TrustBets: betting over an IOU network

We consider the problem of operating a gambling market where players pay with IOUs instead of cash, and where in general not everyone trusts everyone else. Players declare their degree of trust in other players---for example, Alice trusts Bob for up to ten dollars, and Bob trusts Carol up to twenty dollars. The system determines what bets are acceptable according to the trust network. For example, Carol may be able to place a bet where she is at risk of losing ten dollars to Alice, even if Alice doesn't trust Carol directly, because the IOU can be routed through Bob. We show that if agents can bet on n events with binary outcomes, the problem of determining whether a collection of bets is acceptable is NP-hard. In the special case when the trust network is a tree, the problem can be solved in polynomial time using a maximum flow algorithm.