In this paper, we study the online collaborative content caching problem from network economics point of view. The network consists of small cell base stations (SCBSs) with limited cache capacity and a macrocell base station (MCBS). SCBSs are connected with their neighboring SCBSs through high-speed links and collaboratively decide what data to cache. Contents are placed at the SCBSs "free of charge" at off-peak hours and updated during the day according to the content demands by considering the network usage cost. We first model the caching optimization as a finite horizon Markov Decision Process that incorporates an auto-regressive model to forecast the evolution of the content demands. The problem is NP-hard and the optimal solution can be found only for a small number of base stations and contents. To allow derivation of close to optimal solutions for larger networks, we propose the rolling horizon method, which approximates future network usage cost by considering a small decision horizon. The results show that the rolling horizon approach outperforms comparison schemes significantly. Finally, we examine two simplifications of the problem to accelerate the speed of the solution: (a) we restrict the number of content replicas in the network and (b) we limit the allowed content replacements. The results show that the rolling horizon scheme can reduce the communication cost by over 84% compared to that of running Least Recently Used (LRU) updates on offline schemes. The results also shed light on the tradeoff between the efficiency of the caching policy and the time needed to run the online algorithm.