Abstract: In this paper, we provided a literature survey on the
artificial stock problem (ASM). The paper began by exploring the
complexity of the stock market and the needs for ASM. ASM
aims to investigate the link between individual behaviors (micro
level) and financial market dynamics (macro level). The variety of
patterns at the macro level is a function of the AFM complexity. The
financial market system is a complex system where the relationship
between the micro and macro level cannot be captured analytically.
Computational approaches, such as simulation, are expected to
comprehend this connection. Agent-based simulation is a simulation
technique commonly used to build AFMs. The paper proceeds by
discussing the components of the ASM. We consider the roles
of behavioral finance (BF) alongside the traditionally risk-averse
assumption in the construction of agent’s attributes. Also, the
influence of social networks in the developing of agents interactions is
addressed. Network topologies such as a small world, distance-based,
and scale-free networks may be utilized to outline economic
collaborations. In addition, the primary methods for developing
agents learning and adaptive abilities have been summarized.
These incorporated approach such as Genetic Algorithm, Genetic
Programming, Artificial neural network and Reinforcement Learning.
In addition, the most common statistical properties (the stylized facts)
of stock that are used for calibration and validation of ASM are
discussed. Besides, we have reviewed the major related previous
studies and categorize the utilized approaches as a part of these
studies. Finally, research directions and potential research questions
are argued. The research directions of ASM may focus on the macro
level by analyzing the market dynamic or on the micro level by
investigating the wealth distributions of the agents.
Abstract: A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.