Possessing numerous applications, the theory of cooperative games is fundamental. However, the set function setting makes cooperative games highly technical to analyze and calculus is generally unapplicable. Its central solution concept, the core, is combinatorial and hard to analyze. In particular, (i) proving whether the core is nonempty is technical, (ii) the core is often large when nonempty, (iii) closed forms are typically unavailable, (iv) implementing the core often requires the existence of a powerful central agent, (v) the core allocation may not be robust, and (v) testing whether a payoff allocation is in the core is often computationally hard. Motivated by the general equilibrium theory, this paper makes advances on these fronts by studying a framework that is based on ordinary functions meeting certain regularity conditions (referred to as cooperative functions). This framework aims at solving an infinite number of related problems in a unified way and makes differential and superdifferential often applicable. Applications of this framework to newsvendor games, linear production games and EOQ games easily reproduce many well-known results and produce several new results.

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