# Theory of agent-based market models with controlled levels of greed and anxiety

## TL;DR

This paper develops a theoretical framework using generating functional analysis to study agent-based market models that incorporate controlled levels of greed and anxiety, revealing complex phase transitions and remanence effects.

## Contribution

It introduces a generalized analytical approach to minority-game type models with psychology-influenced strategy updates, capturing market dynamics with trend following and contrarian behaviors.

## Key findings

- Effective bid process exhibits remanence effects.
- Phase transitions depend on agents' psychological parameters.
- Some models allow direct solution, others require approximations.

## Abstract

We use generating functional analysis to study minority-game type market models with generalized strategy valuation updates that control the psychology of agents' actions. The agents' choice between trend following and contrarian trading, and their vigor in each, depends on the overall state of the market. Even in `fake history' models, the theory now involves an effective overall bid process (coupled to the effective agent process) which can exhibit profound remanence effects and new phase transitions. For some models the bid process can be solved directly, others require Maxwell-construction type approximations.