J. Freixas Bosch, M. Pons Vallès
Boolean functions assign a binary output to any vector of binary components. Monotonic simple games are monotonic Boolean functions, components correspond to voters, coalitions are in one-to-one correspondence with binary vectors and the output indicates if the coalition is either winning or losing. Boolean functions extend to discrete functions in which several values for the variables and several values for the output are allowed. Such functions can be formalized to the so-called (j,k)-functions and we are mainly devoted to those that are monotonic. Still two subclasses deserve our attention: anonymous and threshold (j,k)-functions. We study their relationship and, remarkably, we find that the link between these two subclasses depends on j but not on k. As a consequence, the enumeration of anonymous (2,k)-functions is obtained, and it is given by a nice closed formula.
Palabras clave / Keywords: simple games, anonymous games, enumeration
Programado
Sesión V07 Teoría y Procesos de Decisión
1 de junio de 2018 16:00
Sala 6
