Two-Player Games as Local, Discontinuous Solutions in a Global, Continuous Transfer Space

The transfer space is a biochemical model of enzymatic cooperation and complementation. A substrate is transferred from a source to a sink; together they form an ensemble, a unity of two. Benefit (b) and cost (c) of this substrate are two sides of the same coin but their size and size relation are decided by local conditions in source and sink. Both have linear cost and saturating benefit functions; both contribute to the ensemble´s total net profit. A transfer changes the productivity of each single party and the ensemble in a non-linear way. As the parties are independent of each other, they are orthogonal and form the transfer space of the ensemble. The cost and benefit functions of each party intercept at one point (b=c) and thus cut the transfer space into four subspaces or areas (top-down view). In area I source is cost dominated and wants to get rid of the substrate while sink is benefit dominated and wants to take this substrate. I interpreted this as mutual cooperation at free will (R, in two-player games). In area II both parties are cost dominated and in area III both parties are benefit dominated. In these areas one party has to force or deceive the other party either to take (II, source forces sink) or to give (III, sink forces source) substrate. Exploitation of a cooperating party is called defect; T and S in two-player games. Finally, everywhere in the transfer space the behavioural alternative is not to transfer substrate (area I to IV). This corresponds to mutual defection (P) in two-player games. In the transfer space several symmetric and asymmetric two-player games coexist. Their local outcomes are different hierarchies of rational transfers based on mutual self-interest (cooperation), transfers through force and deception (exploitation), and inaction (mutual defect) within a global transfer space.