Cybersecurity is among the highest priorities in industries, academia and governments. Cyber-threats information sharing among different organizations has the potential to maximize vulnerabilities discovery at a minimum cost. Cyberthreats information sharing has several advantages. First, it diminishes the chance that an attacker exploits the same vulnerability to launch multiple attacks in different organizations. Second, it reduces the likelihood an attacker can compromise an organization and collect data that will help him launch an attack on other organizations. Cyberspace has numerous interconnections and critical infrastructure owners are dependent on each other's service. This well-known problem of cyber interdependency is aggravated in a public cloud computing platform. The collaborative effort of organizations in developing a countermeasure for a cyber-breach reduces each firm's cost of investment in cyber defense.Despite its multiple advantages, there are costs and risks associated with cyber-threats information sharing. When a firm shares its vulnerabilities with others there is a risk that these vulnerabilities are leaked to the public (or to attackers) resulting in loss of reputation, market share and revenue. Therefore, in this strategic environment the firms committed to share cyberthreats information might not truthfully share information due to their own self-interests. Moreover, some firms acting selfishly may rationally limit their cybersecurity investment and rely on information shared by others to protect themselves. This can result in under investment in cybersecurity if all participants adopt the same strategy. This paper will use game theory to investigate when multiple self-interested firms can invest in vulnerability discovery and share their cyber-threat information. We will apply our algorithm to a public cloud computing platform as one of the fastest growing segments of the cyberspace.