Bargaining strength in three-person characteristic-function games with v(i)> 0 a reanalysis of Kahan and Rapoport (1977)

Kahan and Rapoport (1977) investigated the effects of guaranteed payoffs on bargaining in three-person cooperative games by systematically varying different sources of power: the power arising from the 1-person values, the power emerging from the pair coalitions as reflected by the quotas of the non-normalized game, and the grand coalition value. In the present paper it is suggested that one additionally take into account the assumption of strategic equivalence and that one analyze games with v(i)>0 in terms of the quotas of the zero-normalized game. Ostmann's (1984) rather sophisticated game theoretic framework, permitting the standardization of all three-person games, is introduced. A reanalysis of Kahan and Rapoport's data employing this perspective yields results which can be interpreted more easily than those of the original study. Moreover, they are consistent with the findings of almost all studies on 3-person characteristic-function games. It is argued that one could use the introduced analytical framework to investigate the range of empirical validity of the mathematical assumption of invariance under strategic equivalence.