Value Theory without Symmetry

Ori Haimanko

We investigate the non-symmetric values of finite games on a given, possibly finite, univrse of players. It turns out that in the case of values symmetric with respect to some coalitional structure with infinite elements (types), the axioms are powerful enough to force such a value to be a mixture of the random arrival values (or path value in the sense of [Owen(1973)], with identically distributed random arrival times of players inside the same type. The general non-symmetric values are shown to be the random order values (as in[Weber(1988)] for a finite univrse). The non-symmetric semivalues and those symmetric with respect to a coalitional structure with large types are also completely characterized.

March, 1998
Published in: 
International Journal of Game Theory 29 (2000), 451-468.