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lines changed Original file line number Diff line number Diff line change @@ -419,7 +419,7 @@ Least Core values
419419^^^^^^^^^^^^^^^^^
420420
421421Unfortunately, for many cooperative games the Core may be empty.
422- By relaxing the coalitional rationality property by $e \g t 0$,
422+ By relaxing the coalitional rationality property by a subsidy $e \g t 0$,
423423we are then able to find approximate payoffs:
424424
425425$$
@@ -471,14 +471,15 @@ The simplest approximation consists of two relaxations of the Least Core
471471
472472- Using a fraction of all subsets instead of all possible subsets.
473473
474- Combined, this gives us the following property:
474+ Combined, this gives us the $(\e psilon, \d elta)$-*probably approx-
475+ imate least core * that satisfies the following property:
475476
476477$$
477478P_{S\s im D}\l eft[\s um_{x_i\i n S} v_u(x_i) + e^{*} + \e psilon \g eq u(S)\r ight]
478479\g eq 1 - \d elta
479480$$
480481
481- Where $e^{*}$ is the optimal least core value .
482+ Where $e^{*}$ is the optimal least core subsidy .
482483
483484With these relaxations, we obtain a polynomial running time.
484485
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