The Shapley value is one way to distribute the total gains to the players, assuming that they all collaborate.
This means that there must be gains to distribute for anyone to get nonzero credit from that game, and that they in fact “collaborated” (although this could be in name only) to get any credit at all. Ignoring multiverses, infinitely many things have not been invented yet, but maybe infinitely many things will be invented in the future. In general, I don’t think that Leibniz cooperated in infinitely many games, or even that infinitely many games have been played so far, unless you define games with lots of overlap and double counting (or you invoke multiverses, or consider infinitely long futures, or some exotic possibilities, and then infinite credit doesn’t seem unreasonable).
Furthermore, in all but a small number of games, he might make no difference to each coalition even when he cooperates, so get no credit at all. Or the credit could decrease fast enough to have a finite sum, even if he got nonzero credit in infinitely many games, as it becomes vanishingly unlikely that he would have made any difference even in worlds where he cooperates.
The Wikipedia page says:
This means that there must be gains to distribute for anyone to get nonzero credit from that game, and that they in fact “collaborated” (although this could be in name only) to get any credit at all. Ignoring multiverses, infinitely many things have not been invented yet, but maybe infinitely many things will be invented in the future. In general, I don’t think that Leibniz cooperated in infinitely many games, or even that infinitely many games have been played so far, unless you define games with lots of overlap and double counting (or you invoke multiverses, or consider infinitely long futures, or some exotic possibilities, and then infinite credit doesn’t seem unreasonable).
Furthermore, in all but a small number of games, he might make no difference to each coalition even when he cooperates, so get no credit at all. Or the credit could decrease fast enough to have a finite sum, even if he got nonzero credit in infinitely many games, as it becomes vanishingly unlikely that he would have made any difference even in worlds where he cooperates.