The anticipation game framework is an extension of attack graphs based on game theory. It is used to anticipate and analyze intruder and administrator concurrent interactions with the network. Like attack-graph-based model checking, the goal of an anticipation game is to prove that a safety property holds. However using this kind of goal is tedious and error prone on large networks because it assumes that the analyst has prior and complete knowledge of critical network services. In this paper we address this issue by introducing a new kind of goal called "strategy objectives". Strategy objectives mixes logical constraints and numerical ones. Combining these two types allows to performs a new range of analysis. which is more usable for network security analysis purpose. In order to achieve these strategy objectives, we have extended the anticipation games framework with cost and reward. Additionally this extension allows us to take into account the financial dimension of attacks during the analysis. We prove that finding the optimal strategy is decidable and only requires linear space. Finally we show that anticipation games with strategy objectives can be used in practice even on large networks by evaluating the performance of our prototype.