We define the notion of social rumor in a standard game-theoretic framework, and assume each agent in the rumor game with individual rationality. In this framework, individual agent can interact with its neighboring agents, and word-of-mouth communication is employed during interaction. We introduce a simple and natural strategy-select rule, called behavior update rule (BUR). The BUR uses an accumulative influence force (CIF) with considering the authority influence of neighboring agents rather than simple accumulative number of information from neighboring agents. The BUR can provide rules to restrict agents’ behavior to one particular strategy and lead to emergence of social rumor or anti-rumor. Most importantly, we give simple natural rules of rumor and anti-rumor information transmission, and investigate the efficiency with which social rumors and anti-rumors (agent claims that rumor information is false or doesn’t exist) are achieved.