Game Theory & Mean-Field Games

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulat

This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion framework. First, we provide a sufficient and necessary condition for

In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial feature of controlling the term rate’s variances over large time

We present a new discrete time version of Kyle’s (1985) classic model of insider trading, formulated as a generalised extensive form game. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise

Maximal Extractable Value (MEV) is value extractable by temporary monopoly power commonly found in decentralized systems. This extraction stems from a lack of user privacy upon transaction submission and the ability of a monopolist validator to reorder, add, and/or censor transactions. There are two

In recent years, explainable machine learning methods have been very successful. Despite their success, most explainable machine learning methods are applied to black-box models without any domain knowledge. By incorporating domain knowledge, science-informed machine learning models have demonstrate

Designing automated market makers (AMMs) is crucial for decentralized token exchanges in cryptoeconomic systems. At the intersection of software engineering and economics, AMM design is complex and, if done incorrectly, can lead to financial risks and inefficiencies. We developed an AMM taxonomy for

We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the reinsurer is uncertain about the insurers’ claim severity distribut

In this paper we show how the relaxation techniques can be used to establish the existence of an optimal contract in presence of information asymmetry. The method we illustrate was initially motivated by the problem of designing optimal brokerage fees, but it does apply to other optimal contract pro

Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogene

This paper investigates a Stackelberg game between an insurer and a reinsurer under the $α$-maxmin mean-variance criterion. The insurer can purchase per-loss reinsurance from the reinsurer. With the insurer’s feedback reinsurance strategy, the reinsurer optimizes the reinsurance premium in the Stack

We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while players with an initially long position are only allowed to sell

We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the Nash equilibrium of the game semi-explicitly in terms of operat

We develop a variational approach to address risk-sensitive optimal control problems with an exponential-of-integral cost functional in a general linear-quadratic-Gaussian (LQG) single-agent setup, offering new insights into such problems. Our analysis leads to the derivation of a nonlinear necessar

In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as wel

This paper introduces a heterogeneous macroeconomic model of a Proof-of-Stake (PoS) network to analyze the long-term centralizing effects of external traditional finance (TradFi) yields. We model a continuum of rational actors divided into two distinct classes: investors, who optimize portfolios bet

This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic differential equations (BSDEs). These equations encapsulate

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solu

In this paper we derive a novel characterization result for time-consistent stochastic control problems with higher-order moments, originally formulated by Wang et al. [SIAM J. Control. Optim., 63 (2025), 1560–1589], and newly explore many solvable instances including a mean-variance-excess kurtosi

The state of economic theory and accumulated facts from the different branches of the economic science require to analyze the concept of the description of economy systems. The economic reality generates the problems the solution of that is only possible by a new paradigm of the description of econo

This study evaluates ethanol blending as a practical near-term strategy for significant transportation decarbonization in the United States. Despite rapid growth in electric vehicle adoption, gasoline is projected to remain dominant, with annual demand around 135 billion gallons by 2035, necessitati

We introduce the first formal model capturing the elicitation of unverifiable information from a party (the “source”) with implicit signals derived by other players (the “observers”). Our model is motivated in part by applications in decentralized physical infrastructure networks (a.k.a. “DePIN”), a

This paper delves into financial markets that incorporate a novel form of heterogeneity among investors, specifically in terms of their beliefs regarding the reliability of signals in the business cycle economy model, which may be biased. Unlike most papers in this field, we not only analyze the equ

In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the relative wealth and consumption to her competitors. Due to the pres

Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity Theorem in a plausible general class of economic models: with

We consider a novel class of portfolio liquidation games with market drop-out (“absorption”). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular round-trips are not admissible. This can be viewe

This paper is concerned with the problem of budget control in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a regional financial network. Motivated by Tang and Tsai (Ann. Probab., 46(2018), pp. 1597{

This paper proposes a formal multi-agent architecture for implementing enterprise AI in regulated insurance firms, integrating economic theory with institutional design. The framework synthesises three core theoretical perspectives: Arrow’s risk pooling theory to formalise risk transformation under

This paper examines the computational complexity of the \emph{Core Identification Problem} (CIP) in one-sided matching markets governed by the Top Trading Cycles (TTC) algorithm. The central contribution is a formal complexity separation: this paper proves that identifying which agents receive a cor

