pFedGame uses game theory for decentralized federated learning in dynamic networks.
problem Performance bottlenecks, data bias, model convergence issues, and model poisoning attacks in federated learning.
method pFedGame employs game theory to decentralize federated learning, avoiding a central aggregation server and addressing dynamic network challenges.
result pFedGame achieves higher accuracy (over 70%) in heterogeneous data compared to existing methods.
Game theory helps analyze ESOs/EBIs in production and service sectors.
problem Economic incentives affect traditional production/service functions and create intangible capital.
method Uses game theory to analyze interactions in ESO/EBI transactions.
result No perfect Nash Equilibria for two-stage games involving many participants.
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be…
Neural operators approximate Stackelberg game solutions.
problem Intractability of follower's best-response operator in dynamic Stackelberg games.
method Used attention-based neural operators to approximate the best-response operator.
result Approximate best-response operator yields close game value.
The paper analyzes strategic interactions in a multi-agent reinsurance chain using game theory.
problem Strategic behavior and competition among insurers and reinsurers in a multi-layer reinsurance chain.
method Employed Stackelberg differential games and non-zero-sum game models to characterize strategic interactions. Used dynamic programming and game theory to derive equilibrium strategies for investment and reinsurance.
result Intensified competition leads to reduced safety loadings in reinsurance contracts.
GT-DDP optimizer trains residual networks using game theory.
problem Applying DDP to residual networks.
method Game-theoretic DDP optimizer for residual networks.
result Improved training convergence and variance reduction.
We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…
New game theory approach to bond market liquidity and participant behavior.
problem Uncertainty in market maker types and regulatory structure.
method Liquidity Game theory applied to UK bond market interactions.
result Strategies and structures for market makers and regulators.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
We introduce the minority game theory for two kinds of the Korean treasury bond (KTB) in Korean futures exchange markets. Since we discuss numerically the standard deviation and the global efficiency for an arbitrary strategy, our case is found to be approximate to the majority game. Our result presented will be compar…
A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game th…
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this work, we derive mean field game partial differential equation systems from determi…
Study examines large banks' role in interbank markets using game theory.
problem Understanding systemic risk in interbank markets with large banks.
method Mean-field game framework, convex analysis, Monte Carlo simulations.
result Large banks can positively or negatively impact market stability.
Expands MFGs to handle real-world asymmetric multi-agent games efficiently.
problem Applying mean-field games to real-world, heterogeneous multi-agent systems.
method Develops a method to symmetrize and extend finite-player games to infinite-player MFGs, proving approximation bounds and convergence guarantees.
result TD learning converges to approximate Nash equilibria in finite-sample settings, enabling symmetrized learning without explicit MFG models.
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with finite heterogeneous learning rates. In each case, we characterize the macroscopic…
Unified framework for estimating reward functions in competitive games.
problem Estimating unknown reward functions in competitive games.
method Unified framework with entropy regularization for reward function recovery.
result Strong theoretical guarantees and practical effectiveness demonstrated.
New framework recovers reward and rationality parameters from game behavior.
problem Statistical ambiguity in identifying reward and rationality parameters in competitive games.
method Blind Inverse Game Theory (Blind-IGT) using entropy-regularized Quantal Response Equilibrium and Normalized Least Squares (NLS) estimator.
result Optimal convergence rate of O(N−1/2) for joint parameter recovery. New learning dynamics achieve fast convergence in games without needing to know utility scales.
problem Fast convergence guarantees in learning games require prior knowledge of utility scales.
method Developed scale-free and scale-invariant learning dynamics using optimistic follow-the-regularized-leader with adaptive learning rates and clipping techniques.
result Achieved fast convergence rates to Nash and correlated equilibria without prior utility scale knowledge.
We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical systems theory. For both general-sum and potential games, we characterize a non…
We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functi…
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
Algorithm learns from changing zero-sum games with no regret.
problem Learning in time-varying zero-sum games.
method Developed a single parameter-free algorithm with three performance measures.
result Algorithm recovers best known results for fixed games and adapts to non-stationarity.
The paper explains how simple methods can converge to optimal solutions in complex neural games.
problem Finding optimal solutions in neural games with non-convex objectives.
method Theoretical framework using hidden convexity and overparameterization, with path-length bounds and PŁ conditions.
result Simple gradient methods can converge to Nash equilibria in non-convex min-max games under certain conditions.
AlphaZero assesses new chess variants for balance and dynamics.
problem Designing engaging and balanced game rules, especially for chess variants.
method Used AlphaZero to learn near-optimal strategies for nine chess variants.
result AlphaZero reveals novel strategic and tactical patterns in chess variants.
New framework values football players based on in-game interactions.
problem Valuing football players based on in-game performance.
method Combining financial models and network theory using a passing matrix.
result Dynamic and individualized player valuation framework.
