 Rather than using effectivity functions, each player \(i\) is associated with an equivalence relation \(\approx_i \subseteq W\times W\), whose induced partition represent the choices he or she can perform. These equivalence relations describe the exact set of choices that a group of players can perform and the originating models are referred to as consequentialist in the literature (see for instance Belnap, Perloff, &amp; Ming 2001).