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach doe

We extend the results of (Liu and Firoozi, 2025), which develops the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, by incorporating a common noise. This common noise is modeled as an infinite-dimensional Wiener process affecting the dynamics of all agents. In the presenc

We study the high-frequency limit of an $n$-trader optimal execution game in discrete time. Traders face transient price impact of Obizhaeva–Wang type in addition to quadratic instantaneous trading costs $θ(ΔX_t)^2$ on each transaction $ΔX_t$. There is a unique Nash equilibrium in which traders choo

We study regularity properties of the unique solution of a mean-field $G$-SDE. More precisely, we consider a mean-field $G$-SDE with square-integrable random initial condition and establish its first and second order Fréchet differentiability in the random initial condition and specify the $G$-SDEs

This paper explores the interplay between transfer policies, R&D, corruption, and economic development using a general equilibrium model with heterogeneous agents and a government. The government collects taxes, redistributes fiscal revenues, and undertakes public investment (in R&D, infrastructure,

As restaking protocols gain adoption across blockchain ecosystems, there is a need for Actively Validated Services (AVSs) to span multiple Shared Security Providers (SSPs). This leads to stake fragmentation which introduces new complications where an adversary may compromise an AVS by targeting its

We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented by market makers. For market makers, order flows become endo

We study partial information Nash equilibrium between a broker and an informed trader. In this setting, the informed trader, who possesses knowledge of a trading signal, trades multiple assets with the broker in a dealer market. Simultaneously, the broker offloads these assets in a lit exchange wher

This paper analyzes the equilibrium of insurance market in a dynamic setting, focusing on the interaction between insurers’ underwriting and investment strategies. Three possible equilibrium outcomes are identified: a positive insurance market, a zero insurance market, and market failure. Our findin

In this work, we study the effectiveness of employing archetypal aperiodic sequencing – namely Fibonacci, Thue-Morse, and Rudin-Shapiro – on the Parrondian effect. From a capital gain perspective, our results show that these series do yield a Parrondo’s Paradox with the Thue-Morse based strategy out

Machine-learning technologies are seeing increased deployment in real-world market scenarios. In this work, we explore the strategic behaviors of large language models (LLMs) when deployed as autonomous agents in multi-commodity markets, specifically within Cournot competition frameworks. We examine

This paper employs an intra-personal game-theoretic framework to investigate how decreasing impatience influences irreversible investment behaviors in a continuous-time setting. We consider a capacity expansion problem under weighted discount functions, a class of nonexponential functions that exhib

Milionis et al.(2023) studied the rate at which automated market makers leak value to arbitrageurs when block times are discrete and follow a Poisson process, and where the risky asset price follows a geometric Brownian motion. We extend their model to analyze another popular mechanism in decentrali

This paper presents a comprehensive study of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, generalizing the classic LQ MFG theory to scenarios involving $N$ agents with dynamics governed by infinite-dimensional stochastic equations. In this framework, both state and control proces

In this paper, we study a non-zero-sum game with two players, where each of the players plays what we call Bermudan strategies and optimizes a general non-linear assessment functional of the pay-off. By using a recursive construction, we show that the game has a Nash equilibrium point.

Blackjack or “21” is a popular card-based game of chance and skill. The objective of the game is to win by obtaining a hand total higher than the dealer’s without exceeding 21. The ideal blackjack strategy will maximize financial return in the long run while avoiding gambler’s ruin. The stochastic e

In the dynamic discrete-time trading setting of Kyle (1985), we prove that Kyle’s equilibrium model is stable when there are one or two trading times. For three or more trading times, we prove that Kyle’s equilibrium is not stable. These theoretical results are proven to hold irrespectively of all K

Triangle fees are a novel fee structure for AMMs, in which marginal fees are decreasing in a trade’s size. That decline is proportional to the movement in the AMM’s implied price, i.e. for every basis point the trade moves the ratio of assets, the marginal fee declines by a basis point. These fees c

We introduce the notions of Collective Arbitrage and of Collective Super-replication in a discrete-time setting where agents are investing in their markets and are allowed to cooperate through exchanges. We accordingly establish versions of the fundamental theorem of asset pricing and of the pricing

