We study the public goods game in the noisy case by considering the players with inhomogeneous activity teaching on a square lattice. It is shown that the introduction of the inhomogeneous activity of teaching of the players can remarkably promote co
operation. By investigating the effects of noise on cooperative behavior in detail, we find that the variation of cooperator density $rho_C$ with the noise parameter $kappa$ displays several different behaviors: $rho_C$ monotonically increases (decreases) with $kappa$; $rho_C$ firstly increases (decreases) with $kappa$ and then it decreases (increases) monotonically after reaching its maximum (minimum) value, which depends on the amount of the multiplication factor $r$, on whether the system is homogeneous or inhomogeneous, and on whether the adopted updating is synchronous or asynchronous. These results imply that the noise plays an important and nontrivial role in the evolution of cooperation.
We study the effects of inhomogeneous influence of individuals on collective phenomena. We focus analytically on a typical model of the majority rule, applied to the completely connected agents. Two types of individuals $A$ and $B$ with different inf
luence activity are introduced. The individuals $A$ and $B$ are distributed randomly with concentrations $ u$ and $1- u$ at the beginning and fixed further on. Our main result is that the location of the order-disorder transition is affected due to the introduction of the inhomogeneous influence. This result highlights the importance of inhomogeneous influence between different types of individuals during the process of opinion updating.
We propose an extended public goods interaction model to study the evolution of cooperation in heterogeneous population. The investors are arranged on the well known scale-free type network, the Barab{a}si-Albert model. Each investor is supposed to p
referentially distribute capital to pools in its portfolio based on the knowledge of pool sizes. The extent that investors prefer larger pools is determined by investment strategy denoted by a tunable parameter $alpha$, with larger $alpha$ corresponding to more preference to larger pools. As comparison, we also study this interaction model on square lattice, and find that the heterogeneity contacts favors cooperation. Additionally, the influence of local topology to the game dynamics under different $alpha$ strategies are discussed. It is found that the system with smaller $alpha$ strategy can perform comparatively better than the larger $alpha$ ones.
