Download Algorithmic Game Theory: 9th International Symposium, SAGT by Martin Gairing, Rahul Savani PDF

By Martin Gairing, Rahul Savani

This e-book constitutes the refereed court cases of the ninth overseas Symposium on Algorithmic video game concept, SAGT 2016, held in Liverpool, united kingdom, in September 2016.The 26 complete papers provided including 2 one-page abstracts have been rigorously reviewed and chosen from sixty two submissions.
The authorised submissions conceal numerous vital aspectsof algorithmic online game concept reminiscent of computational features of video games, congestion video games and networks, matching and vote casting, auctions and markets, and mechanism design.

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Extra resources for Algorithmic Game Theory: 9th International Symposium, SAGT 2016, Liverpool, UK, September 19–21, 2016, Proceedings

Example text

Since by Claim 1, there can be no more than two vertices of Yj ∪ Nj that are in Lc for every j, therefore, by maximality of j0 we get |Lc | ≤ |X| + 2j0 = 2(n + j0 ). In particular, observe that if |Lc | = 2(n + j0 ) then X ⊆ Lc and for every 1 ≤ j ≤ j0 there are exactly two vertices in Yj ∪Nj with colour c. So, let us prove that |Lc | = 2(n+j0 ), that will prove the claim. By the choice of j0 , there is some 1 ≤ t ≤ 3 such that atj0 ∈ Lc or btj0 ∈ Lc . In particular, |Lc | ≥ min{|Atj0 |, |Bjt0 |} + 1 = 2(n + j0 ) − 2 or else, every vertex vjt0 ∈ Lc ∩ {atj0 , btj0 } would increase her payoff by choosing the colour of the vertices in her private group (that is a colour class by Claim 3), thus contradicting the hypothesis that we are in a Nash equilibrium.

Simple approximate equilibria in large games. In: Proceeding of EC, pp. 753–770 (2014) 4. : Approximating Nash equilibria and dense bipartite subgraphs via an approximate version of Caratheodory’s theorem. In: Proceeding of STOC 2015, pp. 361–369 (2015) 5. : New algorithms for approximate Nash equilibria in bimatrix games. Theor. Comput. Sci. 411(1), 164–173 (2010) 6. : Biased games. In: Proceeding of AAAI, pp. 609–615 (2014) 7. : Anchoring, activation, and the construction of values. Organ. Behav.

Computing a Nash equilibrium for coloring games is PTIME-hard. In order to prove Theorem 2, we will reduce from a variation of the wellknown Monotone Circuit Value problem, defined as follows. Problem 1 ( Monotone Circuit Value). Input: A boolean circuit C with m gates and n entries, a word w ∈ {0, 1}n such that: – the gates are either AND-gates or OR-gates; – every gate has exactly two entries (in-degree two); – a topological ordering of the gates is given, with the mth gate being the output gate.

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