We develop a formalism for reasoning about trading on decentralized exchanges on blockchains and a formulation of a particular form of maximal extractable value (MEV) that represents the total arbitrage opportunity extractable from on-chain liquidity. We use this formalism to prove that for blockcha

We theorize the financial health of a company and the risk of its default. A company is financially healthy as long as its equilibrium in the financial system is maintained, which depends on the cost attributable to the probability that equilibrium may decay. The estimate of that probability is base

Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive a necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and cha

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation proce

We study a monopolistic insurance market with hidden information, where the agent’s type $θ$ is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this frame

Universal basic income (UBI) is a tax scheme that uniformly redistributes aggregate income amongst the entire population of an economy. We prove the existence of an equilibrium in a model that implements universal basic income. The economic agents choose the proportion of their time to work and earn

This paper studies a continuous-time portfolio selection problem under a general distribution of random risk aversion (RRA). We provide a complete characterization of all deterministic equilibrium strategies in closed form. Our results show that the structure of the solution depends crucially on the

This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing regularization method: first, we introduce an entropy-based regulariza

We investigate the effects of wariness (defined as individuals’ concern for their minimum utility over time) on poverty traps and equilibrium multiplicity in an overlapping generations (OLG) model. We explore conditions under which (i) wariness amplifies or mitigates the likelihood of poverty traps

This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio selection is interconnected through relative performance conc

This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a random horizon that depends endogenously on the company’s dividen

We study an overlapping generations (OLG) exchange economy with an asset that yields dividends. First, we derive general conditions, based on exogenous parameters, that give rise to three distinct scenarios: (1) only bubbleless equilibria exist, (2) a bubbleless equilibrium coexists with a continuum

This paper explores stochastic control models in the context of decarbonization within the energy market. We study three progressively complex scenarios: (1) a single firm operating with two technologies-one polluting and one clean,(2)two firms model and (3) two firms without any regulatory incentiv

We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences r

In competitive supply chains (SCs), pricing decisions are crucial, as they directly impact market share and profitability. Traditional SC models often assume continuous pricing for mathematical convenience, overlooking the practical reality of discrete price increments driven by currency constraints

This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we obtain the closed-form solutions and show that the optimal

This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients and square-integrability of the market price of risk. Our m

We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting functi

Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth $W_t$ quantifies the evidence against the null hypothesis after $t$ rounds, and the null can be rejected at level $α$ whenever $W_t \geq 1/α$. A key

We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions, which include the class of extrem

We investigate a market with a normal-speed informed trader (IT) who may employ mixed strategy and multiple anticipatory high-frequency traders (HFTs) who are under different inventory pressures, in a three-period Kyle’s model. The pure- and mixed-strategy equilibria are considered and the results p

We study a reinsurance Stackelberg game in which both the insurer and the reinsurer adopt the mean-variance (abbr. MV) criterion in their decision-making and the reinsurance is irreversible. We apply a unified singular control framework where irreversible reinsurance contracts can be signed in both

The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some predetermined schedule; the best choice of this schedule depe

For constants $γ\in (0,1)$ and $A\in (1,\infty)$, we prove existence and uniqueness of a solution to the singular and path-dependent Riccati-type ODE \begin{align*} \begin{cases} h’(y) = \frac{1+γ}{y}\big( γ- h(y)\big)+h(y)\frac{γ+ \big((A-γ)e^{\int_y^1 \frac{1-h(q)}{1-q}dq}-A\big)h(y)}{1-y},\quad y

This paper examines optimal risk sharing for empirically realistic risk attitudes, providing results on Pareto optimality, competitive equilibria, utility frontiers, and the first and second theorems of welfare. Contrary to common theoretical assumptions, empirical studies find prevailing risk seeki

We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic game in which two financially-constrained firms operate in the

We consider an augmented version of Merton’s portfolio choice problem, where trading by large investors influences the price of underlying financial asset leading to strategic interaction among investors, with investors deciding their trading rates independently and simultaneously at each instant, i

In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also relative performance compared to the average of other agents.

