# Dynamic complexity of Stackelberg-Bertrand game with one-way R&D spillovers, effective information and government subsidies

## TL;DR

This paper studies how R&D spillovers, information, and subsidies affect market stability in a competitive economic model.

## Contribution

The study introduces one-way R&D spillovers and effective information into a Stackelberg-Bertrand model with government subsidies.

## Key findings

- Improved information and subsidies help stabilize equilibrium prices.
- Product homogeneity can cause price volatility, while differentiation boosts leader profits.
- Moderate R&D spillovers stabilize prices and benefit enterprise clusters.

## Abstract

The phenomena of bounded rationality, asymmetric information, research and development (R&D) spillovers represent ubiquitous characteristics in economic systems, yet research simultaneously investigating R&D spillovers and information asymmetry within a bounded rationality framework remains scarce. This study innovatively incorporates one-way R&D spillovers, effective information, and government R&D subsidies into a dynamical two-stage Stackelberg-Bertrand model. Through application of Jury criterion, we systematically analyze the stability characteristics of all equilibrium points, derive stability conditions and stable regions, and investigate the complex dynamics of this discrete system. The principal findings reveal that: (1) Enhanced effective information for the R&D leader and increased government R&D subsidies exhibit stabilizing effects on equilibrium prices; (2) Excessive product homogeneity may induce substantial price volatility or chaotic dynamics, whereas greater product differentiation enhances profitability for the leader; (3) Moderate levels of R&D spillovers contribute to price stabilization, and while partially reducing leading firms’ profits, they generate positive externalities for enterprise cluster development. This research provides significant theoretical insights and practical implications for innovation strategies and differentiated product development in oligopolistic markets.