The Gravity Model Analysis

Gravity model is a theory hypothesis proposed by geologist, sociologists and economists to explain and forecast peoples’ interactions in economy, society and polity, which is established by using classical mechanics of Newton’s universal gravitation law. J.Q.Stewart (1941) was inspired from the law, first proposed the Gravity model in economics, which was considered the bridge connecting physics and economics. The gravity model was first applied in an analysis of international flows of commodities by Tinbergen (1962). Pöyhönen (1963) and Linnemann (1966) also joined the precursor group. Gravity models have been widely applied to economic trade analysis due to their high explanatory power (Cinar et al., 2016; Cullinan, Duggan, 2016). Distance

Because the essence of NIIP’s adoption is that there exists an innovation gravitational field which likes a giant “magnetic field”, emitting magnetic force to attract agents via “magnetic induction lines”. The line linked two agents can be considered as “magnetic induction lines”. According to the fact of NIIP’s adoption, due to the shortage of cognitive experience, when faced with NIIP, consumers would like to seek advice from people around, especially the adopters. The non-adopter will be “magnetized” as it receives advises from adopters. When a non-adopter becomes an adopter, it forms a new gravitational field, influencing other agents. Because of the superposition of gravitational field, the potential energy of an agent is also superposed. That means an agent will be influenced largely when the number of adopters around the agent increases. The additive potential energy reflects the influence of the network externalities on agent’s decision making. The NIIP becomes more valuable as the number of adopters increases and then more agents will adopt

Assume that John and Lily are WeChat friends and there are three comments made by John in Lily’s friend cycle while two comments made by Lily in John’s friend cycle. Moreover, both Lily and John have made a comment in Alice’s friend cycle once. Then, the interactional activities . Furthermore, assume that John (agent) totally takes participate in 20 activities and Lily (agent) joins in 30 activities, then and . As a consequence, for John (agent), the intimacy with Lily (agent ) is and for Lily (agent), the intimacy with John (agent ) is.

For agent, the link-depth with agent refers to the link-depth from agent to agent defined as: （9）

3.3.5 The additive gravitational potential energy of agent .

According to the Gravity model, introduced the formula of link-depth into formula (10), the potential energy of agent influenced by agent on decision making can be defined as: （10）

Considering the superposition of gravitational field, when there are adopters connected with agent , the additive potential energy of agent can be rewritten as: (11)

Where，is the diffusion ability of adopter ; refers to NIIP’s characteristics diffused by adopter ; is the link-depth from adopter to agent