Replication by cloned players in coalitional games

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

Given a coalitional game, clone players are a special type of symmetric players. A k-replica of a coalitional game is obtained from the original game by adding k-1 clones of each player. We focus on the class of balanced games and study in detail the core of the k-replica. Dirichlet distributions provide a flexible way to select allocations within the core of a game (with clones). We study the convergence under replication of solutions that are not invariant under replication, that is, our main results analyze if the aggregate value that the solution assigns to each group of clones in the k-replica of a game converges to the value assigned by a solution to the group representative in the initial game. In particular, we establish strong connections between the core-center solution, the Dutta-Ray solution, and the weighted coalitional Nash solution.

Keywords: Dutta-Ray solution, core-center solution, weighted coalitional Nash solution, Dirichlet values, clone players, convergence under replication

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