An Agent-based Model for Competitive Agents

Continuous-time Markov chains have been employed for decades to model a broad spectrum of stochastic systems, including queuing systems (e.g., [3]) and financial markets (e.g., [5, 7]). These models often represent agent behavior in interactive environments, where local and global interaction rules are used to simulate various physical processes (e.g., see [2, 6, 4] for examples). A key question in the analysis of these models is how to derive the transient or stationary probability distributions that capture the system's evolving dynamics or long-term behavior. In this paper, we develope a straightforward stochastic agent-based model for the analysis of agents displaying competitive behavior, striving to survive within a competitive environment. This model has applications across applied finance and social science (see [1]). For instance, in financial markets, firms compete to attract more customers and clients; job market participants frequently switch employers to better fulfill their financial needs; governments work to strengthen their economies, and so forth. In the subsequent section, we begin with a microscopic model where numerous groups or agents exist, each containing a finite number of subagents.