The security community has witnessed a significant increase in the number of different types of security threats. This situation calls for the design of new techniques that can be incorporated into security protocols to meet these challenges successfully. An important tool for developing new security protocols as well as estimating their effectiveness is game theory. This game theory framework usually involves two players or agents: 1) a protector and 2) an adversary, and two patterns of agent behavior are considered: 1) selfish behavior, where each of the agents wants to maximize his payoff; and 2) leader and follower behavior, where one agent (the leader) expects that the other agent (the follower) will respond to the leader's strategy. Such an approach assumes that the agents agree on which strategy to apply in advance. In this paper, this strong assumption is relaxed. Namely, the following question is considered: what happens if it is unknown a priori what pattern of behavior the adversary is going to use, or in other words, it is not known, what game he intends to play? Using a simple game-theoretic model, it is shown that the protector can lose if he does not take into account the possibility that the adversary can play a game other than the one the protector has in mind. Further considered is a repeated game in which the protector can learn about the presence of an adversary, and the behavior of belief probabilities is analyzed in this setting.