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Table 2 Utility table of the second stage in the game for noisy networks

From: Community detection in networks: a game-theoretic framework

uvTruth-tellingNot Truth-telling
(a) When u,v are linked in the first stage.
Truth-telling1, 1g2(xu,xv),g1(xu,xv)
Not Truth-tellingg1(xu,xv),g2(xu,xv)0, 0
(b) When u,v are not linked in the first stage.
Truth-telling1, 1g4(xu,xv),g3(xu,xv)
Not Truth-tellingg3(xu,xv),g4(xu,xv)0, 0