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Unformatted text preview: • On these lager two, we know quite a bit – Upper bounds independent of graph G, dependent on broad proper0es of f and g – Lower bounds achieved by speciﬁc graphs G, dependent on broad proper0es of f and g Price of Anarchy • Fix the game <G,f,g,K_R,K_B>; then PoA for this game is •
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• MSW/worst NE payoﬀ where MSW is the maximum number of eventual infec0ons with budget K_R+K_B, and worst NE payoﬀ is the smallest sum of payoﬀs at Nash equilibrium Compares (non
compe00ve) max social welfare solu0on to Nash Mainly interes0ng under par0al adop0on Our upper bounds will hold for any G, lower bounds for speciﬁc G Both depend on proper0es of f and g Price of Budgets • Fix the game <G,f,g,K_R,K_B> with K_R >= K_B; then PoB for this game is •
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• max { [payoﬀ(R)/payoﬀ(B)]/[K_R/K_B] where payoﬀ(R) is the eventual number of infec0ons for R, and the max is taken over all Nash equilibria for the game E.g. if K_R/K_B = 3 but payoﬀ(R)/payoﬀ(B) = 30 in worst NE, PoB = 10 Measures extent to which network dynamics amplify budget inequality Our upper bounds will hold for any G, lower bounds for speciﬁc G Both depend on proper0es of f and g Summary of Results: PoA g linear g polarizing g equalizing f concave PoA < constant for any graph G * PoA some0mes bounded f convex Exist G with unbounded PoA (even for slight convexity); • Threshold result for the speciﬁc family f(x) = x^r, g linear: r...
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This document was uploaded on 02/03/2014.
 Spring '14

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