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Mar 18, 2012 at 21:58 comment added Ariel Rubinstein Thanks. We do need the result for small values as well (and not just for large numbers). Note that for general |A| and |B| (not for the case that |A|=|B|) we need the condition that $2>$1: Consider the case that the transfer between a member of A and a member of B (which is now $1) is very very high then if |A|>|B|, the probability of a member of B to win will be larger (the transfers inside B will be negligible).
Mar 18, 2012 at 18:48 history answered Ori Gurel-Gurevich CC BY-SA 3.0