In this paper, distributed iterative algorithms for consensus problems are considered for multiagent networks. Each agent randomly contacts with other agents at each instant and receives corrupted information due to the noisy channel from its neighborhood. Neighbors of each agent are cooperative or competitive, i.e., the elements in the adjacent weight matrix may be positive or negative. In such a framework, asymptotic consensus and mean square consensus problems are investigated, based on random graph theory and stochastic stability theory. The control gains have been designed such that cooperation-competition random multiagent networks can reach almost sure consensus and mean square consensus. Simulation examples are finally given to illustrate the effectiveness of the obtained results.