We solve a continuous-time game-theoretic problem for Kihlstrom-Mirman preferences.
problem Dynamic inconsistency in preferences due to multiattribute utility theory.
method Formalized an equilibrium control theory for continuous-time Markov processes.
result Equilibrium strategy and value function as solution to extended HJB system.
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we propose an actor-critic reinforcement learning algorithm that provably converges t…
Modeling dynamic groundwater markets with price formation and trading strategies.
problem Understanding competitive effects in environmental markets with groundwater banking.
method Stochastic models and game theory with machine learning algorithms.
result Sub-game perfect Nash equilibria characterized by groundwater price processes.
Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances. First, in the single-player case (corresponding to an agent tryi…
Study dynamic asset allocation in incomplete markets using game theory and nonlocal BSDEs.
problem Dynamic mean-variance asset allocation in general incomplete markets with non-exponential discounting.
method Game-theoretic approach, decomposition into myopic and hedging strategies, nonlocal BSDEs, fixed-point theorem.
result Well-posedness of solutions to BSDEs, existence of equilibrium control policy.
A game-theoretic analysis of DEX competition through dynamic trading fees.
problem Competition between decentralized exchanges (DEXs) and their impact on trading fees and slippage.
method Characterization of an approximate Nash equilibrium via coupled system of partial differential equations and closed-form expressions for equilibrium fees.
result The equilibrium trading fees shift from the oracle price to a weighted average of the oracle and competitors' exchange rates under competition.
We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes restricted to the real line represent well-understood classes of problems, like minimi…
Study of LQ MFGs in infinite-dimensional Hilbert spaces.
problem Mean field games in infinite-dimensional settings with stochastic dynamics.
method Analysis of coupled semilinear infinite-dimensional stochastic evolution equations, development of Nash equilibrium.
result Characterization of unique Nash equilibrium in the limit of many agents.
Study explores algorithmic collusion in repeated games using various learning dynamics.
problem Understanding algorithmic collusion in repeated games with different learning dynamics.
method Examines Q-learning, gradient learning, and other dynamics in a general repeated game setting. result Characterizes the set of payoff vectors achievable by these dynamics, revealing possibilities for collusion.
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…
New learning dynamics adapt to corrupted games, improving performance in real-world scenarios.
problem Learning dynamics in games are limited to honest players, ignoring real-world corruption.
method Adaptive learning dynamics that adapt to player deviations from prescribed algorithms.
result Learning dynamics achieve better performance in corrupted games, matching honest regime bounds.
Paper introduces metrics for evaluating multi-agent policies using best response dynamics.
problem Evaluation and ranking of multi-agent policies in reinforcement learning.
method Adopting strict best response dynamics (SBRD) to model selfish behaviors, proposing perturbed SBRD for dynamic and non-stationary settings.
result Proposed perturbed SBRD can observe policies with maximum metrics and differ from optimal by any given tolerance.
We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic loses, whereas a periodic or random seque…
The paper analyzes reinsurance strategies in a competitive multi-agent system.
problem Strategic interactions and competitive behavior in multi-layer reinsurance chains.
method Stochastic differential games and non-zero-sum game models to characterize strategic interactions. Dynamic programming and game theory to derive equilibrium strategies.
result Intensified competition reduces safety loadings in reinsurance contracts.
In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Can…
New control methods improve dynamic measure transport paths.
problem Improving paths for dynamic measure transport.
method Connecting mean-field games to optimization problems for learning paths, advocating for smoothness of velocities.
result Our method recovers more efficient and smooth transport models compared to untilted paths.
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a …
The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.
problem Asset pricing in a market with partial observation and heterogeneous agents.
method Mean field game theory, exponential quadratic Gaussian framework, Kalman-Bucy filtering theory.
result Characterization of equilibrium risk premium through mean field BSDE and construction of unobservable risk premium process.
Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.
problem Gradient-based methods for two-player games suffer from drift due to discrete update steps.
method Derived modified continuous dynamical systems to closely follow the discrete dynamics of games.
result Identified distinct components of discretization drift that can alter or destabilize game performance.
Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
problem Learning dynamics in zero-sum polymatrix games under different information settings.
method Two-timescale learning dynamics combining smoothed best-response updates and TD-learning for estimating local payoff functions.
result Polynomial-time finite-sample guarantees for convergence to an ε-Nash equilibrium in the minimal information case.
Federated learning linked to mean-field games for large-scale learning.
problem Large-scale distributed and privacy-preserving learning algorithms.
method Established a connection between federated learning and mean-field games, presenting federated learning as a differential game.
result Properties of the equilibrium of the federated learning game were discussed.
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the…
The extragradient method accelerates convergence in complex game dynamics.
problem Complex interactions in game dynamics cause simple methods to diverge, necessitating more sophisticated approaches.
method A polynomial-based analysis to identify three scenarios for accelerated convergence of the momentum extragradient method.
result The momentum extragradient method achieves faster convergence under specific eigenvalue conditions.