This paper considers a communication network characterized by an endogenous architecture and an imperfect transmission of information as in Bala and Goyal (2000). We propose a similar network's model with the difference that it is characterized by an endogenous rate of information decay. Endogenous decay is modelled as dependent on the result of a coordination game, played by every pair of directly linked agents and characterized by 2 equilibria: one efficient and the other risk dominant. Differently from other models, where the network represents only a channel to obtain information or to play a game, in our paper the network has an intrinsic value that depends on the chosen action in the coordination game by each participant. Moreover the endogenous network structure affects the play in the coordination game as well as the latter affects the network structure. The model has a multiplicity of equilibria and we produce a full characterization of those are stochastically stable. For sufficiently low link costs we find that in stochastically stable states network structure is ever efficient; individuals can be coordinated on efficient as well as on risk dominant action depending on the decay difference among the two equilibria in the single coordination game. For high link costs stochastically stable states can display networks that are not efficient; individuals are never coordinated on the efficient action.