All assignment games with the same core have the same nucleolus

Universitat de Barcelona. Espai de Recerca en Economia, Working Papers in Economics 01/2004;
Source: RePEc

ABSTRACT There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyerseller exact representative.

Download full-text


Available from: Marina Nuñez, Feb 06, 2015
7 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this note we prove that the kernel of a bilateral assignment game is always included in the core. This solves an outstanding open problem for bilateral assignment games.
    International Journal of Games Theory 10/1998; 27(2):301-303. DOI:10.1007/s001820050073 · 0.58 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyer-seller exact games and satisfy the condition that each mixed-pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyer-seller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer-seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a “45o-lattice” by means of the core of an assignment game can now be answered.
    International Journal of Games Theory 05/2003; 31(3):423-436. DOI:10.1007/s001820300128 · 0.58 Impact Factor
  • Mathematics of Operations Research 11/1979; 4(4-4):303-338. DOI:10.1287/moor.4.4.303 · 1.31 Impact Factor
Show more