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We study situations in which autonomous systems (ASes) may have incentives to send BGP announcements differing from the AS-level paths that packets traverse in the data plane. Prior work on this issue assumed that ASes seek only to obtain the best possible outgoing path for their traffic. In reality, other factors can influence a rational AS's behavior. Here we consider a more natural model, in which an AS is also interested in attracting incoming traffic (e.g., because other ASes pay it to carry their traffic). We ask what combinations of BGP enhancements and restrictions on routing policies can ensure that ASes have no incentive to lie about their data-plane paths. We find that protocols like S-BGP alone are insufficient, but that S-BGP does suffice if coupled with additional (quite unrealistic) restrictions on routing policies. Our game-theoretic analysis illustrates the high cost of ensuring that the ASes honestly announce data-plane paths in their BGP path announcements.