compcontagion11

# R and the max is taken over all nash equilibria for

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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 •  •  •  •  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 •  •  •  •  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.

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