Resumen de A glove-market partitioned matrix related to the assignment game

Marina Núñez Oliva , Carles Rafels Pallarola

• Shapley and Shubik (1972) de ne the assignment game as a cooperative model for a bilateral market with transferable utility, and prove the nonemptiness of the core. Given any assignment game we de ne another assignment game with the same set of agents in the following way: the joint pro t of a mixed-pair in the new game is the di erence between their minimum joint payo in the core of the initial market and the addition of their individual minimum core payo s. This related assignment game is proved to be exact and it is the unique exact assignment game with a core that is a translation of the core of the initial market. The vector of translation is the vector of minimum core payo s.

  After that, we ask whether other solutions to an assignment market can be obtained by translation of the same solution applied to its related exact assignment game. The question is armatively answered in the case of two other well-known solutions, the kernel and the nucleolus.