On the meaning of player weights in the weighted Shapley value
We analyze in detail two refinements of symmetric players in coalitional games: clone and dual-clone players. We show that any coalitional game can be reconstructed from a subgame comprising one representative from each group of (dual-)clones. Moreover, the aggregate Shapley value of a group of (dual-)clones coincides with the payoff assigned by the weighted Shapley value (with player weights in proportion to the sizes of the groups of (dual-)clones) to their representative in the subgame. Extending the notion of replication, which is natural in several classes of problems, to arbitrary coalitional games, we define a property of solution invariance under replication and examine the strategic implications of replication under the Shapley value.
Palabras clave: symmetric players clones dual-clones Shapley value replication