By Krzysztof R. Apt, Sunil Simon (auth.), Maria Serna (eds.)
This booklet constitutes the refereed court cases of the fifth overseas Symposium on Algorithmic video game idea, SAGT 2012, held in Barcelona, Spain, in October 2012. The 22 revised complete papers awarded including 2 invited lectures have been rigorously reviewed and chosen from sixty five submissions. The papers current unique examine on the intersection of Algorithms and video game concept and tackle a number of present issues comparable to answer options in online game concept; potency of equilibria and cost of anarchy; complexity sessions in video game conception; computational elements of equilibria; computational features of fixed-point theorems; repeated video games; evolution and studying in video games; convergence of dynamics; coalitions, coordination and collective motion; recognition, suggestion and belief structures; graph-theoretic elements of social networks; community video games; cost-sharing algorithms and research; computing with incentives; algorithmic mechanism layout; computational social selection; selection conception, and pricing; public sale algorithms and research; monetary facets of disbursed computing; web economics and computational advertising.
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Extra info for Algorithmic Game Theory: 5th International Symposium, SAGT 2012, Barcelona, Spain, October 22-23, 2012. Proceedings
86–87 (2003) 4. : The Evolution of Cooperation. Basic Books (1984) 5. : 2. The Handbook of Experimental Economics. In: Public Goods: A Survey of Experimental Research, pp. 111–194. Princeton University Press (1995) 6. : Slightly altruistic equilibria in normal form games. pdf 7. : The Impact of Altruism on the Eﬃciency of Atomic Congestion Games. , Rauschmayer, A. ) TGC 2010, LNCS, vol. 6084, pp. 172–188. Springer, Heidelberg (2010) 8. : The Robust Price of Anarchy of Altruistic Games. , Koutsoupias, E.
LNCS, vol. 5385, pp. 402–413. Springer, Heidelberg (2008) 14. : Setting Lower Bounds on Truthfulness. In: Proc. of 18th SODA, pp. 1143–1152 (2007) 15. : Algorithmic Mechanism Design. Games and Economic Behavior 35, 166–196 (2001) 16. : Algorithmic Game Theory. Cambridge University Press (2007) 17. : Counterspeculations, auctions and competitive sealed tenders. Journal of Finance 16, 8–37 (1961) 18. : Truthful mechanisms for two-range-values variant of unrelated scheduling. O. cy Abstract. We revisit the complexity of deciding, given a (ﬁnite) strategic game, whether Nash equilibria with certain natural properties exist; such decision problems are well-known to be N P-complete [2, 6, 10].
Lemma 5. In a Nash equilibrium σ ∈ N E(SG) \ N E(SG), σ1 (L) · σ2 (L) > 0. Next, we prove that in a Nash equilibrium σ ∈ N E(SG)\N E(SG), the two special players play each pair of literals and with the same positive probability. Lemma 6. In a Nash equilibrium σ ∈ N E(SG) \ N E(SG), it holds that σi ( ) + σi ( ) = σi (L)/n > 0 for any i ∈  and for any ∈ L. Next, we prove that in a Nash equilibrium σ ∈ N E(SG) \ N E(SG), all the nonspecial players adopt δ as a pure strategy. Lemma 7. In a Nash equilibrium σ ∈ N E(SG)\N E(SG), it holds that σi (δ) = 1 for each player i ∈ [r] \ .
Algorithmic Game Theory: 5th International Symposium, SAGT 2012, Barcelona, Spain, October 22-23, 2012. Proceedings by Krzysztof R. Apt, Sunil Simon (auth.), Maria Serna (eds.)