The classical mean-variance portfolio selection problem induces time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach and look for (sub-game perfect Nash) equilibrium strategies, w

We study an optimal reinsurance problem under a diffusion risk model for an insurer who aims to minimize the probability of lifetime ruin. To rule out moral hazard issues, we only consider moral-hazard-free reinsurance contracts by imposing the incentive compatibility constraint on indemnity functio

We study a continuous time economy where throughout time, insiders receive private signals regarding the risky assets’ terminal payoff. We prove existence of a partial communication equilibrium where, at each private signal time, the public receives a signal of the same form as the associated inside

A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the decomposition of functions with real arguments, a popular metho

We consider existence and uniqueness of Nash equilibria in an $N$-player game of utility maximization under relative performance criteria of multiplicative form in complete semimartingale markets. For a large class of players’ utility functions, a general characterization of Nash equilibria for a gi

This paper studies a central planner’s decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude function that reflects the aggregation rule chosen by the c

Trust can attract fraud when it delays verification. We develop a two-market signaling model in which generative AI lowers fabrication, verification, and targeting costs. When fabrication becomes profitable before verification, claim credibility first falls and later recovers. Across markets, higher

This paper studies the regularity of the value function arising from a multidimensional continuous-time principal-agent model with separable, nonquadratic effort costs. The associated stochastic control problem has the output and the agent’s continuation utility as state variables, and its Hamilton-

Although market participants generally have access to a common information set, they make decisions based on forecasts formed over heterogeneous horizons. Because market impact depends on aggregate positions rather than trader identities, these decisions feed back into prices through their collectiv

We investigate a portfolio selection problem involving multi competitive agents, each exhibiting mean-variance preferences. Unlike classical models, each agent’s utility is determined by their relative wealth compared to the average wealth of all agents, introducing a competitive dynamic into the op

We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui’s representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mea

Price benchmarks are used to incorporate market price trends into contracts, but their use can create opportunities for manipulation by parties involved in the contract. This paper examines this issue using a realistic and tractable model inspired by smart contracts on blockchains like Ethereum. In

We study the existence of equilibrium when agents’ preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspond

We show that, in a market economy, the aggregate production level depends not only on the aggregate variables but also on the distribution of individual characteristics (e.g., productivity, credit limit, …). We prove that, due to financial frictions, the equilibrium aggregate production may be non-m

We study $N$-player optimal execution games in an Obizhaeva–Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas without regularization, there is no equilibrium. We prove th

In this paper, we focus on a class of time-inconsistent stochastic control problems, where the objective function includes the mean and several higher-order central moments of the terminal value of state. To tackle the time-inconsistency, we seek both the closed-loop and the open-loop Nash equilibri

We explore brokerage between traders in an online learning framework. At any round $t$, two traders meet to exchange an asset, provided the exchange is mutually beneficial. The broker proposes a trading price, and each trader tries to sell their asset or buy the asset from the other party, depending

We study a new “laminated” queueing model for orders on batched trading venues such as decentralised exchanges. The model aims to capture and generalise transaction queueing infrastructure that has arisen to organise MEV activity on public blockchains such as Ethereum, providing convenient channels

We study an information acquisition problem in which an informed trader acquires costly information prior to trading in the Kyle equilibrium. The cost of information acquisition is represented by an entropy cost. Regardless of the prior distribution of the asset payoff, continuous signals are optima

We study the Merton portfolio management problem within a complete market, non constant time discount rate and general utility framework. The non constant discount rate introduces time inconsistency which can be solved by introducing sub game perfect strategies. Under some asymptotic assumptions on

Modern financial networks are highly connected and result in complex interdependencies of the involved institutions. In the prominent Eisenberg-Noe model, a fundamental aspect is clearing – to determine the amount of assets available to each financial institution in the presence of potential defaul

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria ar

We study a discrete-time financial market with a single constrained trader, competitive market makers, and noise traders. Within the class of linear equilibria, the equilibrium structure is shown to be uniquely determined by two state variables: the market maker’s expectation of the trader’s remaini

We consider islamic Profit and Loss (PL) sharing contract, possibly combined with an agency contract, and introduce the notion of {\em $c$-fair} profit sharing ratios ($c = (c_1, \ldots,c_d) \in (\mathbb R^{\star})^d$, where $d$ is the number of partners) which aims to determining both the profit sh