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Incentive auctions let several participants to cooperate for clearing a set of offers and requests, ensuring that each participant cannot do better than by inputting his true utility. This increases the social welfare by efficient allocations, and is proven to have similar outcomes as the tradition English Auctions. The desk-mates (stable matchings) problem comes from the need of placing students in pairs of two for working in projects or seating in two-seats desks. The stable marriages problem consists of finding matches of a man and a woman out of two sets of men, respectively women. Each of the persons in the previous two problems has a (hopefully stable) secret preference between every two possible partners. The participants want to find an allocation satisfying their secret preferences and without leaking any of these secret preferences, except for what a participant can infer from the identity of the partner/spouse that was recommended to her/him. We use a distributed weighted constraint satisfaction (DisWCSP) framework where the actual constraints are secrets that are not known by any agent. They are defined by a set of functions on some secret inputs from all agents. The solution is also kept secret and each agent learns just the result of applying an agreed function on the solution. The new framework is shown to improve the efficiency in modeling the aforementioned problems. We show how to extend our previous techniques to solve securely problems modeled with the new formalism, and exemplify with the two problems in the title.

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