On the meaning of player weights in the weighted Shapley value

Á. de Prado Saborido, M. Á. Mirás Calvo, E. Sánchez Rodríguez

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.

Keywords: symmetric players, clones, dual-clones, Shapley value, replication

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