The concurrent growth of on-line communities exhibiting large-scale social structure, and of large decentralized peer-to-peer file-sharing systems, has stimulated new interest in understanding networks of interacting agents as economic systems. Here we formulate a model for query incentive networks, motivated by such systems: users seeking information or services can pose queries, together with incentives for answering them, that are propagated along paths in a network. This type of information-seeking process can be formulated as a game among the nodes in the network, and this game has a natural Nash equilibrium. In such systems, it is a fundamental question to understand how much incentive is needed in order for a node to achieve a reasonable probability of obtaining an answer to a query from the network. We study the size of query incentives as a function both of the rarity of the answer and the structure of the underlying network. This leads to natural questions related to strate...