely analyse markets, but actively shape them. This effect, known as performativity, describes how financial theories and the subsequent actions based on them influence market processes, by creating self-fulfilling prophecies. Although discussed in the literature on economi

Passive investing has gained immense popularity due to its low fees and the perceived simplicity of focusing on zero tracking error, rather than security selection. However, our analysis shows that the passive (zero tracking error) approach of waiting until the market close on the day of index recon

This paper studies the competition among multiple fund managers with relative performance over the excess logarithmic return. Fund managers compete with each other and have expected utility or mean-variance criteria for excess logarithmic return. Each fund manager possesses a unique risky asset, and

This paper studies dynamic mean-variance (MV) asset allocation problems in general incomplete markets. Besides of the conventional MV objective on portfolio’s terminal wealth, our framework can accommodate running MV objectives with general (non-exponential) discounting factors while in general, any

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties a

We study Just-in-time (JIT) liquidity provision in blockchain-based decentralized exchanges. A JIT liquidity provider (LP) monitors pending swap orders in public mempools of blockchains to sandwich orders of their choice with liquidity, depositing right before and withdrawing right after the order.

In this paper, we study an investor’s optimal entry and exit decisions in a liquid staking protocol (LSP) and an automated market maker (AMM), primarily from the standpoint of the investor. Our analysis focuses on two key investor actions: the initial allocation decision at time $t=0$, and the optim

Quantilized mean-field game models involve quantiles of the population’s distribution. We study a class of such games with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative to the population’s $α$-quantile value, $α\in (0,1)$. This ev

Systemic risk measures aggregate the risks from multiple financial institutions to find system-wide capital requirements. Though much attention has been given to assessing the level of systemic risk, less has been given to allocating that risk to the constituent institutions. Within this work, we pr

In this paper, we present Deep-MacroFin, a comprehensive framework designed to solve partial differential equations, with a particular focus on models in continuous time economics. This framework leverages deep learning methodologies, including Multi-Layer Perceptrons and the newly developed Kolmogo

We consider an insurance market with hidden information, where the agent’s type is private information and is drawn from an arbitrary type space. We study implementability of a collection of retention functions, namely, how to select premium schedules so that the resulting menu of contracts is incen

Many of the thousands of existing cryptocurrencies suffer from declining adoption, low liquidity and weak security, and merging two of them into a single ecosystem is a natural alternative to abandonment. No rigorous framework exists, however, for determining a fair exchange rate in such a merger. U

We develop a stochastic game-theoretic model for intraday dispatch of grid-scale battery energy storage systems (BESSs). We assume that each BESS operator competitively manages her state-of-charge to maximize energy arbitrage revenues, driven by the endogenized electricity price that depends on the

This paper develops a dynamic equilibrium model of the insurance market that jointly characterizes insurers’ underwriting, investment, recapitalization, and dividend policies under model uncertainty and financial frictions. Competitive insurers maximize shareholder value under a subjective worst-cas

This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the insurance companies under a Bonus-Malus System (BMS) framew

We study a continuous-time portfolio choice problem for an investor whose state-dependent preferences are determined by an exogenous factor that evolves as an Itô diffusion process. Since risk attitudes at the end of the investment horizon are uncertain, terminal wealth is evaluated under a set of u

A mutual insurance company (MIC) is a type of consumer cooperative owned by its policyholders. By purchasing insurance from an MIC, policyholders effectively become member-owners of the company and are entitled to a share of the surplus, which is determined by their own collective claims and premium

In recent years, machine learning models have achieved great success at the expense of highly complex black-box structures. By using axiomatic attribution methods, we can fairly allocate the contributions of each feature, thus allowing us to interpret the model predictions. In high-risk sectors such

Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for mode

We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time horizon. The firm generates profits with a stochastic dynamics a

This is the third paper in a series concerning the game-theoretic aspects of position-building while in competition. The first paper set forth foundations and laid out the essential goal, which is to minimize implementation costs in light of how other traders are likely to trade. The majority of res

This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in the space of trading strategies where action sets are tradin

Motivated by recent empirical findings on the periodic phenomenon of aggregated market volumes in equity markets, we aim to understand the causes and consequences of periodic trading activities through a game-theoretic perspective, examining market interactions among different types of participants.