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

ISBN-10: 3642413919

ISBN-13: 9783642413919

ISBN-10: 3642413927

ISBN-13: 9783642413926

This ebook constitutes the court cases of the sixth foreign Symposium on Algorithmic video game conception, SAGT 2013, held in Aachen, Germany, in October 2013. The 25 papers offered during this quantity have been rigorously reviewed and chosen from sixty five submissions. They disguise a variety of very important points of algorithmic online game idea, akin to answer ideas in online game concept, potency of equilibria and the cost of anarchy, computational features of equilibria and video 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 facets of social networks, vote casting and social selection, in addition to algorithmic mechanism design.

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When they cannot change the outcome by a unilateral deviation. Such voters are referred to as truth-biased voters in [6]. This twist, which is the focus of our work, turns out to be quite powerful. For the Plurality rule, this was empirically evaluated in [11]. , models with truth-bias may have more predictive power than models without. However, there has thus far been no theoretical study on the properties of Nash equilibria with truth-bias. Further, the interaction between truth-bias and other equilibrium refinements such as the concept of strong Nash equilibrium has not yet been investigated.

In each state, there must be at least one deviation, otherwise this state is an NE: ∀s ∈ S, ∀t ∈ S : ∀s ∈ S : ds,t ∈ {0, 1} t∈D(s) ds,t ≥ 1 (4) (5) Now, we introduce constraints related to the preferences of the candidates. For this purpose, we introduce a binary variable pi,j,k , indicating that agent i prefers candidate j over candidate k. If there is indeed a deviation from s to t, the deviating agent must prefer the winner of the new state over the winner of the previous state: ∀s ∈ S, ∀t ∈ D(s), ∀i ∈ X, ∀j ∈ X : ws,i + wt,j + ds,t − pa(s,t),j,i ≤ 2 (6) Finally we ensure that the preferences are irreflexive and transitive10 , and respect the constraint of being self-supported: ∀i ∈ X, ∀j ∈ X : pi,j,j = 0 ∀a ∈ X, ∀i ∈ X∀j ∈ X, ∀k ∈ X : pa,i,j + pa,j,k − pa,i,k ≤ 1 ∀i ∈ X, ∀j ∈ X : 10 pi,i,j = 1 (7) (8) (9) Notice that this ILP does not necessarily contain complete preferences: the program only needs to check those preference relations that correspond to possible deviations.

Now, let z ∈ X \ Dom(c). Since z ∈ Dom(c), we have c →P z and hence, z →P c, as n is odd. Since x ∈ U C(P ), there must be y ∈ Dom(c) such that y →P z. This implies that x ∈ U C(P ↓Dom(c)∪{z} ), which, due to tie-breaking priority, yields that c is the UC winner in P ↓Dom(c)∪{z} . Thus, z has no incentive to join Dom(c). Note that the proofs of Propositions 7 and 8 also show that for Copeland0 and U C, there always exists an NE in which the winning candidate is the winner in the full profile (with all candidates present)9.

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Algorithmic Game Theory: 6th International Symposium, SAGT 2013, Aachen, Germany, October 21-23, 2013. Proceedings by Piotr Skowron, Lan Yu, Piotr Faliszewski, Edith Elkind (auth.), Berthold Vöcking (eds.)

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