Isomorphic transition from cooperative to defective versions of the prisoners dilemma and cournot duopoly

We show that games which are equivalent with respect to individual preferences can be nonequivalent with respect to cooperative gains. This phenomenon is present in games with strong competitive vs cooperative tension (social dilemmas, exemplified here by the prisoner's dilemma) as well as games of market concurrency with prospect for cartel creation (oligopolies, exemplified here by the Cournot duopoly). To make precise meaning of strategically equivalent games we introduce the notion of isomorphism of games. Cooperative gains are calculated as sums of payoffs of players.