Agent-based spin model for financial markets on complex networks: Emergence of two-phase phenomena

We study a microscopic model for financial markets on complex networks, motivated by the dynamics of agents and their structure of interaction. The model consists of interacting agents (spins) with local ferromagnetic coupling and global antiferromagnetic coupling. In order to incorporate more realistic situations, we also introduce an external field which changes in time. From numerical simulations, we find that the model shows two-phase phenomena. When the local ferromagnetic interaction is balanced with the global antiferromagnetic interaction, the resulting return distribution satisfies a power law having a single peak at zero values of return, which corresponds to the market equilibrium phase. On the other hand, if local ferromagnetic interaction is dominant, then the return distribution becomes double peaked at nonzero values of return, which characterizes the out-of-equilibrium phase. On random networks, the crossover between two phases comes from the competition between two different interactions. However, on scale-free networks, not only the competition between the different interactions but also the heterogeneity of underlying topology causes the two-phase phenomena. Possible relationships between the critical phenomena of spin system and the two-phase phenomena are discussed.

Figure 1

(Color online) (a) Time evolution of $R\left(t\right)$ on RN and (b) plot of $P\left(R\right)$ when $T=3.0$ (near $T_c^0$), $\alpha =4$, and $\sigma =2.5$. The solid line represents Eq. (5) with $\mu =1.5$. (c) Plot of $R\left(t\right)$ and (d) $P\left(R\right)$ for $T=0.5$, $\alpha =1$, and $\sigma =2.5$. (e) Segregation function for various $T$ when $f\left(t\right)=0$.

Figure 2

(Color online) Plot of $P\left(R\right)$ on SFN when $\sigma =2.5$ and $\gamma =3.5$ with (a) $\alpha =1$ and $T=1$, (b) $\alpha =4$ and $T=1$, and (c) $\alpha =4$ and $T=4$ which is relatively close to $T_c^0$ $(\approx 6)$. The solid line in (c) represents Eq. (5) with $\mu =1.9$.

Figure 3

Plot of $P\left(R\right)$ on SFN with $\sigma =2.5$, $\alpha =4$, and $\gamma =2.5$ when (a) $T=1$, and (b) $T=16$ which is close to $T_c^0$ ($\approx 25$ for $N={10}^4$).