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Unconditional security is the key-feature of quantum cryptography, which makes it superior to any classical encryption scheme. Most research in this area focuses on analyzing the theoretical properties and performance of particular quantum key distribution protocols, but a rigorous analysis on the network level seems to be missing. We present a game-theoretic approach which gives simple and tight bounds to the risk of communication that any two peers in a quantum network have to take when communicating, even if quantum cryptography is used. This work is motivated by recent (IM)possibility results regarding unconditionally secure message transmission in arbitrary networks, which puts stringent constraints on the network topology. Hence, our model naturally accounts for a given graph topology (existing fibre-optic networks which are natural candidates for a roll-out of a quantum network), as well as measuring risk in terms of probability or the designers subjective understanding. As a by-product, our model gives optimal path selection strategies, and the optimal design of network topologies under given constraints (like geographic or monetary ones).