arXiv subjects

Jake J. Xia

Publications and source records attributed to Jake J. Xia.

3 recordsLinked to original sources

arXiv2026

Optimal Order of Multi-Agent and General Many-Body Systems

This paper develops a general framework for analyzing multi-agent systems with feedback loops between agents actions and collective observations. The framework is built on two fundamental agent-level variables: power, which measures agent influence on collective outcomes, and response functions, which determine how agents react to observations. We derive how macroscopic properties, including total power, useful power, entropy, order, fragility, and mobility, emerge from these two variables of heterogeneous agents. To study the trade off between growth and resilience, we introduce a system-level utility function parameterized by a risk-appetite coefficient and derive an optimal degree of order that balances productivity, stability, and adaptability. The analysis suggests that stronger synchronization can increase collective output but may also increase systemic fragility and reduce mobility. We further argue that order, entropy, information, and useful energy are task-dependent and system-relative concepts whose meanings depend on the objectives of the system. By measuring and designing agent power distributions and response functions, it may be possible to better understand, predict, and optimize collective behavior and identify the conditions under which collective intelligence and optimal order emerge.

q-fin.RM↗

arXiv2024

Emergence of Power-Law and Other Wealth Distributions in Crowd of Heterogeneous Agents

This study investigates the emergence of power-law and other concentrated distributions through a feedback loop model in crowd interactions. Agents act by their response functions to observations and external forces, while observations change by the aggregated actions of all agents, weighted by their respective influence, i.e. power or wealth. Agents wealth dynamically adjust based on the alignment between an agents actions and observation outcomes: agents gain wealth when their actions align with observed trends and lose wealth otherwise. A reward function, that describes the change of agents wealth at each time step, manifests the differences of response functions of agents to observations. When all agents responses are set to zero and feedback loop is broken, agents wealth follow a normal or lognormal distribution. Otherwise, this response-reward iterative feedback mechanism results in concentrated wealth distributions, characterized by a small number of dominant agents and the marginalization of the majority. Contrasted to past studies, such concentration is not limited only to asymptotic behavior at the upper tail for large variables, nor does it require the reward function to be linear to agents previous wealth as formulated in random growth model and network preferential attachment. Probability density functions for various distributions are more visually distinguishable for small values at the lower tail. In application of this model, key differences in income and wealth distributions in the US vs Japan are attributed to different response functions of agents in the two countries. The model applicability extends beyond social systems to other many-body systems with analogous feedback mechanisms, where power-law distributions represent a rare subset of general concentrated outcomes.

econ.GN↗

arXiv2016

A Model of Synchronization for Self-Organized Crowding Behavior

This paper proposes a general model for synchronized crowding behavior. An order parameter is introduced to quantify the level of synchronization which is shown a function of percentage of agents in reactive state. Further, synchronization is shown to be driven by the most active agents with the highest volatility. A tipping point is identified when crowd becomes self-amplifying and unstable. By applying this model, financial bubbles, market momentum and volatility patterns are simulated.

q-fin.GN↗