A glove-market partitioned matrix related to the assignment game
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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 dierence
between their minimum joint payo in the core of the initial market and the addition
of their individual minimum core payos. 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 payos.
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.