By Ron Lavi

This ebook constitutes the refereed court cases of the seventh overseas Symposium on Algorithmic online game concept, SAGT 2014, held in Haifa, Israel, in October 2014. The 24 complete papers and five brief papers provided have been rigorously reviewed and chosen from sixty five submissions. They conceal numerous very important facets of algorithmic online game concept, corresponding to matching conception, online game dynamics, video games of coordination, networks and social selection, markets and auctions, cost of anarchy, computational elements of video games, mechanism layout and auctions.

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Extra info for Algorithmic Game Theory: 7th International Symposium, SAGT 2014, Haifa, Israel, September 30 – October 2, 2014. Proceedings

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Also, Rt is the partial matching constructed by RSD after t steps, and ν (Rt ) be its welfare. For an agent a let Oa ∈ I be the item to which a is matched in O. , { a ∈ At | va (Oa ) = 1}. Therefore |Y t | = ν (Ot ) for every t. It can happen that at time t, an agent does not 1-value any of remaining items I t , even though he could have 1-valued some of the items in I 0 . Thus let Z t ⊆ At be the agents who 0-value all items in I t . Let us denote y t = |Y t | and z t = |Z t | for brevity. Consider step t + 1 of RSD, and assume we have all information available after first t steps, represented by Ht .

Then P (I) = ∅ if and only if I admits a stable matching. Furthermore any fractional point x ∈ P (I) can be efficiently rounded to a stable matching solution for I. Proof. The first direction is trivial since if I admits a stable matching then the incidence vector corresponding to this stable matching is clearly in P . Now assume P = ∅ and let x be any point in P . We will show how to efficiently round x to a stable matching, thus completing the proof of the theorem. For each b ∈ B let f (b) be b’s most preferred woman in the set {c ∈ C : xbc > 0}.

11]. Fact 1 Consider the following instance of a problem. , n}. Define the valuations: va (i) = 1 if a = i ∈ {1, . . , k} or a ∈ 1, . . , k2 ∧ i ∈ k2 , . . , k , and 0 otherwise. The optimum solution in this case is obviously k. 28. Taking different values of k or z did not significantly changed the outcome of simulations. 5 Normalized Von Neumann-Morgenstern Preferences and RSD Theorem 3 Random Serial Dictatorship always returns an assignment in which 2 in one-sided matching problems with the expected social welfare is at least 1e ν(O) n normalized von Neumann- Morgenstern preferences, where ν (O) is the maximum social welfare.

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