Dynamic order allocation in a duopoly hybrid workforce of competition: A machine learning approach

Xinyu Wang, Yuxing Zhang and Shuhua Zhang

European Journal of Operational Research, 2024, vol. 315, issue 2, 668-690

Abstract: We develop a continuous-time stochastic differential game model that aims to capture market demand and stochastic cross-network effects, and we seek to find equilibrium order allocation strategies between the firm and the platform. By solving the Hamilton–Jacobi–Bellman (HJB) partial differential equation system, we obtain the feedback equilibrium. For a simple scenario, we derive the analytical solution which indicates that the equilibrium expenditures depend only on the marginal market thickness, and that market thickness is consistently advantageous for the value function. For the complex scenario, we propose a machine learning approach based on the Deep Galerkin Method to solve high-dimensional nonlinear HJB systems, and we demonstrate its good convergence properties. Based on reliable parameter values, our simulation results show that: (1) For higher market thickness, value functions exhibit greater sensitivity to changes in cross-network effects. (2) For a given cross-network effect, the equilibrium acquisition and retention expenditures display significant sensitivity to market thickness and time, respectively. To show the interaction between the two platforms, we present the following two results. One is that for the platform adopting a high pricing strategy, its acquisition expenditures exceed those of its competitor, while retention expenditures are the opposite. The other is that as the cross-network effect of the platform increases, its maximum profit initially rises and then declines, and the time of occurrence of the maximum profit monotonically decreases. In contrast, the competitor’s maximum profit initially declines and then rises, and the time of occurrence of the maximum profit monotonically increases.

Keywords: Machine learning; Market thickness; Hybrid workforce; Dynamic duopoly; Stochastic differential game (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221723009761
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:315:y:2024:i:2:p:668-690

DOI: 10.1016/j.ejor.2023.12.026

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().