Multinomial values, necessary and nullifyimg players

M. Domènech Blázquez, J. M. Giménez Pradales, M. A. Puente del Campo

We focus on multinomial values. They were introduced in reliability by Freixas and Puente with the name of ``multibinary probabilistic values''. Later on, Carreras and Puente extended them to all cooperative games and began to use the current term ``multinomial''.
The main characteristics of these values are: (1) each one of them is defined by n parameters (n being the number of players) and (2) the weighting coefficients of the value are generated in terms of these parameters. We attach to each parameter the meaning of tendency of each player to form coalitions.
Here we consider two special classes of players: necessary and nullifying players. Introducing new properties that propose reasonable payoffs for these players and considering some classical properties as linearity, null player property and null player exclusion property, we provide new axiomatic characterizations of each multinomial probabilistic value.

Keywords: cooperative game, multinomial probabilistic value.

Scheduled

Games theory
June 9, 2022  5:10 PM
A14

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