The progressively ubiquitous connectivity in the present information systems pose newer challenges to security. The conventional security mechanisms have come a long way in securing the well-defined objectives of confidentiality, integrity, authenticity and availability. Nevertheless, with the growth in the system complexities and attack sophistication, providing security via traditional means are increasingly becoming unachievable. A novel theoretical perspective and an innovative approach are thus required for understanding security from a decision-making and strategic viewpoint. One of the analytical tools which may assist the researchers in designing security protocols for computer networks is game theory. The game-theoretic concept finds extensive applications in security at different levels, including the cyberspace and is generally categorized under security games. It can be utilized as a robust mathematical tool for modelling and analyzing contemporary security issues. Game theory offers a natural framework for capturing the defensive as well as adversarial interactions between the defenders and the attackers. Furthermore, defenders can attain a deep understanding of the potential attack threats and the strategies of attackers by equilibrium evaluation of the security games. In this paper, the concept of game theory has been presented, followed by game-theoretic applications in cybersecurity, including cryptography. Different types of games, particularly those focused on securing the cyberspace, have been analysed and varied game-theoretic methodologies including mechanism design theories have been outlined for offering a modern foundation of the science of cybersecurity.