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

This booklet constitutes the lawsuits of the sixth foreign Symposium on Algorithmic video game thought, 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 conceal a variety of very important features of algorithmic online game thought, reminiscent of resolution suggestions in video game idea, potency of equilibria and the cost of anarchy, computational points 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 elements of social networks, balloting and social selection, in addition to algorithmic mechanism design.

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

This publication constitutes the court cases of the sixth overseas Symposium on Algorithmic video 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 quite a few very important elements of algorithmic online game idea, comparable to resolution ideas in video game concept, potency of equilibria and the cost of anarchy, computational elements 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 elements of social networks, balloting and social selection, in addition to algorithmic mechanism layout.

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

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A dictionary of voting paradoxes. Journal of Economic Theory 48 (1989) 17. : Election results and a partial ordering for positional ordering. J. ) Collective Decision-Making: Social Choice and Political Economy, pp. 93–110. Kluwer (1996) Appendix: ILP Formulation Let S be the set of (2|X| ) states, and A(s) be the set of agents candidating in state s. Choice functions without NE. We introduce a binary variable wsi , indicating that agent i wins in state s. We add constraints enforcing that a winner in each state s is unique: ∀i ∈ X, ∀s ∈ S : ws,i ∈ {0, 1} ∀s ∈ S : i∈X ws,i = 1 ∀s ∈ S, ∀i ∈ X ∈ A(s) : ws,i = 0 (1) (2) (3) Now we denote by D(s) the set of possible deviations from state s (states where a single agent’s candidacy differs from s).

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. 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.

We then move on to strong Nash equilibria, where we obtain analogous characterizations. Finally, we also observe some relations between strong Nash equilibria and Condorcet winners, which demonstrate that this notion forms an even better refinement of stable profiles. 1 Introduction We study Plurality-based voting systems from a game-theoretic point of view. Voting mechanisms constitute a popular tool for preference aggregation and decision making in various contexts involving entities with possibly diverse preferences.

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