This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 18-02-2016, available online: http://www.tandfonline.com/10.1080/02331934.2016.1147035. ; We investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games. ; Peer Reviewed ; Postprint (author's final draft)


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