By Piotr Skowron, Lan Yu, Piotr Faliszewski, Edith Elkind (auth.), Berthold Vöcking (eds.)

This booklet constitutes the court cases of the sixth overseas Symposium on Algorithmic online game idea, SAGT 2013, held in Aachen, Germany, in October 2013. The 25 papers provided during this quantity have been conscientiously reviewed and chosen from sixty five submissions. They hide a variety of vital features of algorithmic video game idea, akin to resolution suggestions in online game conception, potency of equilibria and the cost of anarchy, computational features of equilibria and online game theoretical measures, repeated video games and convergence of dynamics, evolution and studying in video games, coordination and collective motion, community video games and graph-theoretic features of social networks, balloting and social selection, in addition to algorithmic mechanism design.

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Additional resources for Algorithmic Game Theory: 6th International Symposium, SAGT 2013, Aachen, Germany, October 21-23, 2013. Proceedings

Example text

Lemma 5. t. cj , with T 1 = ∅. Suppose that b = a is a Nash equilibrium such that cj = f (b) and T is the set of all threshold candidates in b. Then the set of candidates who have s points in b is {cj } ∪ T 1 . Lemma 6. Under the same assumptions as in Lemma 5, (a) sc(c , b) ≤ s − 1 ∀c ∈ K 1 , (b) sc(c , b) ≤ s − 2 ∀c ∈ K 2 . As in the previous case, in analogy to the sets U 1 , U 2 , U 3 , here we need the sets: ck and cj c }, W 2 = {c ∈ C : n = W 1 = {c ∈ C : n = s, ∀ck ∈ T 1 c s, c cj }. Theorem 6.

5 (more often referred to as Copeland), Dom(c) is generally no more an NE, and we do now know whether the existence of an NE is guaranteed or not. Proposition 8. For UC, with any number of candidates, and an odd number of voters, there is always an NE. Proof. , the highest-priority candidate in U C(P ). Consider (again) Dom(c) = {c} ∪ {y|c →P y}. We claim that Dom(c) is an NE. Since c is a Condorcet winner in the restriction of P to Dom(c), and a fortiori, in the restriction of P to any subset of Dom(c), it is the UC winner in Dom(c) and in any of its subsets, and no candidate in Dom(c) wants to leave.

Xm }. Let X = X ∪ {xm+1 }, P the profile obtained from P by adding xm+1 at the bottom of every vote, and P X be the candidate profile obtained by adding xm+1 at the bottom of every ranking of a candidate xi , i ≤ m, and whatever ranking for xm+1 . Let Y ⊆ X. Because Y is not an NE for Γ , some candidate xi ∈ X has an interest to leave or to join, therefore Y is not an NE either for Γ . Now, consider Y = Y ∪ {xm+1 }. , join) Y , therefore Y is not an NE. 8 For instance, we may have two profiles P , P both corresponding to G4 , such that r(P ) = a and r(P ) = b; the proof perfectly works in such a case.

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