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The statement "The monotonicity of B means that ..." is not precise enough. (For example, the identity mapping, the mapping defined by B(V) = V for any V, is monotone, but iteration of it does not converge to the set of SPE payoff profiles.)
Other (minor) comments I typed yesterday but which disappeared:
(1 - delta)
max_x c^T x
min_x c^T x