arXiv subjects

Shihua Wang

Publications and source records attributed to Shihua Wang.

5 recordsLinked to original sources

arXiv2025

Dynamic Data Pricing: A Mean Field Stackelberg Game Approach

This paper studies the dynamic pricing mechanism for data products in demand-driven markets through a game-theoretic framework. We develop a three-tier Stackelberg game model to capture the hierarchical strategic interactions among key market entities: a single data buyer, an intermediary broker, and a competitive seller group. To characterize the temporal dynamics of data quality evolution, we establish a coupled system of stochastic differential equations (SDEs) where sellers' quality investments interact through mean field effects. Given exogenous pricing policies, we derive approximate Nash equilibrium adjustment strategies for competitive sellers using the mean field game (MFG) approach. The broker's optimal pricing strategy is subsequently established by solving a Stackelberg leadership problem, while the buyer's procurement policy is determined through an optimal control formulation involving conditional mean field forward-backward SDEs (FBSDEs). Under some regularity conditions, the proposed strategies are shown to collectively form an $(\epsilon_1,\epsilon_2,\epsilon_3)$-Stackelberg equilibrium.

math.OC↗

arXiv2025

EV Charging in Smart Grids: Mean Field Equilibrium and Approximate Non-Cooperative and Cooperative Strategies

We study the optimal charging strategies for large-scale electric vehicles in smart grids within a finite-horizon mean field game framework. We first establish the existence and uniqueness of the solution to the consistency condition equation, which characterizes the optimal charging behavior in the mean field limit. Building on this result, we construct approximate optimal charging strategies for a finite population of vehicles in both non-cooperative and cooperative settings. Finally, we provide numerical analyses that illustrate and compare the approximate strategies in the non-cooperative and cooperative games.

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arXiv2024

Mean field game problem for the optimal control of neuronal spiking activity

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to synchronize with others, thereby giving rise to a finite-player game problem. To address this, we first examine the corresponding mean field game problem and characterize the mean field equilibrium by solving a fixed point problem. Subsequently, leveraging the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the finite-player game as the number of neurons is large.

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arXiv2024

A mean field game approach to equilibrium consumption under external habit formation

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a log-normal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude some financial implications caused by consumption habits from a mean-field perspective. In each problem with n agents, we construct an approximate Nash equilibrium for the n-player game using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained.

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arXiv2023

Mean Field Game of Optimal Relative Investment with Jump Risk

This paper studies the n-player game and the mean field game under the CRRA relative performance on terminal wealth, in which the interaction occurs by peer competition. In the model with n agents, the price dynamics of underlying risky assets depend on a common noise and contagious jump risk modelled by a multi-dimensional nonlinear Hawkes process. With a continuum of agents, we formulate the MFG problem and characterize a deterministic mean field equilibrium in an analytical form under some conditions, allowing us to investigate some impacts of model parameters in the limiting model and discuss some financial implications. Moreover, based on the mean field equilibrium, we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large. The explicit order of the approximation error is also derived.

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