By Ron Lavi
This e-book constitutes the refereed lawsuits of the seventh foreign Symposium on Algorithmic video game concept, SAGT 2014, held in Haifa, Israel, in October 2014. The 24 complete papers and five brief papers provided have been conscientiously reviewed and chosen from sixty five submissions. They hide numerous vital features of algorithmic online game concept, resembling matching thought, video game dynamics, video games of coordination, networks and social selection, markets and auctions, expense of anarchy, computational facets of video games, mechanism layout and auctions.
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Additional resources for Algorithmic Game Theory: 7th International Symposium, SAGT 2014, Haifa, Israel, September 30 – October 2, 2014. Proceedings
This concludes the proof of the theorem. 3 A Polyhedral Characterization In this section we provide a polyhedral description for SMG, that is an analogue of the well studied stable marriage polytope, ﬁrst introduced in . It is well known that the latter polytope is integral, meaning that the optimization version of SM can be solved in polynomial time. For our setting, we show that our polytope can be used to eﬃciently decide the feasibility of an SMG instance with asymmetric preferences, thus giving an alternative proof of Theorem 2.
The preferences are deﬁned cyclically (A over B, B over C, and C over A) and are complete total orders over the corresponding sets. A triple (a, b, c) is blocking with respect to a 3D matching M if (a, b, c) ∈ / M, b a M(a), c b M(b) and a c M(c). Note that if (a, b, c) is a blocking triple then a, b and c must be part of three disjoint 30 L. Farczadi, K. Georgiou, and J. K¨ onemann triples in M. A 3D matching M is stable if it has no blocking pairs. It follows from this deﬁnition that any stable 3D matching must be a perfect matching.
It follows from Lemma 1 that N is a perfect matching and every man is matched to an acceptable woman. To see that there are no blocking pairs, consider any pair (b, c) ∈ / N such that (b, c) is an acceptable pair, that is b ∈ P (c) and c ∈ P (b). Assume now that in I man b strictly prefers c to N (b). Since c ∈ P (b) it follows that b also strictly prefers c to N (b) in J . Hence, since N is a stable matching for J , we must have (N (c), b) ∈ Rc . From the way we deﬁned Rc this implies that N (c) is acceptable to c, and c prefers N (c) at least as much as b in I.